WO2017114539A1

WO2017114539A1 - Device and method for determining a fluidic parameter

Info

Publication number: WO2017114539A1
Application number: PCT/DK2016/050476
Authority: WO
Inventors: Fridolin OKKELS
Original assignee: Fluidan Aps
Priority date: 2015-12-29
Filing date: 2016-12-29
Publication date: 2017-07-06
Also published as: EP3397941A1

Abstract

The present invention relates to a method and device for determining a fluidic parameter of a fluid. The device preferably comprises a C-device comprising a flow channel with an inlet and an outlet. The flow channel being defined by at least two opposite curved wall segments comprising respectively a first wall segment and a second wall segment. The two opposite curved wall segments extend asymmetrically to each other at least along a part of the channel so as to define the flow channel to comprise a diverging flow channel followed by a converging flow channel. A constriction is defined upstream of the outlet which constriction terminates the converging flow channel geometry. Further, pressure sensors are arranged in or at the wall segments to determine a pressure difference over at least a part of the C-device.

Description

DEVICE AND METHOD FOR DETERMINING A FLUIDIC PARAMETER FIELD OF THE INVENTION

The present invention relates to a method and device for determining a fluidic parameter of a fluid. The device preferably comprises a C-device comprising a flow channel with an inlet and an outlet. The flow channel being defined by at least two opposite curved wall segments comprising respectively a first wall segment and a second wall segment. The two opposite curved wall segments extend asymmetrically to each other at least along a part of the channel so as to define the flow channel to comprise a diverging flow channel followed by a converging flow channel . A constriction is defined upstream of the outlet which constriction terminates the converging flow channel geometry. Further, pressure sensors are arranged in or at the wall segments to determine a pressure difference over at least a part of the C-device. In preferred embodiments the method relates rheology and the method determines one or more of the following fluidic parameters: elastic moduli (GO, the complex moduli (G*), viscous moduli (GO-

A method according to the invention utilises the device according to the invention and preferably also a functional relationship between a pressure difference determined by use of the C-device, volume flow through the C-device and the fluidic parameter, the functional relationship being a functional relationship calibrated to produce values for the fluidic parameter. A method according to the present invention preferably further comprises: feeding the fluid at known or determined, varying or constant flow rates through the C- device, while the pressure difference determined by use of the C-device and the volume flow are recorded and determining on the basis of the functional relationship the fluidic parameter.

BACKGROUND OF THE INVENTION

The flow properties (rheology) of liquids are important parameters in the defining the quality of many liquids, such as paints, foods, beverages, household care products, personal care products and many others. Likewise, the flow properties of liquid intermediate products often determine the quality of downstream processes, such as coating or granulation or drying. When such liquids are non- Newtonian and have flow properties that are a function of the flow of the fluid, the analysis and monitoring of such properties is a complicated and time- consuming task and often requires that a sample of the fluid to be characterized is taken out and analysed under highly controlled laboratory conditions Such process are expensive and difficult to carry out and suffers from the drawback that they cannot be in-lined in a production of e.g. fluid having such properties.

As the known process suffers from the above drawbacks, production of the fluid is typically carried out in a batch process where each batch is analysed after the production and the batch is only used if the full fills certain requirements.

Therefore, it often the case that a produced batch must be reprocessed or even discarded and a new batch produced, hopefully fulfilling the requirements. As this obviously is not a very efficient way of producing such fluid, an improved method and device for characterizing a fluid would be advantageous, and in particular a more efficient and faster method and device would be advantageous.

OBJECT OF THE INVENTION

An object of the invention is to provide a device and method for characterizing a fluid in a fast and efficient way.

It is a further object of the present invention to provide a device and method for characterizing a fluid, which device and method is suitable for being in-lined in a production process.

It is a further object of the present invention to provide an alternative to the prior art. SUMMARY OF THE INVENTION

Thus, the above described object and several other objects are intended to be obtained in a first aspect of the invention by a method for determining a fluidic parameter of a fluid, the method utilizes

a C-device comprising a flow channel with an inlet and an outlet, the flow channel being defined by at least two opposite curved wall segments comprising respectively a first wall segment and a second wall segment, the two opposite curved wall segments extend asymmetrically to each other at least along a part of the channel so as to define the flow channel to comprise a diverging flow channel followed by a converging flow channel, wherein a constriction is defined upstream of the outlet and terminating the converging flow channel geometry, and pressure sensors are arranged in or at the wall segments to determine a pressure difference over at least a part of the C-device,

a functional relationship between a pressure difference determined by use of the C-device, volume flow through the C-device and the fluidic parameter, the functional relationship being a functional relationship calibrated to produce values for the fluidic parameter,

the method comprising

feeding the fluid at known or determined, varying or constant flow rates through the C-device, while the pressure difference determined by use of the C-device and the volume flow are recorded,

determining on the basis of the functional relationship the fluidic parameter. It is suggested that a geometry of the C-device as presented herein amplify the non-linear signal related to the elastic properties of the fluid rendering it relatively simple to determine one or more of the fluidic parameters: elastic moduli (GO, the complex moduli (G*), viscous moduli (G"). An optimization of the C-device can be performed by use of computational fluid dynamic, e.g. by use of a finite element method, to perform calculations based on a mathematical modelling of the fluid; this may be combined with a topology optimization.

It is noted that is its considered within the scope of "determining the volume flow through the C-device" is a situation where the volume flow is known by use of a volumetric pump or in general from a pumps characteristic.

In the present context terms are used in manner being ordinary for the skilled person. However, a number of terms are detailed below: Fluid is preferably used to mean a liquid, gas, plasma and/or combinations thereof. The fluid may further contain solid matter e.g. in the form of particles

Fluidic parameter is preferably used to reference a fluid property, such as a fluid flow property, e.g. the complex moduli i.e. consisting of the elastic moduli, and the viscosity moduli (also denoted the damping moduli), and intrinsic temporal properties such as thixotropy. Furthermore the rate of pseudo-plasticity (also denoted rate of shear-thinning) shear-stress and viscosity is considered within the scope of Fluidic parameter. "Elastic moduli" and "moduli of elasticity" are used interchangeably herein. In this context, parameters such as shear rate and shear stress may also be considered fluidic parameters.

Q-device is preferably used to reference a flow device preferably used to determine volume flow through the C-device (see below) and/or for providing an estimate of a shear rate (y) . The device may be in the form of a capillary device preferably in the sense that capillary refers to a flow in which substantially no or even no intrinsic non-linear effects occur while intrinsic non-linear effects occur in a downstream C-device. A Q-device may comprise one or more restricted flow passages or be in the form of a straight channel.

C-device is preferably used to reference a flow device in which intrinsic non-linear effects occur.

QC-device is preferably used to denote a measuring device comprising a Q-device immediately upstream of a C-device or a Q-device arranged immediately downstream of the C-device.

In-line is preferably used to reference a method and/or device being included in a production facility where the device and method operates on the fluid when it is produced.

Downstream is preferably used to denote the direction that a fluid is flowing. Upstream is preferably used to denote the opposite direction than downstream. A constriction is preferably used to mean that the cross sectional area of a flow channel is locally reduced. A constriction may be provided by a bump or narrowing section in the flow channel. Calibration is preferably used to reference the process of fitting a mathematical relationship between values determined by a device according to the present invention and the fluidic parameter(s), such as those fluidic parameter(s) to be determined so the same value(s) for the fluidic parameter(s) is(are) reached as if they were determined by a standard rheometer.

Calibrated Proportionality Factor or similar expressions are typically used to reference a factor, such as a proportionality factor, that relates parameters to each other, which factor is determined through a calibration. A standard rheometer is preferably used to reference a measuring device accepted by the skilled person to provide fluidic parameters. Such a rheometer may be one operating according to a standard, such as ASM standard. An example of such standard rheometer is a Haake MARS II rheometer. Pressure sensor "arranged in or at the wall segment" is preferably considered also to include a situation where the pressure sensor is arranged in a sidelet as disclosed herein.

