WO2023047176A1

WO2023047176A1 - Microelectrorheometer for characterizing electrorheological fluids

Info

Publication number: WO2023047176A1
Application number: PCT/IB2021/059053
Authority: WO
Inventors: Francisco Jose Galindo ROSALES; Paulo Vicente Da Silva Marques; Hugo Jorge Da Nóbrega Abreu FERREIRA
Original assignee: University of Porto; Instituto de Engenharia de Sistemas e Computadores Tecnologia e Ciência
Current assignee: University of Porto; Instituto de Engenharia de Sistemas e Computadores Tecnologia e Ciência
Priority date: 2021-09-27
Filing date: 2021-10-01
Publication date: 2023-03-30
Anticipated expiration: 2024-03-27

Abstract

The present invention relates to a microelectrorheometer comprising an elongated main microchannel (1) comprising an inlet (5) and an outlet (6), characterized in that it further comprises two auxiliary microchannels (2) filled with a metal or a metal alloy, wherein said auxiliary microchannels (2) are parallel to each other; and wherein each of the two auxiliary microchannels (2) is arranged axially along each side of the main microchannel (1); or one of the two auxiliary microchannels (2) is arranged transversally to the main microchannel (1) and upstream to the inlet (5) thereof, and the other of the two auxiliary microchannels (2) is arranged transversally to the main microchannel (1) and downstream to the outlet (6) thereof, such that in operation the said auxiliary channels (2) operate as electrodes for generating an electrical field to be applied onto an ERF sample. The invention lies in the technical field of microfluidics devices designed for measuring and characterizing the rheological properties of ERFs.