In a further aspect, the invention relates to a method for determining a fluidic parameter of a fluid, the method determines one or more of the following fluidic parameters: elastic moduli (GO, the complex moduli (G*), viscous moduli (G"), and utilizes

a functional relationship between

a pressure difference determined by use of the C-device, or a pressure difference derived therefrom, a characteristic shear-rate, and/or a volume flow through the C-device, and

the fluidic parameter to be determined,

the functional relationship being a functional relationship calibrated to produce values for the fluidic parameter,

the method comprising

feeding the fluid at,

varying flow rates or at least one constant flow rate

through the C-device, while said pressure difference determined by use of the C-device is recorded,

- determining the characteristic shear-rate(s) resulting from the

feeding of the fluid and/or a volume flow through the C-device; determining on the basis of the functional relationship the fluidic parameter. In some preferred embodiments, the pressure difference determined by use of the C-device may be the magnitude of a pressure peak occurring at increasing volume flow through the device, or the pressure difference determined by the C-device at steady-state, or substantially steady-state, flow through the C-device. In some preferred embodiments, the method may utilize a Q-device comprising a straight channel and at least two pressure sensors arranged to determine a pressure difference along at least a part of the channel.

In some preferred embodiments, the Q-device, may further comprise a constriction and the pressure sensors of the Q-device may be arranged upstream and downstream of the constriction.

In some preferred embodiments, the Q-device may be arranged immediately upstream or downstream of the C-device, so that fluid leaving the Q-device flows directly into the C-device or the fluid leaving the C-device flows directly into the Q-device.

In some preferred embodiments, the derived pressure difference may be the pressure difference originating from the visco-elastic effects in the fluid flow in the C-device, and the derived pressure difference may be determined by subtracting the pressure difference originating from the viscous effects of the fluid flow in the C-device from the pressure difference determined by use of the C-device, and may further comprise determining the elastic moduli (GO on the basis of said derived pressure difference and the characteristic shear rate for the flow in the C-device.

In some preferred embodiments, the pressure difference originating from the viscous effects in the flow in the C-device may be approximated by scaling the pressure difference determined by the Q-device with a calibrated proportionality factor.

In some preferred embodiments, the pressure difference originating from the viscous effects of the flow in the C-device may be approximated to be zero, resulting in that said pressure difference originating from the visco-elastic effects in the flow in the C-device may be approximated by the pressure difference determined by use of the C-device.

In some preferred embodiments, the characteristic shear rate for the flow in the C-device may be estimated as a proportionality of the volume flow through the C-device preferably with a calibrated proportionality factor.

In some preferred embodiments, the method may comprises or may further comprise determining the characteristic shear-stress preferably by scaling the pressure difference determined by the Q-device preferably with a calibrated proportionality factor and preferably determining the complex moduli (G*) on the basis of characteristic shear-stress and a characteristic shear-rate for the flow in the Q-device. In some preferred embodiments, the characteristic shear-rate for the flow in the Q-devicemay be determined by scaling the volume flow through the Q-device preferably with a calibrated proportionality factor. In some preferred embodiments, the fluidic parameter determined may be the elastic moduli and the functional relationship may be

, _ (AP_cy

^G QC - ^C _†2 (a-1)

wherein C, a are determined by the calibration, γ is determined as Q is the volume flow through the C-device, R is a characteristic radius of the device, such as half of the hydraulic diameter of the Q-device, and wherein AP_C may be either hP_c-_relax being the mean pressure difference by the C-device occurring after an overshoot resulting from an increase in volume flow through the C-device, or

the pressure difference determined by the C-device, such as said pressure difference derived therefrom, preferably at steady-state, or substantially steady-state, flow through the C-device.

In some preferred embodiments, the fluidic parameter determined may be the shear-rate and the functional relationship may be

Y_QC = ^ wherein Q is the volume flow through the C-device and R is a

characteristic radius of the device, such as half of the hydraulic diameter of the Q-device.

In some preferred embodiments, the step of feeding the fluid at, preferably known or determined, varying flow or constant rates may comprise varying the volume flow between two values, wherein the variation may be a ramp-up from the first volume flow to a second volume flow, preferably followed by a time period with constant volume flow equal the second volume flow, followed by a ramp-down to the first volume flow. Preferably, the first volume flow may be equal to zero.

In some preferred embodiments, the constriction may be defined by the second wall segment having a sharp bend and the first wall segment may have a relatively to the sharp bend a more smooth bend. In some preferred embodiments, one of the pressure sensors, to determine a pressure difference over at least a part of the C-device, may be arranged downstream or upstream of the sharp bend in the first wall segment. In some preferred embodiments, the first wall segment comprising a sharp bend and one of pressure sensors to determine a pressure difference over at least a part of the C-device may be arranged upstream or downstream of the sharp bend in the first wall segment. In some preferred embodiments the calibration may comprise

obtaining by use of a standard rheometer corresponding values of shear rate, stress components and elasticity moduli (GO for a fluid

feeding said fluid at known or determined, varying flow rates, or constant flow rates, through the C-device, while the pressure difference determined by use of the C-device and the volume flow are recorded thereby obtaining corresponding values of the volume flow and pressure difference, determining calibration constants in a functional relationship between elasticity moduli (GO, volume flow and pressure difference by equating the elasticity moduli (GO obtained by the standard rheometer with the elasticity moduli determined by the mathematical equation.

In a second aspect, the invention relates to a device for determining a fluidic parameter of a fluid, the device preferably comprises

- a C-device comprising a flow channel with an inlet and an outlet, the flow channel being defined by at least two opposite curved wall segments comprising respectively a first wall segment and a second wall segment, the two opposite curved wall segments extend asymmetrically to each other at least along a part of the channel so as to define the flow channel to comprise a diverging flow channel followed by a converging flow channel, wherein a constriction is defined upstream of the outlet and terminating the converging flow channel geometry, and pressure sensors are arranged in or at the wall segments to determine a pressure difference over at least a part of the C-device. The fluidic parameter may be one or more of the following fluidic parameters: elastic moduli (GO, the complex moduli (G*), viscous moduli (G"), but other fluidic parameters may be determined by a method and/or a device according to the present invention.

I some preferred embodiments the device may further comprising a Q-device comprising a straight channel and at least two pressure sensors arranged to determine a pressure difference along at least a part of the channel. I some preferred embodiments, the Q-device may further comprise a constriction and the pressure sensors of the Q-device may be arranged upstream and downstream of the constriction.

In some preferred embodiments, the Q-device may be arranged immediately upstream of the C-device, so that fluid leaving the Q-device flows directly into the C-device.

In some preferred embodiments, the device may further comprise a pump, such as a volumetric pump, preferably configured for feeding fluid through the device at varying volume flows, preferably the variation of volume flow may be a ramp- up from the first volume flow to a second volume flow, preferably followed by a time period with constant volume flow preferably equal the second volume flow, preferably followed by a ramp-down to the first volume flow. In some preferred embodiments the constriction may be defined by the second wall segment having a sharp bend and the first wall segment may have a relatively to the sharp bend a more smooth bend.

In some preferred embodiments, one of pressure sensors, to determine a pressure difference over at least a part of the C-device, may be arranged downstream or upstream of a sharp bend in the first wall segment.

In some preferred embodiments, the second wall segment may comprise a sharp bend and one of the pressure sensors to determine a pressure difference over at least a part of the C-device may be arranged upstream or downstream of the sharp bend.

In a further aspect, the invention relates to a computer program product being adapted to enable a computer system comprising at least one computer having data storage means in connection therewith to control a device according to the second aspect of the invention so as to carry out the method according to the first aspect.

This aspect of the invention is particularly, but not exclusively, advantageous in that the present invention may be accomplished by a computer program product enabling a computer system to carry out the operations of the apparatus/ system according to the invention when down- or uploaded into the computer system. Such a computer program product may be provided on any kind of computer readable medium, or through a network.

The individual aspects of the present invention may each be combined with any of the other aspects. These and other aspects of the invention will be apparent from the following description with reference to the described embodiments and the accompanying claims.

BRIEF DESCRIPTION OF THE FIGURES

The present invention and in particular preferred embodiments thereof will now be described in more detail with reference to the accompanying figures. The figures show ways of implementing the present invention and are not to be construed as being limiting to other possible embodiments falling within the scope of the attached claim set. Figure 1 illustrates schematically a horizontal cross sectional view of a measuring device according to the present invention;

Figure 2 is a plot illustrating a temporal variation of a pressure difference determined by use of the Q- and the C-device by feeding fluid through the device of Fig. 1. Figure 3 illustrates schematically the horizontal cross sectional view of the C- device depicted in fig. 1 - it is noted that the shape shown resembles one example on the actual shape of the C-device. Figure 4 illustrates schematically a horizontal cross sectional view of a Q-device according to a further embodiment of the invention.

Figure 5a-e are flowchart illustrating various levels of assumptions including a generalized model (fig. 5a) representing embodiments according to the present invention.

Figure 6 is a graph illustrating Shear-stress vs. shear-rate for LBG 1% with QC- device measurements as points and standard rheometer-measurements collected in a curve. LBG 1% shows according to the measurements no sign of yield-stress.

Figure 7 is a graph illustrating shear-stress vs. shear-rate for Xanthan 0.2% with QC-device measurements as points and standard rheometer measurements collected in a curve with points. In addition, two 2nd polynomial fits for each measuring is shown, wherein yield-stress is emphasized by bold lettering

(St.rheo = 3.63 Pa and RheoStream = 3.93 Pa).

Figure 8 is a graph illustrating viscosity vs. shear-rate (log-log) for LBG 1% with RheoStream measurements as points and standard rheometer measurements collected into a curve. In addition, a power fit is shown with values K = 3.88 Pa*s and n = 0.40.

Figure 9 is a graph illustrating Viscosity vs. shear-rate (log-log) for Xanthan 0.2% med RheoStream™ measurements points and standard rheometer measurements collected into a curve. In addition, a power fit is shown with values K = 1.56 Pa*s and n = 0.28. Due to time effects (e.g. thixotropi) the RheoStream measurements are divided according to pulse order (in the measurement scheme).

Figure 10 is an illustration of "Stress-overshoot" which occur as prevailing at pump-pulse start (marked by dotted vertical line). Figure 11 is a graph illustrating Elasticity moduli (G') vs. frequency for LBG 1% (log-log) with RheoStream measurements as points and standard rheometer measurements collected in a curve. Figure 12 is a graph illustrating Modulus-norm (G*) vs. Elastic moduli (G') for LBG 1% with RheoStream measurements as points and standard rheometer measurements collected in a curve.

Figure 13 is a graph illustrating Elasticity moduli (G') vs. frequency for pectin fluid (ref. 0128- 1720) with RheoStream measurements as points and standard rheometer measurements collected in a curve.

Figure 14 is a graph illustrating Modulus-norm (G*) vs. Elastic moduli (G') for pectin fluid (ref Pectin I) with RheoStream measurements as points and standard rheometer measurements collected in a curve.

Figure 15 is a graph illustrating Elastic moduli (G') vs. frequency for pectin liquid Pectin II (log-log) with RheoStream measurements as points and standard rheometer measurements collected in a curve.

Figure 16 is a graph illustrating Modulus-norm (G*) vs. Elastic moduli (G') for pectin liquid Pectin II (log-log) with RheoStream measurements as points and standard rheometer measurements collected into a curve. Figur 17 is a graph illustrating Pressure differences APQ and dpc on each axis; in the graph, the horizontal arrow indicates the di rection of increasing flow rates and the vertical arrow indicates the direction of increasing Wi number (Weissenberg number) . Figure 18 is a g raph illustrating Normalized pressure difference (ΔΡς/ΔΡς) as a function of AQ ~ flow rate.

Figure 19 is a g raph as in figure 18, but normalized with APMC

see e.g . fig. 1) which contrary to APQ has a clear dependency on Wi. Figures 20-22 are graphs illustrating results obtained by a QC-device according to the present invention; in fig. 20 the flow curve is presented, in fig. 21, G' is presented and in fig. 22 G" is presented. The results obtained by the method is Labelled "RS-FC" "RS-G"' and RS-G"" whereas comparative results obtained by a standard rheometer is labelled "St.Rheo-FC", "St.Rheo-G"' and St.Rheo-G".

DETAILED DESCRIPTION OF EMBODIMENTS

The present invention utilizes a measuring device as illustrated schematically in fig. 1. As illustrated in this figure 1, the measuring device comprising a Q-device 2 immediately upstream of a C-device 3 (it is noted that the Q-device may be arranged immediately downstream of the C-device); this combination of a Q- and C-device is for short herein called a QC-device 1. During use, fluid is fed into the QC-device 1 at the inlet 4 of the Q-device 2 by a pump (not illustrated). The pump used is preferably a volumetric pump by which the exact amount of fluid pumped into QC-device 1 is known as function of time, i.e. the volume flow is known - or in general determined e.g. from the pumping characteristics - as Q(t) where Q is in liter per seconds (or other units). In figure 1, the arrows shown at the inlet 4 to the Q-device, the arrow at the inlet of the C-device and the arrow at the outlet of the C-device illustrates the flow direction.

The Q- and C-device shown in fig. 1 is shown in a cross sectional view seen from above. The channels 9 and 10 formed inside the Q- and C-devises are typically formed by parallel top and bottoms walls and side walls extending perpendicular to the bottom and the top wall segment. With reference to figure 1, the top and bottom walls each have the shape of the cross sectional view shown and the side wall extend out of the plane of the figure. However, the cross section of the Q-device may preferably be circular.

The dimension of the QC-device may be in the mm range, and in a preferred embodiment, the following dimensions are used Ll =75mm, L2=50mm and a channel height = 100mm (direction normal to the sheet on which the figure is drawn). Such as device has been found suitable for flows in the order of 100-600 liter per hour. It is noted that the dimensions may be one or more orders of magnitude smaller. In other embodiments, the dimensions of the C-device is in the order of, L2=0.5-lmm, L3=5-10mm, L4=5-10 mm and a channel height = 5-20mm. Such a device is suitable for flow in orders of 0.1-1 liters per hour.

The Q- and C-devices may preferably be produced by milling out the geometry in a block of material.

As illustrated in fig. 1, the volume flow fed into the device varies typically in a pulsed manner where the volume flow alternate between to values Qi and Q₂, where each value of Qi and Q₂ is kept constant for period of time (see lower left of fig. 1). However, the invention is not limited to such pulsed flows.

The Q-device is typically formed as a straight channel with at least two pressure sensors 5, 6 arranged to determine a pressure difference along at least a part of the channel. As illustrated in fig. 4, the Q-device may further comprise a constriction 21 and the pressure sensors 5, 6 of the Q-device may be arranged upstream and downstream of the constriction 21.

Further, the Q-device is typically arranged immediately upstream or downstream of the C-device, so that fluid leaving the Q-device flows directly into the C-device or the fluid leaving the C-device flows directly into the Q-device.

It is noted that the Q-device may be used to determine the volume flow by using a relation correlating Q with dP. In such cases, it may be preferred to provide the Q-device with a constriction in between the two positions 5 and 6 in order to emphasize the pressure difference dp between the positions 5 and 6 to provide a more accurate determination of the volume flow.

As also illustrated in fig. 1, the QC-device comprising pressure sensors 5, 6, 7, 8 for determining the pressures:

as illustrated in fig. 1, so as to determine e.g. dp_Q (t) = P_{Q 2} - P_{Q 1} and dp_c(t) = P_C2 - P_C1 As also illustrated in fig. 1, the C-device may in certain embodiments comprise two additional pressure sensors 11, 12. These sensor may be used to determine an estimate for volumetric flow rate through the c-device as such volumetric flow rate may be determined (or estimated) as Q = f(P₁₂ - Pn ) wherein f is a e.g. a calibrated function. This approach may find use in situations where for instance, there is not enough space available for using a Q-device and the volumetric flow rate determined in this manner takes the place of the volume flow otherwise determined by a Q-device in the following. Such pressure sensors are preferably arranged flush with the wall geometry of the Q- and C-devices thereby not introducing any disturbances into the flow past the pressure sensors. Alternatively, the pressure sensors may be arranged at the distal end of sidelets (a channel) extending outwardly from the wall geometry so that the fluid flows across a cavity provided in the wall geometry and the pressure sensors are in fluid communication with the measuring points 5, 6, 7 and 8 (in fig. 1).