Description

MICROELECTRORHEOMETER FOR CHARACTERIZING ELECTRORHEOLOGICAL FLUIDS FIELD OF THE INVENTION The present invention relates to microelectrorheometers designed to perform electrorheometry at microscale, or in other words to perform microelectrorheometry, either shear microelectrorheometry or extensional microelectrorheometry. The invention lies in the technical field of microfluidics devices designed for measuring and characterizing the rheological properties of electrorheological fluids. BACKGROUND OF THE INVENTION Electrorheological fluids (ERFs) are suspensions of extremely fine and electrically active particles in an electrically insulating fluid. Under the presence of an external electric field, their rheological properties (viscosity, yield stress, shear modulus, etc.) change reversibly with response time on the order of milliseconds. Under the electric field, ERFs can suddenly increase their viscosity and even change from liquid-like state to solid-like state accomplished by yield stress to resist shearing deformation. This phenomenon is called the electrorheological effect. ERFs have attracted considerable interest in recent decades due to their wide potential use in active control of conventional and intelligent devices. These fluids are typically used in fast-acting clutches, hydraulic valves, brakes, shock absorbers, tactile displays and flexible electronics. Several comprehensive reviews have been published on ERFs and the mechanism of the electrorheological effect. A generally accepted description for the electrorheological effect is based on the induced electric polarization mechanism. Let us consider a suspension of particles in a fluid medium. The particles and the fluid are assumed to be electrically nonconducting or only slightly conducting. Due to the difference in the dielectric constant of the fluid and solid, the particles will be electrically polarized when an electric field is applied. Under this condition, the random dispersion is not the lowest energy state of the system according to the resulting induced dipole- dipole interaction between the particles. Consequently, the particles tend to aggregate and form chains along the direction of the applied electric field. The presence of these chains is synonym of an internal microstructure within the carrier fluid and is responsible for the increase in the viscosity and even for the solid-like behaviour under the presence of an electric field. For a complete description and better understanding of the performance of any complex fluid, and particularly of ERFs, under real applications, their rheological properties must be measured in two canonical flows, namely shear and extensional flows. Microfluidics is the science and technology of systems that process or manipulate very small amounts of fluids in geometries with characteristic lengthscales below one millimetre, and it is recently established as a new field of research. The small characteristic lengthscales of microfluidics enable the generation of flows with high deformation rates while keeping the Reynolds number (Re) small. These unique flow features result in the ability to promote strong viscoelastic effects, quantified by the elasticity number (El) that scales inversely with the square of the characteristic length (L), which are highly enhanced as the scale is reduced. These distinctive flow characteristics together with the development and growth of microfluidic techniques provide a rich platform for rheologists to perform rheometric investigations of non-Newtonian fluid flow phenomena at small scales and new opportunities for material property characterization. The prior art allows to measure steady shear flow curves by means of a microrheometer containing three flush mounted microelectromechanical systems (MEMS) pressure sensors, as used in the m-VROC^TM microfluidic shear rheometer commercialized by Rheosense Inc. US 7290441 B2, entitled “Micro slit viscometer with monolithically integrated pressure sensors”, discloses an improved micro slit viscometer including a combined micrometer depth rectangular slit flow channel with monolithically integrated multiple pressure sensors in the flow channels and a pumping system that injects a test sample to the channel at a desired flow rate. Pressure sensing diaphragm of the monolithically integrated pressure sensors is smooth to minimize the flow disturbance thereby measuring accurate local pressures. With the measurement of the pressures at various locations of the channel the true viscosity of test sample can be calculated. The viscometer may consist of multiple flow channels and thus the true viscosity at multiple shear rates can be measured simultaneously for a given flow rate thereby obtaining a full viscosity curve as a function of shear rate of non-Newtonian liquids in a much faster manner. The viscometer needs only a miniscule amount of sample, which minimizes a waste of test material. The microchannels and the monolithically integrated pressure sensors are fabricated using microfabrication processes on wafers and combined, which greatly reduce the production costs. US 8104329 B2, entitled “Method and installation for determining rheological characteristics of a fluid, and corresponding identifying method”, discloses an optical microfluidic viscometer where the determination of the viscosity does not rely on pressure transducers and a method comprising: causing a reference fluid (F2) having known rheological characteristics, and an unknown fluid (F1) to flow in parallel in a microchannel (126); identifying at least one data item representative of the interface (I) between these fluids in the parallel flow, and in particular the position of said interface; and determining the rheological characteristics of the unknown fluid, from the or each identified data item. WO 2013164587 A1 by Zimmerman and Ress, entitled “Rheometer and rheometric method”, proposed a different approach which would not only allow to obtain the constitutive viscous parameters for GNF fluids running just one experiment at steady flow conditions, but also the constitutive parameters for viscoelastic fluids under transient flow conditions in a T-junction microfluidic device. Summing up, the advent of microfluidic technology has not only increased the need for rheological information about complex fluids but also provided a new platform for developing and testing new rheometric devices. Specifically, it discloses an apparatus responsive to constitutive parameters of the rheological properties of