The below discloses the coordinates for the C-device illustrated in fig. 1

Set of x-coordinates for points:

First wall segment:

'-12' Ό' (Ό') '3.5' '4' '4.2' ('6.5') ('8.421') '9.018' ('9.31') ΊΟ' ' 14'

Second wall segment:

'14' '9.6894' ('8.8694') Ό' Ό' '-12' Set of y-coordinates for points:

First wall segment:

'6.5' '6.5' (' 10.1139') '10.1139' '9.7639' '9.3439' (ΊΟ') ('7.0188') '7.4828' ('8') '8' '8'

Second wall segment:

'6' '6' '6.7319' ('-1.8167') '4.5' '4.5'

All Coordinates in parenthesis are Bezier-help-points. Fillet of radius 0.18 at points no. 2, 4, 5, and 17. Fillet of radius 0.06 at point no. 6 and 15. Fillet of radius 0.35 at point no. 14. As will become apparent from the following, some of the embodiments disclosed herein does not include determination of dp_Q (t) and in still further embodiments, the Q-device may be dispensed with. However, in order to detail the concepts of the invention, these concepts are disclosed with reference to fig . 1 where the measuring unit comprising a QC-device, with pressure sensors arranged as illustrated in fig . 1 to determine the pressure differences over the Q-device and the C-device respectively, and where the fluidic parameter to be determined is the moduli of elasticity G. Thus, during a use of the QC-device the following quantities are typically determined :

Q(t) dp_Q(t dp_c(t) It is noted that Q(t) and dp_Q (t) may be interchangeably in qualitative sense as the volume flow and pressure difference are correlated so that only one of the quantities may need to be determined . These quantities (or at least

Q(t) and dp_c(t)) are used to estimate the moduli of elasticity, G', according to the disclosure presented herein.

In the following a first embodiment is disclosed and a more detailed disclosure will be presented after this first embodiment.

It is noted, that the generally used notation is herein so that G' refers to the moduli of elasticity and G" is the viscous moduli . In terms of directions, C and G" are perpendicular to each other and (G^*)² = (C)² + (G")².

The moduli of elasticity, C may according to the Cox-Merz relation be calculated as:

where C, a are fitted constants and subscript st indicates that the correlation is valid for a standard rheometer. σ and a₂₂ are the stress components (ordinary notation used) and y is the shear stress. While this correlation is derived and valid for a standard rheometer such as a Haake MARS II rheometer, the present invention resides inter alia in that is has been realized that for a device comp a Q-device and a C-device, the terms:

O_n - σ₂₂) and γ preferred embodiments be estimated by

O_n - σ₂₂) = F(AP_C)

Y = H(Q, R) where F and // are functional relationships (which will be detailed belowe.g. H may as equation (5) and F may be as proportionality scaling) and dp_c is a pressure difference determined the C-device, Q is the volume flow through the device and R is the radius of the tube of the Q-device (or hydraulic diameter divided by 2 in case the Q-device does not have a circular cross section).

Thus, as it appears from the above, the invention provides (in accordance with preferred embodiments) : the Q-device provides a measure for the shear rate γ, and

the C-device provides a measure for (σ^ - σ₂₂).

In embodiments of the present invention, the above is implemented by (please refer to fig. 2 for AP_c__relax) :

where subscript QC indicates that the relation is for the QC-device and C, a are constants to be determined (e.g. by calibration). As will be outlined above, instead of using AP_c-_rei_ax the pressure difference AP_C can be used in equation (4) :

Where AP_C is pressure difference determined by the C-device at steady-state, or substantially steady-state, flow through the C-device as illustrated in fig. 2. The shear rate to be used in the above equation may be determined by:

Where Q is the volume flow through the QC-device and R is the radius (or hydraulic diameter divided by 2).

It is noted that if Q varies over time between Qi and Q₂, the value of Q is the value of Q after which the overshoot in fig. 2 occurs (e.g. 15 sec < Time < 60 sec) which is Q₂. It is noted that if Q₂ fluctuates, a timely averaging may be applied.

APc-reiax or AP_C are each considered to be a characteristic pressure difference. In fig. 2 the pressure responses from the Q- and C-device are illustrated as function of time. The infeed is as illustrated in fig. 1, namely a pulsed infeed where Qi=0 m³/n. In fig. 2 dpo refers to PQ₂-PQI and dpc refers to Pc2-Pci. As shown in fig. 2, dpc has progress in a manner characteristic for non-Newtonian fluids and in particular the pressure peak which may considered to be an overshoot from a mean pressure at t in the interval [5,10] sec is found to be a characteristic pressure difference useable in the above equation (4). The curves of fig. 2 show the evolution of the pressure during single pulse of volume, i.e. at t=0 the volume flow is increased from Qi=0 m³/h to Q₂= 1.3 χ 10^"8 m³/sec. The rate of increase in volume flow is 1.3 χ 10^"7 m³/sec².

As it appears in the above equation (4) the constants C and a needs to be assigned a value and these are determined by calibrating

G Qc against G _st

The calibration process comprises the steps of using a standard rheometer such as a Haake MARS II rheometer and obtaining corresponding values for y, (¾i - σ₂₂) andG'_st . The same fluid is fed into a QC-device as disclosed herein and corresponding values of y_QC,AP_c__relax and/or AP_C are recorded. With these data at hand, the constants C and a are determined so that G_QC = G_st. It is noted that as both above equations (4) and (5) takes as argument equation (4) may be re-written as:

And, as Q may be known (determined e.g. by the use of a volumetric pump), the need for determining can be avoided. It is however noted that in the above, the elasticity moduli G' is the only parameter considered and in case further parameters are to be determined may be used to determine such other parameters.

It is noted that the compact form (eq. (6)) typically is used when is not determined as such. However, if for instance the viscosity is to be determined

^V^ ⁼ 1 + (1 y)^1""

Where is the shear-rate [1/s]. The remaining parameters are considered to be constants (typically derived based on measurements) and the below table summarizes these parameters and provides an indication on their magnitudes (a not to be construed as limiting for the present invention) :

Thus, in preferred embodiments of the invention, the following steps are carried out. 1. A number of measurements are carried out on a fluid by a standard rheometer and corresponding values of G'_st and y_st are recorded where subscript st indicates that the values are obtained by use of a standard rheometer

2. The same fluid is fed through the QC-device at known (or determined) volume flows. The volume flow is varied overtime, e.g. in pulsed manner and/or fed with a constant volume flow

3. During feeding of the fluid through the QC-device the pressure difference are recorded over the C-device and the Q-device (if needed), and the characteristic pressure difference (e.g. AP_c__retax or AP_C) is extracted.

4. With the recorded values of Q and/or AP_Q and AP_c__reiax or AP_C the constants C and a are determined so that

^G'QC = ^G'st The geometry of the device disclosed in fig. 1 of the C-device will now be disclosed in greater details with reference to fig. 3. As illustrated in fig. 3, the flow channel 10 of the C-device is a curved channel defined by two opposite curved wall segments being respectively a first wall segments 13 and a second wall segments 14, the two opposite curved wall segments 13 and 14 extending asymmetrically to each other throughout the channel 10 (it is noted that the two wall segments may extend parallel to each other along a part of the channel). In figure 3, the channels are extending from first positions 13a, 14a and to second positions 13b, 14b each being defined as being located where the walls end with respectively starts to extend parallel to each other. The flow channel 10 has an inlet 19 for receiving fluid and an outlet 20 for outletting fluid - with reference to the figures herein, the fluid flows from left to right.

As illustrated in fig. 3, the channel comprising (from inlet to outlet) a diverging flow channel followed by a converging flow channel and a constriction 15 is defined in distance from the outlet. The constriction 15 is defined by the wall segment 13 having a sharp bend 16 (typically in the region of 90°) and the wall segment 14 having a relatively to the sharp bend 16 a more smooth bend 17. As shown, the pressure sensor 8 is arranged at or in the downstream surface of the sharp bend 16. As also illustrated in fig. 3, the wall segment 14 (extending for 14a to 14b) comprising a sharp bend 18 and the pressure sensor 7 is arranged at or in the upstream surface of the sharp bend 18. The sharp bend 18 and the pressure sensor 7 may preferably be arranged at a position between 0.25 <r<0.75 where r is a curve-linear coordinate along the inner surface wall segment 14 of the C-device with values between [0; 1] where 0 is the inlet and 1 is at the outlet

In the above, the wording sharp has been used to reference a bend which is defined by two straight segments merging in the corner of the bend. A smooth bend has been used to reference a bend defined by two curved segments merged in the corner of the bend. Typically and preferably, the first derivative of the curve resembling the bend is substantially smooth across the corner of a smooth bend whereas the first derivative of the curve is substantially discontinuous across the corner of a sharp bend (where substantially refers to the machining accuracy).