complex fluids comprising: a flow path for the fluid that comprises a shear feature that results in multiple shear patterns between adjacent elements of the flow stream of the fluid as it transitions the shear feature; means to sense flow parameters of the flow stream along the flow path, wherein said flow parameters are selected to be sensitive to changes in rheological parameters of complex fluids; wherein said flow stream is pulsed, whereby time-dependent transient effects as a result of the complex rheological properties of the fluid affect the flow parameters sensed over and after the period of the pulse and are detected by the apparatus. The apparatus also determines constitutive parameters of the rheological properties of complex fluids by including computational means to calculate on the basis of said sensed flow parameters by inverse interpolation according to appropriate models of said rheological properties. All the previously mentioned microfluidic rheometers and methods impose shear flow to the fluid sample and none of them can impose an external electric field, neither parallel nor perpendicularly to the flow direction. Therefore, there are no solutions in the prior art to perform shear electrorheometry at microscale. Regarding the rheological characterization under extensional flow in microfluidic devices, the company Rheosense Inc. commercializes the eVROC^TM viscometer, which is able to determine the viscosity and the elasticity of a complex fluid, due to the presence of a hyperbolic contraction/expansion zone in the middle of the microchannel and four monolithically integrated MEMS pressure sensors. This is disclosed in US 7770436 B2, entitled “Micro rheometer for measuring flow viscosity and elasticity for micron sample volumes”. The hyperbolically-shaped contraction in planar configurations allow to impose strong extensional flow with an approximately constant extension rate along its centerline of the microchannel, although there is an important contribution of the shear flow close to the lateral walls. This is the main reason why the eVROC^TM microdevice includes four pressure sensors, for evaluating separately the pressure drop due to the viscous shear stresses in the fully developed region (upstream and downstream the throat) and the pressure drop across the contraction/expansion zone. By substracting them, it would be possible to determine the pressure drop associated with the pure extensional flow. More specifically US 7770436 B2 discloses a micro-rheometer for measuring flow characteristics such as viscosity, elasticity, and flow rate of a sample liquid combines well defined micro-fabricated flow channels having geometry changes forming a constriction region therein to a monolithically fabricated pressure sensor array. The pressure sensor array positions pressure sensors to measure the viscosity of the sample liquid while flowing in a uniform length of the flow passage and to measure the extensional viscosity while flowing through the constriction region of the passage. The invention can improve the measurement accuracy of the flow rate, viscosities, or elasticities over a wide range of shear rate. The accuracy of the viscosity over a broader range of shear rate or flow rate measurement over broader range of flow rates can be accomplished by employing monolithically integrated pressure sensors fabricated with different sensitivities disposed in a known manner. The invention further includes necessary components such as a display, a pumping system, valve manifolds, and software for a portable or laboratory measurement instrument, process control, and high throughput measurements. Thus, the apparent extensional and the elasticity can be obtained with the eVROC^TM microdevice. Nevertheless, it cannot perform extensional electrorheometry. The microelectrorheometers of the prior art cannot provide information about the electrorheological properties of ERFs. As such, there is a need in the art to overcome this drawback. SUMMARY OF THE INVENTION Microelectrorheometer comprising: an elongated main microchannel (1) comprising an inlet (5) and an outlet (6), characterized in that it further comprises two auxiliary microchannels (2) filled with a metal or a metal alloy, wherein said auxiliary microchannels (2) are parallel to each other; and wherein each of the two auxiliary microchannels (2) is arranged axially along each side of the main microchannel (1); or one of the two auxiliary microchannels (2) is arranged transversally to the main microchannel (1) and upstream to the inlet (5) thereof, and the other of the two auxiliary microchannels (2) is arranged transversally to the main microchannel (1) and downstream to the outlet (6) thereof, such that in operation the said auxiliary channels (2) operate as electrodes for generating an electrical field to be applied onto an ERF sample. Preferably, said main microfluidic channel (1) is straight and planar-shaped. In an embodiment, said main microfluidic channel (1) comprises a contraction zone (23). In another embodiment, said main microfluidic channel (1) further comprises pressure sensors (7, 8). In a further embodiment, the microelectrorheometer further comprises a dispensing device, which is preferably a syringe. The microelectrorheometer of the invention further comprises a power supply and a microscope. In a preferred embodiment, the main microchannel (1) and the auxiliary microchannels (2) of the microelectrorheometer are embedded in a PDMS chip (11) and closed with a substrate (12), preferably the substrate (12) is a glass slide. In another preferred embodiment, the main microchannel (1) and the auxiliary microchannels (2) of the microelectrorheometer are embedded in a PDMS chip (11) and closed with another PDMS chip (13). In a further preferred embodiment, the main microchannel (1) and the auxiliary microchannels (2) of the microelectrorheometer are embedded in a single chip (14), which chip (14) is preferably made of fused silica, PMMA, COC, COP, PC, PSU or PI. BRIEF DESCRIPTION OF THE DRAWINGS The present invention is described below with reference to the accompanying drawings, given solely as non-limiting examples, in which: Fig. 1 shows schematic views of embodiments of the present invention: a) the shear flow occurring in the main microchannel (1) and the external electric field (4) between the auxiliary microchannels (2) acting as electrodes by means of the voltage supplier (3) are parallel to each other; b) the shear flow occurring in the main microchannel (1) and the external electric field (4) between the auxiliary microchannels (2) acting as electrodes by means of the voltage supplier (3) are perpendicular to each other; c) the extensional flow occurring in the main microchannel (1) and the external electric field (4) between the auxiliary microchannels (2) acting as electrodes by means of the voltage supplier (3) are parallel to each other; d) the extensional flow occurring in the main microchannel (1) and the external electric field (4) between the auxiliary microchannels (2) acting as electrodes by means of the voltage supplier (3) are perpendicular to each other. Reference number (24) designates the flow direction of the fluid sample. FIG. 2 is a top view for four preferred embodiments of the invention: a) the fluid sample enters into the main microchannel (1) through inlet (5) and exits through outlet (6), being undergone to a shear flow, which is parallel to the external electric field (4) provided by the electric circuit formed by using two auxiliary microchannels (2) acting as electrodes and a voltage supplier (3), the pressured drop in the flow is measured by two pressure sensors (7, 8); b) the fluid sample enters into the main microchannel (1) through inlet (5) and exits through outlet (6), being undergone to a shear flow, which is perpendicular to the external electric field (4) provided by the electric circuit formed by using two auxiliary microchannels (2) as electrodes and a voltage supplier (3), the pressure drop in the flow is measured by two pressure sensors (7, 8); c) the fluid sample enters into the main microchannel (1) through inlet (5) and exits through outlet (6), being undergone to a extensional flow in a contraction zone (23) of the main microchannel (1), the fluid flow is parallel to the external electric field (4) provided by the electric circuit formed by using two auxiliary microchannels (2) as electrodes and a voltage supplier (3), the pressure in the flow is measured by four pressure sensors (7, 8, 9, 10); d) the fluid sample enters into the main microchannel (1) through inlet (5) and exits through outlet (6), being undergone to a extensional flow in a contraction zone (23) of the main microchannel (1), which fluid sample flow is perpendicular to the external electric field (4) provided by the electric circuit formed by using two auxiliary microchannels (2) as electrodes and a voltage supplier (3), the pressure in the flow is measured by four pressure sensors (7, 8, 9, 10). FIG. 3 shows a cross section view of different embodiments for any of the perpendicular configurations: a) the main microchannel (1) containing the fluid sample and two auxiliary microchannels (2) operating as electrodes connected to the voltage supplier (3) for the generation of the electric field (4) are embedded in a PDMS chip (11) and closed with a substrate (12), for example a glass slide; b) the main microchannel (1) containing the fluid sample and the auxiliary microchannels (2) operating as electrodes connected to the voltage supplier (3) for the generation of the electric field (4) are embedded in a PDMS chip (11) and closed with a another PDMS chip (13); c) the main microchannel (1) containing the fluid sample and the auxiliary microchannels (2) operating as electrodes connected to the voltage supplier (3) for the generation of the electric field (4) are embedded in a single chip (14), which can be made out of fused silica, PMMA or PET, for example. FIG. 4 is a sketch showing the characteristic dimensions of the different features of the invention for one of the four possible embodiments mentioned before. In Fig. 4a (1) is the main microchannel containing the fluid sample, (2) are the auxiliary microchannels filled with a metal or metal allow so as to operate as electrodes, the auxiliary microchannels (2) are connected to a voltage supplier (3) to generate the electric field (4), whereas the dashed line (15) represents the top view of a cross section plane of the ideal fabrication. Fig.4b represents the top view dimensions of the invention, where reference number (16) designates the width (also referred to as Ws in the equations below) of the main microchannel (1) containing the fluid sample, reference number (17) designates the length of the auxiliary microchannels (2), reference number (18) designates the width (also referred to as We in the equations below) of the auxiliary microchannels (2), and reference number (19) designates the separation (also referred to as S in the equations below) between the main microchannel (1) and the auxiliary microchannels (2). However, the real dimensions are always different from the nominal ones and the main microchannel (1) and the auxiliary microchannels (2) may have different heights (20 and 21) and the walls of the auxiliary microchannels (2) may not be perfectly perpendicular to the base, but deviated a small angle (22), as shown in Fig.4c. FIG. 5 contains a graph showing the homogeneity of the electric field generated within the volume of the fluid sample for different parametric conditions. DETAILED DESCRIPTION OF THE INVENTION The present invention relates to microelectrorheometers namely to microfluidic chips designed to perform electrorheometry at microscale, or in other words to perform microelectrorheometry, either shear microelectrorheometry or extensional microelectrorheometry. In particular, microelectrorheometers designed as microfluidic chips are disclosed. Prior art solutions for microrheometry were not able to provide large and homogeneous electric field throughout the whole volume of a fluid sample, which have discouraged the exploration and development of electrorheometry at microscale. Such prior art microrheometers cannot retrieve the information about the electrorheological properties of ERFs. The present invention fills the gap of the prior art allowing for the electrorheological characterization of ERFs in four possible configurations shown in Fig. 1. In particular, for shear flow and perpendicular external electric field, and for the extensional flow and parallel electric field, the invention can provide information about the electrorheological properties for shear and extension rates beyond the limits of the prior art rheometers at macroscale. Additionally, compared with the electrorheometry at macroscale, the microelectrorheometers proposed in this invention would allow to characterize ERFs with much lower concentration of particles and under much larger intensities of electric field, because the distance between electrodes decreases considerably