In a further embodiment, the pressure sensor 7 is arranged downstream of the sharp bend 18, such as immediately downstream of the sharp bend 18. By immediately downstream of the sharp corner is preferably meant that pressure sensor is arranged as close as practical possible to the sharp bend 18, which also includes that the pressure sensor may form at least a part of the sharp bend 18. Similarly, the pressure sensor 8 may be arranged upstream of the sharp bend 16, such as immediately (as disclosed above) upstream of the sharp bend 16. Thus, the pressure sensor 7 may be arranged upstream or downstream of the sharp bend 18 and the pressure sensor 8 may be arranged upstream or downstream of the sharp bend 16.

Fig. 4 illustrates a further embodiment of a Q-device according to the present invention. As shown, the Q-device comprising a flow channel 9 having a centrally arranged constriction 21 with a converging flow channel part upstream and a diverging flow channel part downstream of the constriction 21. Upstream of the converging channel part is a straight channel part and downstream of the diverging channel part is a straight channel part. The pressure sensors 5, 6 are preferably arranged in or at the wall of these straight channel parts. The cross section of the channel is preferably square. It is noted that the constriction is considered an optional feature not necessarily implemented in embodiments of the invention.

In the following a generalized framework of the invention will be presented.

On a generalized framework of the invention

Reference is in the following made to figures 5a-e being flowcharts illustrating various steps according to preferred embodiments of the present invention and in particular illustrating the procedure/algorithm of converting the raw pressure signals from the QC-device to standard rheological quantities. Arrows indicate the direction of analysis-steps, and symbols in gray boxes are the final rheological quantities. References inside circles refer to further explanation/reference below. The figures are divided in two parts by a horizontal dashed line. Upper part illustrates the process of performing the viscometry analysis, while the lower part illustrates the process of performing the visco-elasticity analysis.

The figures 5b-e each represent different assumptions that have proven to be useful in connection with the present invention and figure 5a represent a generalized disclosure on which the figures 5b-e are derived from by the assumptions. Firstly, the generalized disclosure will be presented with reference to fig. 5a where after the different assumptions will be presented. Further, reference symbols used in fig. 5a are re-used in fig.s 5b-e for the elements which are present in these figures. In the figures 5a-e and the accompanying text, Δρ are ΔΡ are used interchangeably.

In the figures 5a the following reference symbols are used as (please note that reference symbols are placed in circles in these figures whereas parenthesis are used in the below text) : (1) : Fluid Sample to be characterized by the apparatus. The same sample of fluid is supplied to both the Q-device and the C-device. Its set of rheological properties is denoted S.

(2) : The Q-device and the C-device are both feed with fluid sample and a given flowrate at which the fluid sample is flowing through the respective device. Figures 5a illustrates two separate measurements by the Q-device as they serve two different purposes and result in the characterization of two different rheological quantities. Three different measurements are represented in Figures 5a, in general denoted x that takes the values Q, V and C, and for which a given device with a given flowrate Q_x give rise to a corresponding recorded pressure- signal Px(t). In the present analysis the important quantity extracted from the signal p_x(t) of a measurement is preferably the final (equilibrium) change in pressure Δρ_χ between the apparatus-state with sample flowrate Q_x and the apparatus-state at which the fluid is at rest. Detailed description of the signal analysis leading to Δρ_χ is given in subsection "On description of (equilibrium) change in pressure Δρχ" below.

(3) : To each measurement, in general denoted x, a characteristic shear-rate†_x is related that is dependent on specific quantities through the functional relationship A (for the Q-device) and B (for the C-device) as illustrated in Figure 5. Please note that the notation A(Q_X,Q_X,S_X) is used to reference a functional relationship, A, between shear-rate and volume flow Q, geometry Ω and sample fluid S. These shear-rate values (Y_C,†V.†Q) depend on : the given flowrate Q_x, the given geometrical shape of the device-flow-channel Ω_Χ, and rheological properties of the sample fluid S.

A simple embodiment of the functional relationships A and B are assuming proportionality with the related flowrate Q_x, such that γ_χ≡ ^χ/_£χ · With these assumptions Qv and Qc are related as: Q_v≡ ε_νγ_ν = ε_νγ_€ == ^Q_c . The parameters εχ has to be determined through calibration depending on the overall rheological type of fluid and the channel geometry of the Q- or the C-device (QQ, QC) .

However, more complex relationships can be used.

If in one embodiment of the geometrical shape of the Q-device-flow-channel QQ is a cylindrical tube then the resulting shear-rate†_Q is considered constant (e.g. by assuming fully developed flow) on the cylindrical (inner) surface, and the quantity of Y_Q is well-defined. Since the geometrical shape of the C-device-flow-channel Qc is not a cylindrical tube then the resulting shear-rate value vary spatially, depending on the position within the (inner) channel-surface. Therefore, as y_c(r) is not constant (where r represented e.g. a curve-linear coordinate along the inner surface of the C-device), the quantity†_c in Figure 5a is preferably defined to be the characteristic shear-rate value within the C-device returned by the functional relationship B and based on a given spatial averaging of y_c(r), that depends the properties: Qc, Ωο, and S. Again, a simplified embodiment of this functional relationship B can be a simple proportionality with Qc, as described in the earlier paragraph.

(4) : In general, the pressure drop in the Q-device can be related to the viscous properties of the sample fluid. The Rabinowitsch-Mooney equation assumes proportionality between the pressure drop Δρχ and the shear-stress σχ, while a more refined relation exists, elaborated in subsection "Capillary viscometry" below. The parameter το has to be determined through calibration (e.g. as disclosed above) depending on the overall channel geometry of the Q-device (QQ) .

(5) : Knowing the shear-stress for given different shear-rates, denoted as a_Q j_Q), represents the "Flow curve" related to the given fluid sample. By definition the viscometry (meaning the dependence of the viscosity on given different constant shear-rates) can be computed from the Flow curve as:

Assuming that the sample fluid can be described as a "Power-law fluid" (other assumption for the fluid may be applied) the Flow curve can be approximated with the following power-law relation : a_{Q Q})≡ K†_Q ⁿ with the rheological quantities K and n. Finding the limit of the shear-stress for vanishing small shear-rates is one method of determining the Yield Stress (a quantity also sometimes denoted the Flow-Point) :

σ₀ = lim O_Q (YQ).

Yo→0

(6) : One application of the measurements from the Q-device is to measure and characterize the shear-stress and the viscosity for a given sample fluid for one or more different shear-rates. These measurements can be further analyzed by e.g. assuming that the fluid can be described by as a Power law fluid such that the quantities K and n can be determined, and/or that the fluid has Yield Stress, quantized by σο. An often central part in quantifying the visco-elastic properties of the sample fluid according to the present invention is to separate the pressure difference measured by the C-device (Ape) into a part from the viscous effects (Apc,v) and a part from the visco-elastic effects (APVE), given by the relation at reference (9) in Figure 5. The Q-device is used to estimate this pure viscous contribution as it has been found that a pure cylindrical flow, or substantially cylindrical flow, or even a parallel flow suppress the visco-elastic effects, making the measured pressure- drop of the Q-device be caused dominantly by the viscous dissipation. (7) : The estimated viscous part of the pressure difference in the C-device (Apc,v) must be determined at the same flow-conditions as the visco-elastic part (ΔρνΕ) . This is obtained by ensuring the same flow-conditions at the respective measurements at both the Q- and the C-devices i .e. assuring the same characteristic shear-rate (†_v =†_c) . This condition should be applied to the below item (8) . For the simplified description of the functional relationships, the two flowrates Qv and Qc are proportional as described in (3) in fig. 5a and as disclosed above.

(8) : To estimate the value of the viscous pressure difference in the C-device (Δραν) from the specific shear-stress σν the following relation is used : Apc,v = ξ σν, with the proportionality-factor ξ depending on the channel geometries of both the Q- and the C-device (QQ, ΩΟ) . ξ is preferably a calibrated value preferably obtained by following the calibration procedure outlined above. (9) : As presented in fig . 5a the pressure difference measured by the C-device (Ape) may be considered as a superposition of viscous part of the pressure difference in the C-device (Apc,v) and the part from the visco-elastic effects (APVE), i .e.

More details about this are given in the subsection "Separation of Ape" below.