in view of the microscale. Making reference to Fig. 1 and 2, the present invention relates to a microelectrorheometer comprising: an elongated main microchannel (1) comprising an inlet (5) and an outlet (6), the microelectrorheometer characterized in that it further comprises two auxiliary microchannels (2) filled with a metal or a metal alloy, wherein said auxiliary microchannels (2) are parallel to each other; and wherein each of the two auxiliary microchannels (2) is arranged axially along each side of the main microchannel (1); or one of the two auxiliary microchannels (2) is arranged transversally to the main microchannel (1) and upstream to the inlet (5) thereof, and the other of the two auxiliary microchannels (2) is arranged transversally to the main microchannel (1) and downstream to the outlet (6) thereof, such that in operation the said auxiliary channels (2) operate as electrodes for generating an electrical field to be applied onto an ERF sample. In the context of the present invention, microchannels are conducts with characteristic length scales less than one millimetre that are typically used in microfluidic devices and methods allowing to process, control or manipulate very small amounts of fluid. Surprisingly, the present invention makes it possible to obtain a uniform electrical field to be applied to the ERF sample despite the microscale conditions suggested otherwise. In fact, so far, the microscale conditions have diverted the skilled person from trying to apply a homogeneous electrical field onto the ERF sample, since such tiny dimensions under 1 mm for the microelectrorheometer do not provide anticipable favourable results regarding said homogeneity for the electric field. Making reference again to Fig. 1, the microelectrorheometer of the present invention comprises a main elongated microchannel (1), that control the flow-type imposed to the fluid sample, either simple shear flow (Fig. 1a and 1b) or extensional flow (Fig. 1c and 1d); and auxiliary microchannels (2) filled up with metals, so that they serve as electrodes when connected to an external voltage supplier (3) in order to apply an electric field (4) perpendicular (Fig. 1b and 1d) or parallel (Fig. 1a and 1c) to the flow of the fluid sample, said auxiliary microchannels (2) either aligned, respectively, with the direction of the flow (Fig. 1b and 1d) or perpendicular to the flow (Fig. 1a and 1c), so that the full electrorheological characterization of electrorheological fluids (also termed herein as ERFs) can be performed. Fig.2 shows plan views of embodiments of the present invention. In all cases, the MERs comprise a main microchannel (1) through which the ERF flows from an inlet (5) towards an outlet (6); and two auxiliary microchannels (2) filled out with a metal or a metal alloy serving as electrodes. The electrodes must be connected to a voltage supplier (3) in order to generate the electric field (4). The relative orientation between the generated electric field (4) and the flow direction of the fluid sample provides the corresponding experimental configuration, i.e. shear flow parallel (Fig.2a) or perpendicular (Fig.2b) to the direction of the electric field (4) and extensional flow parallel (Fig.2c) or perpendicular (Fig.2d) to the direction of the electric field (4). Preferably, for the two shear microelectrorheometers (SMERs), the main microchannel (1) is straight and planar-shaped, as shown in Figures 1a), 1b), 2a), 2b), 4a). The changes in the viscosity of an ERF will be determined by means of the following equation: [1] where is the viscosity of the ERF under the influence of an external electric field (E) and at a certain shear rate ; and is the shear stress at the wall under the influence of an external electric field (E) and at a certain shear rate . The force balance between the pressure ( ) acting across the cross-sectional area of the channel and the viscous shear stresses present at the walls is given by Eq. [2]: [2] being and the width and depth of the main microchannel, and the distance between the two pressure sensors. As the measurements of will depend on the imposed flow rate ( ) and the external electric field ( , it is then demonstrated that is also a function of and . For incompressible 2-D flow of a constant viscosity liquid in a rectangular channel, the wall shear rate is a linear function of the imposed flow rate ): [3] For incompressible fully developed 2-D flows of liquids with a rate-dependent viscosity, the calculation of the current shear rate at the wall is more complex because the velocity profile is no longer parabolic. Using Eq. [3] thus results in an apparent shear rate . However, because the channel dimensions are known precisely and the flow is steady and two dimensional, the true wall shear rate can be found using the Weissenberg–Rabinowitsch–Mooney equation [4]: , [4] where τw is calculated from Eq. [2]. To evaluate the derivative in Eq. [4], fitting the variation of with a first or second order polynomial is generally sufficient. The true viscosity function is then computed as Eq. [5]: , [5] Thus, controlling the flow rate and the electric field, it is possible to modify the viscosity of the MRFs. Measurements of the pressure drop would allow to determine the steady shear viscosity curve of the ERFs. Due to the different microstructures generated by the electric field, it is expected that the viscosity curve will also depend on the relative orientation between the shear flow and the electric field. In the case of the extensional microelectrorheometers (EMERs), a hyperbolic contraction/expansion geometry is preferred. This is a unique geometry because it allows to impose a constant, nominal extension rate at the center of the microchannel because its cross- sectional area varies inversely with axial position. The microchannel with the hyperbolic contraction is characterized for its depth ( ), the length of the contraction/expansion ( ), the upstream width ( , width at the contraction throat ( ), which provided a width, ( that varies with the direction of the flow ( and takes the form given by Eq. [6]: , [6] being . At a constant flow rate ( the average velocity at any -position in the contraction is given by Thus, the apparent extension rate is given by Eq. [7]: . [7] The apparent extensional viscosity for fully developed extensional flow in the hyperbolic contraction will depend on the imposed flow rate and the external electric field being given by Eq. [8]: [8] where is the Hencky strain experience by a fluid element