( 10) : Once the pressure difference in the C-device from the visco-elastic effects (Δρνε) has been estimated, it can be related directly to the "First Normal Stress" Ni, as being proportional to ΔρνΕ: N i = ki Δρνε , wherein ki can be determined by calibration. ( 11 ) : The rheological properties extracted from the measurements have been based on the flow-situation of constant shear-rates. However, the derived visco- elastic quantities (G' and G") relate, theoretically, to a frequency analysis, the Cox-Merz relationship between constant and oscillatory shear-rates has been applied to relate a shear-rate to a frequency. The Cox-Merz relationship equals a given characteristic shear-rate†_c with the angular velocity roc such that the related frequency is: f_c = ^ω€/_2π = ^Yc/2n

( 12) : Extending the "application area" of the Cox-Merz relation provides second useful relationship according to the present invention namely (12) in fig. 5:

G' = C N ° y_c ^2(1"a) which relates the elastic moduli G' to the First Normal Stress Ni. The parameters C and a has to be determined through calibration depending on the overall rheological type of fluid and the channel geometries of both the Q- and the

C-device (QQ, QC). And, since the First Normal Stress Ni can be determined from (10)

N = / Ap_VE G' can be determined.

In a preferred embodiment, this resembles:

Determine ΔΡ_ν by the Q-device and ΔΡς by the C-device

- Determine ΔΡνε by use of (8) and (9)

Determine Ni by use of (10)

Determine G' by use of (12)

( 13) : Combining the relations (10) and (12) gives an explicit relation (13) for determining the elastic moduli G', where the new proportionality-factor C has incorporated the other proportionality factor ki raised to the power of a. As G' in standard rheometry is related to a given frequency, fc is used as related frequency. In the special case of a = 1, G' and ΔρνΕ are proportional. ( 14) : Another extension of the Cox-Merz relation may provide an estimate of the complex moduli (G*) from a rescaling of the shear-stress σν. The parameters C and β have to be determined through calibration depending on the overall rheological type of fluid and the channel geometry of the Q-device (QQ). In the special case of β = 1, G* and σν are proportional .

( 15) : Having estimated G* and G', the viscous moduli G" follows pr. definition.

On assumptions used in reducing algorithm complexity

While the above has focused on a generalized disclosure with reference to fig. 5a, the following disclosures 5b-e present some useful assumptions, that can be used as further preferred embodiments of the present invention . Please observe that fig . 5b and fig 5c represents the model with the same assumption, where some intermediate steps have left out in fig. 5c compared to fig . 5b.

Assumption 1: Assuming that the sample fluid can be described as a power-law fluid, where the shear-stress has a power-law dependence to the shear-rate as : σ(γ) = Κ γ^η , then the shear-rates of the Q-device can be estimated from knowing the characteristic power-law exponent no and the radius R of the cylindrical tube in the Q-device (or in general, hydraulic diameter divided by 2) .

Assumption 2: Assuming that the radius R in the Q-device is chosen in accordance with the channel geometry of the C-device (Qc) such that†_c is equal to†_Q for the same flowrate Q = QQ = Qc As consequence of Assumption 2, then a full visco-elasticity characterization of the sample fluid, determining G' and G", can be performed with only one measurement of flowrate Q.

Assumption 3: Assume that the channel geometry of the C-device (Qc) has been adj usted such that Apc,v ~ 0, that is, the pressure signal of the C-device only affect/reacts to the visco-elastic effects of the sample fluid (if there is any) and is not responding on the value of the sample fluid viscosity. As consequence of Assumption 3, then the visco-elastic pressure-difference ΔρνΕ can be

approximated by the direct measured pressure-difference from the C-device Ape. ( 16) : Assuming that the sample fluid can be described as a power-law fluid (see figure 5b-e), then the shear-rates of the Q-device can be estimated from knowing the characteristic power-law exponent no and the radius R of the cylindrical tube in the Q-device. This is a concrete application of the simplified description of the functional relationship A(Q_X,Q_X,S) - n₀ can be determined by use of a standard rheometer/viscometer or other methods, even independently of the present QC-device.

( 17) : Assuming that the radius R in the Q-device is chosen such that†_Q is equal to†c for the same flowrate Q = QQ = Qc, (see fig . 5d and 5e) then a full visco- elasticity characterization of the sample fluid, determining G' and G", can be performed with only one measurement of flowrate Q.

( 18) : Assume that the channel geometry of the C-device (Qc) has been adjusted such that Apc,v * 0, that is, the pressure signal of the C-device only affects/reacts to the visco-elastic effects of the sample fluid (if there is any) and is not responding on the value of the sample fluid viscosity. Then the visco-elastic pressure-difference ΔρνΕ can be approximated by the direct measured pressure- difference from the C-device Ape.

On description of (equilibrium) change in pressure Δρ_χ

To extract the difference in pressure, measured in one of the two devices (Q- or C-device) and caused by the flow of sample fluid at a specific flowrate Q, two approaches can be made depending on the type of pressure measurement. If the zero-point of the used pressure-sensor is assumed not to change over longer periods of time and is set at ambient pressure (the steady state of Q = 0), then Δρο and Ape can be read out directly from the output of the pressure-sensors from the two devices. On the contrary, if a longer period drift of the zero-point can occur, then the following procedure can be applied : Periods of time with no fluid flow (Q = 0) then precedes and succeeds a limited period of time with flow at a given flowrate (Q = Qx) . The pressure-signal is measured over the whole range (including the time-periods of no flow) and the two periods of no flow can be used to give an effective zero-point of the pressure. This procedure is illustrated for two types of signal responses in fig . 2 APQ, APC. On capillary viscometry

Based on the capillary viscometer functionality of the Q-device, the viscometry of the sample fluid can be determined using the Rabinowitsch-Mooney equation that relates the pressure drop along a given section of a cylindrical tube with the shear-stress on the inner wall.

This relation holds for all fluids and if the section length is L and the tube has radius or hydraulic diameter R, then the wall-shear-stress (aQ,_w) is given by:

_ R APg This assumption can be used to estimate τ₀. in step (4) of figure 5a-e.

While this above relation is fully determined, once the tube-geometry is known, the relation in reference (4) of Figure 5 still uses the calibration-parameter το to keep the relation general.

The invention can be implemented by means of hardware, software, firmware or any combination of these. The invention or some of the features thereof can also be implemented as software running on one or more data processors and/or digital signal processors.

The individual elements of an embodiment of the invention may be physically, functionally and logically implemented in any suitable way such as in a single unit, in a plurality of units or as part of separate functional units. The invention may be implemented in a single unit, or be both physically and functionally distributed between different units and processors.

In the following sections, non-limiting examples are presented on the use of a device and a method according to present invention. On QC-device reference measurements

In the following a comparison between measurements carried out in a QC-device (often referred herein to as RheoStream) as illustrated in fig. 1 and

measurements carried out by use of a standard rheometer is presented. Liquid samples

The following three liquids have been subjected to measurements:

Locust Bean Gum (LBG) 1% solution,

Xanthan 0.2% solution,

- Pectin juice (two different samples are used Ref. Pectin I and Pectin II).

Apparatus used:

The standard rheometer used is a Haake MARS II with Z40 DIN sensor. Yield-stress

By applying the proportionality between the flow rate through the Q-device and the active shear-rate on the inner surface of the Q-device in combination with the Hagen-Poiseuilles equation, the following relations are obtained:

π a⁴ 7Γ

Q⁼ 8^L ^{AP =} 4 ^{G † = Qo†} where a is the radius (Qo may be determined by Qo=- a³). Further, by comparing

4

the Hagen-Poiseuilles equation with the definition of shear-stress, a relation between pressure difference over the Q-device and Δρο and shear stress σ:

a

σ = PQ = ^To ^APQ

Again with a scale factor το (which can be determined by calibration). The first measurement is with LBG 1%, which as shown in fig. 6 does not show any observable yield-stress, while the measurements with Xanthan 0.2% show a clear yield-stress from both apparatus. Here the value of yield-stress is determined for both apparatus by fitting a 2^nd degrees polynomium and taking a reading of the constants (emphasized by bolded text in figure 7).

Viscometry

Based on the two scale factors, the viscosity in Pa*s can be calculated from Δρο and a viscometry plot for the same liquids are shown in fig. 8 and 9, where K and n are determined by curve-fitting.

Due to time effects, (eg. thixotropi) some of the following measurement are divided after the sequential pulse order (typically, measurements are carried out over to pulses with different flow rates).