and is the excess pressure drop. The value of is estimated using a 2D lubrication analysis for a power-law fluid: [9] According to a preferred embodiment, the MERs of the invention, further comprise a precision driven dispensing system able to force a liquid sample (ERF) flow through the microfluidic main microchannel at a given flow rate , pressure sensors to measure the pressure of the fluid sample at different locations of the microchannel, a voltage power supply so that an external electric field can be applied to the fluid-flow, and, if required, a microscope to visualize the microstructure developed in the ERF upon the application of an external electric field. Regarding the fabrication of the different MERs, several standard microfluidic fabrication techniques can be used. Fig. 3 shows some examples: Fig.3a shows polydymenthylsiloxane (PDMS) embedding the microchannels and a substrate, like a glass slide or the same, as a cover. The substrate is selected from the group comprising glass slide or any kind of hard plastic cover, such as polycarbonate (PC), Cyclo Olefin Polymer (COP), cyclic olefin copolymer (COC), Polysulphone (PSU), Polyetherimide (PEI) or polymethyl methacrylate (PMMA), Fig.3b shows two sides made of PDMS, and Fig.3c shows the microchannels embedded in a monolithic piece made of fused silica, PMMA, PET (polyethylene terephthalate), or another suitable substrate. A microfluidic-based rheometer-on-a-chip has several practical advantages, such as having no air–liquid interface, that might be of interest for use with biological fluids and fluids prone to evaporation, and additionally it could serve as an online rheological sensor in many industrial processes. Upon the fabrication of the microchip, the electrodes will be created by filling up the auxiliary channels with a metal alloy. This is achieved by using any metal alloy which has a melting point below the temperature for destruction of the microfluidic device that ranges typically between 50 ºC and 80 ºC. Several metal alloys are commercially available, with melting points starting from 47 ºC. Examples of said metal alloys are Bismuth-based eutectic alloy with different content of lead and cadmium that allow a range in their melting point between 47 and 58 ºC. The fabrication of the electrode can be achieved by forcing the metal alloy to flow into the auxiliary microchannels of the MER by means of a syringe or any other similar device, with all the set-up formed by the microfluidic device, tubing and syringe containing the metal alloy being in thermal equilibrium at a temperature above the alloy melting point and below the maximum temperature that may damage any properties of the microfluidic device. EXPERIMENTS/SIMULATIONS In order to understand the homogeneity of the electric field within a fluid sample, several numerical simulations using OpenFOAM^® were carried out. To guide the fabrication procedure, it was important to assert how much freedom exists in four geometrical parameters that define the MER. With the simulation of the electric field, the purpose was confronting the uniformity of the generated field, within the fluid control volume (the service channel, herein also designated by main elongated microchannel) while varying four geometric properties , , and . These parameters can be understood from Figure 4, wherein reference number (16) designates Ws, reference number (18) designates We and reference number (19) designates s. Instead of two different heights (20 and 21) for the auxiliary microchannels (2) and the main microchannel (1), it is assumed for the simulations that they have the same height (H). The electric field between two infinite charged infinite planes, with a difference in the imposed potential in each of them, is known to be uniform in the space between them. To apply this approximation to the region between the two metal channels, it would, in principle, be sufficient conditions that 1) is sufficiently larger than and 2) . The latter condition forces the requirement of a multi-step lithographic fabrication for two different heights, it was decided to investigate whether condition 2) was truly necessary or if it could be alleviated to promote a uni-step lithographic procedure for a uniform height in the service and auxiliary channels. To realize the corresponding numerical simulations, the “electrostaticFoam” solver for OpenFOAM^® was used, which takes as a starting point the formulation of the electrostatic problem [10] subject to adequate boundary conditions on the fields: · is the permittivity of the medium; · is the charge density of the several regions, estimated using a Drude condensed matter model for the several regions which was the initial condition for the metal plates, and zero for all the other domain; and · is the electric potential, which is defined as 0V in one of the metal plates and 2000V in the other for all times, and 0V in the rest of the domain (initial condition), with a zero gradient boundary condition at all external boundaries (initial condition). It is noted that the first equation can be recast in a form that is more familiar for the software’s core of finite volume method, , where , a scalar field, is the volume density of the quantity that is conserved, and , a vector field, is the oriented rate of displacement of that conserved quantity. In particular, we note that the equation of charge conservation can be recast, using the constitutive linear equation , into , which was the equation, coupled with Poisson equation (last equation in Eq. [10]), used to solve for the distribution of the electric field. To determine the uniformity of the electric field, a routine was devised to alleviate the necessity of running by hand the sweeping of a few thousand parametric sets. In that routine, using four "for" loops, each of those four parameters could vary between different values . Then, for each set of four parameters, three simulations were done: the first one used the exact four parameters, with a tilting angle (see Figure 5, reference number (22)), the second one used 95 % of each of the original parameters, and a tilting angle , finally, the third used 105 % of each of the original parameters, and a tilting angle . For each of those three simulations, the following sequence took place: 1) create the mesh for the prescribed geometry, 2) set the initial and the boundary conditions on the fields , and , 3)start the simulation, and 4) once the simulation was obtained, the following quantities were calculated by Eq. [11]-[13]:

[11] [12] [13] where represents the average electric field, is the standard deviation of the electric field and is the uniformity of the electric field. It has been decided that the value of would be a good measurement of the dispersion of the electric field in the region of interest. Thus, the lower the values of , the more homogenous is the electric field within the fluid sample of the MER. This particular sweep of parameters was composed of 8 values for each of the 4 parameters, in a total of total parameter sets. The distribution of values for each parameter is found in Table (1) below. It has been chosen to vary the parameters exponentially in order to have a denser distribution at smaller values. Figure 6 depicts the computational results. To assert the influence of each of the four parameters in the variation of , the quantities were also computed, given by Eq. [14], where the includes all the other parameters other than . [14] Since only the absolute values of the terms are used in Eq. [12], it can be concluded that, for two parameters, the one with more influence in the field homogeneity will have, on average, higher . Thus, it has been computed the average (Eq. [15]) and standard deviation (Eq. [16]) of the over all possible vectors , considering the variation of coordinates : [15] [16] The four values represent how much it is expected to see changes in , therefore in the homogeneity of the electric field, when each of their corresponding parameters is changed by 1 micrometer, so a larger value of represents a parameter with more impact in the homogeneity of the field in the MERs.

Table 1: Simulation sweep parameters, where the 8 values for all the parameters can be found by using the formula , with . The key observations made from the numerical simulations and the respective post-processing are as follows: 1. The global maximum of the standard deviation between different trials associated with the same set of parameters is of about 0.006, meaning that there is no measurable impact of the limitations of the fabrication procedures in the final homogeneity of the produced electric field, thus it should be possible to use standard photolithographic processes to build a functioning prototype. 2. The parameter with the highest impact on the homogeneity of the electric field is the height (21), also referred to as H, of the electrode, followed by the width (16), also referred to as Ws, of the main elongated microchannel. The parameter with the smallest impact is the separation (19), also referred to as s. The electrode's width (18) and separation (19) are more easily tuned to fit constrains regarding the specificities of the fabrication and assembly processes, without compromising the performance of the electrodes in generating a uniform electric field (see Fig.5). 3. The starting point for a good prototype is located at high values of height (21) - - and low width (16) - . In general terms, it has been observed that the parameters that resulted in the global minimum of are (232.25, 50.00, 250, 800) µm. This set of values provided a starting point to define the dimensions of the prototype (see Fig.5). Upon these simulations, a prototype of a preferred embodiment of the present invention has been successfully produced with success. It should be noted that while the invention is described herein making reference to preferred embodiments, a plurality of changes or modifications may be carried out by a person skilled in the art without departing from the scope of the invention defined in the appended claims.