Visco-elasticity

Shear-rate corresponds to a related frequency in an oscillation characteristic by: / = ^γ/_2π· ^Tne Elasticity moduli G' is found by the extended Cox-Merz relation :

„,

Where an - an is the first normal stress difference, which is reflected in the magnitude of Ap_c-_reiax (as discussed herein) where C is a scale factor and is a correction factor (typically in the order of 1).

In order to calculate Ap_c-_reiax , which is used as a the first normal stress difference, it noted that by each pump-pulse start, is produced a stress (pressure) overshoot as illustrated in fig. 10.

In fig. 11, the frequency dependency for G' is plotted for standard rheometer measurements and RheoStream device by use of the above relations. A clear differentiation of the measurements depending on pulse sequence is seen. To produce a "standard" visco-elasticity-plot G" is determined as G* when using the RheoStream measurements. In fig. 12, G* is approximated by: G* ¾ G*o τ, with the scale factor G*o (using the approximation of β=ΐ in relation (14) of fig. 5a) The above referenced visco elasticity plots uses three scale factors: C, and G*o, and it is contemplated that these three parameters will be liquid-type dependent, and may be calibrated for an actual choice of type of liquid. Calibration

In order to examine the three parameters (C, and G*o), they are initially being determined for the pectin liquid (ref: Pectin I), with a plot of the relations presented in fig. 13 and 14.

5

Measurement

After this, the obtained parameters are used in the characterization of another pectin sample (ref Pectin II), showing an agreement between the measurement obtained by the RheoStream device and the standard rheometer (see figs. 15 and 10 16).

On Measuring cell (C-device) geometry

On the basis of a visco elasticity and shear-thinning liquid model, the geometry of the measuring cell (C-device) has been optimized to be sensitive to changes in the 15 degree of visco elasticity. Such an optimization can be performed by use of

computational fluid dynamic (CFD), e.g. by use of a finite element (FE) method, to perform calculations based on a mathematical modelling of the fluid; this may be combined with a topology optimization.

20 The degree of visco elasticity can be characterized by the dimensionless

Weissenberg number Wi. For Wi = 0 the liquid is not visco elastic, although the fluid considered during the optimization still has shear-thinning properties. As Wi number is increased, the visco elastic properties increase in strength, while the shear-thinning properties remain.

25

The Cross-WLF model is used to model the shear-thinning properties of the fluid - here at constant temperature T = 423.15 K (150 °C) :

^V^ ⁼ 1 + (1 y)^1""

where γ is the shear-rate in unit [1/s] and the remaining values are provided e.g. 30 by table look-up:

Parameter Value [unit] Description

P 1150 [kg/m³] Density (used for estimating the Reynolds number being very small ~ 10^"6)

n 0.24714 Power-law index (shear-thinning) ηο 23000 [Pa s] Base-viscosity, calculated for T = 423.15 K

( 150 °c)

λ 0.45 s Critical time scale calculated for T = 423.15 K

( 150 °c)

A quality criteria has been to support the need for the device according to the present invention being sensitive to changes in pure visco elasticity, i .e. varying Wi. As visco elasticity model, the Oldroyd-B model has been implemented . Measuring cell geometry / C-device geometry

The geometry of the measuring cell (also referenced C-device herein) is shown below (which resembles the geometry shown in fig. 1 and 3) . The Arrows illustrate the flow direction and pressure sensors are implemented as illustrated in fig . 3.

To obtain a C-device that maximizes the amplification of the APc-response to changes in viscoelasticity, the flow and pressure in the C-device was modelled by the Oldroyd-B model . Using CFD/FE modelling and varying the Wi-value, a device geometry was optimized as shown in fig. l and 3. The optimized geometry was used for data in the following example. Measuring values estimated on the basis of the above model

In the following simulated results, obtained at the flow rates of 125, 250 and 500 l/hour, are presented.

From figure 17 it can be seen that the estimated pressure difference (ΔΡς) varies ~5 bar for varying Wi, which is at least 50 times higher than the expected device dependent fluctuations when recording the dpc.

It has been found beneficial to normalize ΔΡς by APQ and in figure 18 ΔΡς /APQ is plotted as a function of APQ.

This normalization provides a clear distinction between variations in flow rate (~ APQ) and variations in quality (~ variations Wi in the model) being a function of ΔΡς /ΔΡς . The upper most points in the figure 18 (lined-through by the horizontal line) are for Wi = 0, i .e. for a non-visco-elastic fluid/liquid, where an increase i n Wi will make ΔΡς /APQ to drop.

It could be noted that the numerical model is ideal in many ways and that a calibration based on physical measurements may show a slightly greater variation of APQ as function of Wi .

It is noted that if pressure measurement over the Q-device is not practical, APc can be normalized with APMC being the pressure difference over the C-device (e.g by use of the pressure sensors 11 and 12 (see figure 1) . This is illustrated in the figure 19 which also shows a strong Wi dependency of APMC.

Illustrative example

Figures 20-22 illustrates results obtained by the present invention . The sample fluid is a lightly gel-like detergent and because this fluid's flow behavior while flowing through the QC-device, a small yield-stress is observed and G" dominates over G' for high frequencies. A power-law fit for the flow curve has been added to fig . 20.

Implementation

For measurement of the viscoelastic properties of a highly viscous adhesive, it has been found that the total height of the C-device (e.g . extruded) advantageously can be 100 mm in order to allow the flow to be very close to 2-dimensional . In addition, the inlet and outlet of the C-device may advantageously be 1.5 times the width of outlet/inlet, thereby providing a nearly rectangular inlet/ outlet with the dimensions width= 50mm height 100 mm and length 75mm. It may be

advantageous to round the corners at the bottom and top so as to have a "fillet" in the bottom and in the top (by the word "fillet" is preferably denoted a rounding of a given sharp edge by a circle of given radius/diameter such that the circle is tangent to both the curves meeting in the sharp edge of the devices) . Thereby large drills may be used during milling.

As shown in fig . 1, the C-device may be equipped with four pressure sensors arranged as shown in figure 3. It is noted that the pressure sensor 7 may be arranged closer to the sharp bend 18 than shown in fig. 1 and 3. The two internal sensor (#8 and #7 in figure 1) are arranged so that the measuring surface is flush with the surface of the wall . In case drilling along the upper side of C-device provides a structural weakness, a drilling angle can be applied, preferably without providing a measuring surface of the pressure sensors 5 influencing the flow.

Although the present invention has been described in connection with the specified embodiments, it should not be construed as being in any way limited to the presented examples. The scope of the present invention is to be interpreted in

10 the light of the accompanying claim set. In the context of the claims, the terms "comprising" or "comprises" do not exclude other possible elements or steps. Also, the mentioning of references such as "a" or "an" etc. should not be construed as excluding a plurality. The use of reference signs in the claims with respect to elements indicated in the figures shall also not be construed as limiting the scope

15 of the invention. Furthermore, individual features mentioned in different claims, may possibly be advantageously combined, and the mentioning of these features in different claims does not exclude that a combination of features is not possible and advantageous.

20 LIST OF REFERENCE SYMBOLS USED

1 Measuring device /QC-Device

2 Q-device

3 C-device

4 Inlet to Q-device

25 5 Pressure sensor for PQI

6 Pressure sensor for PQ₂

7 Pressure sensor for Pci

8 Pressure sensor for Pc2

9 Channel of Q-device

30 10 Channel of C-device

11 Additional pressure sensor (optional)

12 Additional pressure sensor (optional)

13 Wall segment (second wall segment)

13a Starting position for wall segment 13

35 13b Ending position for wall segment 13 Wall segment (first wall segment)a Starting position for wall segment 14b Ending position for wall segment 14 Constriction in C-device

Bend on wall segment 13

Bend on wall segment 14

Inlet of C-device

Outlet of C-device

Constriction in Q-device

Claims

1. A method for determining a fluidic parameter of a fluid, the method determines one or more of the following fluidic parameters : elastic moduli (GO, the complex moduli (G*), viscous moduli (G"), and utilizes

a C-device comprising a flow channel (10) with an inlet ( 19) and an outlet (20), the flow channel being defined by at least two opposite curved wall segments comprising respectively a first wall segment (14) and a second wall segment ( 13), the two opposite curved wall segments extend asymmetrically to each other at least along a part of the channel ( 10) so as to define the flow channel to comprise a diverging flow channel followed by a converging flow channel, wherein a constriction ( 15) is defined upstream of the outlet (20) and terminating the converging flow channel geometry, and pressure sensors (7, 8) are arranged in or at the wall segments (13, 14) to determine a pressure (APc) difference over at least a part of the

C-device,

a functional relationship between

a pressure difference determined by use of the C-device, or a pressure difference (APVE) derived therefrom, a characteristic shear- rate (YC. YV. YQ), and/or a volume flow through the C-device, and the fluidic parameter to be determined,

the method comprising

- feeding the fluid at,

varying flow rates or at least one constant flow rate

through the C-device, while said pressure difference (APc) determined by use of the C-device is recorded,

determining the characteristic shear-rate(s) resulting from the feeding of the fluid and/or a volume flow through the C-device; determining on the basis of the functional relationship the fluidic parameter.

2. A method according to claim 1, wherein the pressure difference determined by use of the C-device is

the magnitude of a pressure peak occurring at increasing volume flow through the device, or

- the pressure difference determined by the C-device at steady-state, or substantially steady-state, flow through the C-device.

3. A method according to any of the preceding claims, the method further comprising utilizing a Q-device comprising a straight channel and at least two pressure sensors (5, 6) arranged to determine a pressure difference along at least a part of the channel .

4. A method according to claim 3, wherein the Q-device further comprising a constriction (21) and the pressure sensors (5, 6) of the Q-device are arranged upstream and downstream of the constriction (21).

5. A method according to any of the preceding claim 3 or 4, wherein the Q-device is arranged immediately upstream or downstream of the C-device, so that fluid leaving the Q-device flows directly into the C-device or the fluid leaving the C-device flows directly into the Q-device.

6. A method according to any of the preceding claims, wherein said derived pressure difference (ΔΡνε) is the pressure difference originating from the visco- elastic effects in the fluid flow in the C-device, and said derived pressure difference being determined by subtracting the pressure difference originating from the viscous effects (ΔΡε,ν) of the fluid flow in the C-device from the pressure difference (APc) determined by use of the C-device, and further comprising determining the elastic moduli (GO on the basis of said derived pressure difference (ΔΡνε) and the characteristic shear rate for the flow in the C-device

7. A method according to claim 6, when dependent on claim 3, wherein the pressure difference originating from the viscous effects (ΔΡε,ν) in the flow in the C-device is approximated by scaling the pressure difference (APQ, ΔΡν ) determined by the Q-device with a calibrated proportionality factor (AP_cy = ξ^^) .

8. A method according to claim 6 or 7, wherein the pressure difference originating from the viscous effects {APc,v) of the flow in the C-device is approximated to be zero, resulting in that said pressure difference (ΔΡνε) originating from the visco- elastic effects in the flow in the C-device is approximated by the pressure difference (APc) determined by use of the C-device.

9. A method according to any of the preceding claims, wherein the characteristic shear rate for the flow in the C-device (y_c) is estimated as a proportionality of the volume flow through the C-device with a calibrated proportionality factor (†_c == const Q_c) .

10. A method according to any of the preceding claims, when dependent on claim 3, comprising or further comprising determining the characteristic shear-stress (σ<2, σν) by scaling the pressure difference (APQ, ΔΡν) determined by the Q-device with a calibrated proportionality factor (σ₀ = ΑΡ_ο/τ₀, σ_ν = ΑΡ_ν/τ₀) and determining the complex moduli (G*) on the basis of characteristic shear-stress {OQ, σν) and a characteristic shear-rate for the flow in the Q-device (†_Q,†_V) .

11. A method according to claim 10, wherein the characteristic shear-rate for the flow in the Q-device (†_Q,†_V) is determined by scaling the volume flow through the

Q-device with a calibrated proportionality factor (†₀ == ,†_v ==— ).

12. A method according to any of the preceding claims, wherein the fluidic parameter determined is the elastic mod he functional relationship is

wherein C, a are determined by the calibration, γ is determined as Q is the nR⁶

volume flow through the C-device, R is a characteristic radius of the device, such as half of the hydraulic diameter of the Q-device, and wherein AP_C is either

AP_c__relax being the mean pressure difference by the C-device occurring after an overshoot resulting from an increase in volume flow through the

C-device, or the pressure difference determined by the C-device, such as said pressure difference (ΔΡνε) derived therefrom, preferably at steady-state, or substantially steady-state, flow through the C-device.

13. A method according to any of the preceding claims 3-12, wherein the fluidic parameter determined is the shear-rate and the functional relationship is

Y_QC = wherein Q is the volume flow through the C-device and R is a

14. A method according to any of the preceding claims, wherein the step of feeding the fluid at, preferably known or determined, varying or constant flow rates comprises varying the volume flow between two values (Qi, Q₂), wherein the variation is a ramp-up from the first volume flow to a second volume flow, followed by a time period with constant volume flow equal the second volume flow, followed by a ramp-down to the first volume flow.

15. A method according to claim 14, wherein the first volume flow is equal to zero.

16. A method according to any of the preceding claims, wherein the constriction (15) is defined by the second wall segment (13) having a sharp bend (16) and the first wall segment (14) having a relatively to the sharp bend (16) a more smooth bend (17).

17. A method according to claim 16, wherein one of the pressure sensors (7), to determine a pressure (APc) difference over at least a part of the C-device, is arranged downstream or upstream of the sharp bend (18) in the first wall segment (14).

18. A method according to any of the preceding claims, wherein the first wall segment (14) comprising a sharp bend (18) and one of pressure sensors (8) to determine a pressure (APc) difference over at least a part of the C-device is arranged upstream or downstream of the sharp bend (18) in the first wall segment (14).

19. A method according to any of the preceding claims, wherein the calibration comprising

obtaining by use of a standard rheometer corresponding values of shear rate (y), stress components (σ , σ₂₂) and elasticity moduli (GO for a fluid - feeding said fluid at known or determined, varyi ng flow rates, or constant flow rates, through the C-device, while the pressure difference determined by use of the C-device and the volume flow (Q) are recorded thereby obtaining corresponding values of the volume flow and pressure difference, determining calibration constants in a functional relationship between elasticity moduli (GO, volume (Q) flow and pressure difference (ΔΡ) by equating the elasticity moduli (GO obtained by the standard rheometer with the elasticity moduli determined by the mathematical equation.

20. A device for determining a fluidic parameter of a fluid, comprising

- a C-device comprising a flow channel (10) with an inlet ( 19) and an outlet (20), the flow channel being defined by at least two opposite curved wall segments comprising respectively a first wall segment (14) and a second wall segment ( 13), the two opposite curved wall segments extend asymmetrically to each other at least along a part of the channel ( 10) so as to define the flow channel to comprise a diverging flow channel followed by a converging flow channel, wherein a constriction ( 15) is defined upstream of the outlet (20) and terminating the converging flow channel geometry, and pressure sensors (7, 8) are arranged in or at the wall segments (13, 14) to determine a pressure (APc) difference over at least a part of the C-device.

21. A device according to claim 20, further comprising a Q-device comprising a straight channel and at least two pressure sensors (5, 6) arranged to determine a pressure difference along at least a part of the channel.

22. A device according to claim 21, wherein the Q-device further comprising a constriction (21) and the pressure sensors (5, 6) of the Q-device are arranged upstream and downstream of the constriction (21).

23. A device according to claim 21 or 22, wherein the Q-device is arranged immediately upstream of the C-device, so that fluid leaving the Q-device flows directly into the C-device.

24. A device according to any of the preceding claims 20-23, further comprising a pump, such as a volumetric pump, configured for feeding fluid through the device at varying volume flows, preferably the variation of volume flow is a ramp-up from the first volume flow to a second volume flow, followed by a time period with constant volume flow equal the second volume flow, followed by a ramp-down to the first volume flow.

25. A device according to any of the preceding claims 20-24, wherein the constriction ( 15) is defined by the second wall segment ( 13) having a sharp bend (16) and the first wall segment (14) having a relatively to the sharp bend (16) a more smooth bend ( 17) .

26. A device according to claim 25, wherein one of pressure sensors (7), to determine a pressure (APc) difference over at least a part of the C-device, is arranged downstream or upstream of a sharp bend ( 18) in the fi rst wall segment (14) .

27. A device according to any of the preceding claims 20-26, wherein second wall segment (13) comprising a sharp bend (16) and one of the pressure sensors (8) to determine a pressure (APc) difference over at least a part of the C-device is arranged upstream or downstream of the sharp bend (16).