Claims

CLAIMS 1. Microelectrorheometer comprising: an elongated main microchannel (1) comprising an inlet (5) and an outlet (6), characterized in that it further comprises two auxiliary microchannels (2) filled with a metal or a metal alloy, wherein said auxiliary microchannels (2) are parallel to each other; and wherein each of the two auxiliary microchannels (2) is arranged axially along each side of the main microchannel (1); or one of the two auxiliary microchannels (2) is arranged transversally to the main microchannel (1) and upstream to the inlet (5) thereof, and the other of the two auxiliary microchannels (2) is arranged transversally to the main microchannel (1) and downstream to the outlet (6) thereof, such that in operation the said auxiliary channels (2) operate as electrodes for generating an electrical field to be applied onto an ERF sample.

2. Microelectrorheometer according to claim 1, wherein the said main microfluidic channel (1) is straight and planar-shaped.

3. Microelectrorheometer according to claim 1 or 2, wherein the said main microfluidic channel (1) comprises a contraction zone (23).

4. Microelectrorheometer according to any one of the preceding claims, wherein the said main microfluidic channel (1) further comprises pressure sensors (7, 8).

5. Microelectrorheometer according to any one of the preceding claims, further comprising a dispensing device.

6. Microelectrorheometer according to the preceding claim, wherein the dispensing device is a syringe.

7. Microelectrorheometer according to any one of the preceding claims, further comprising a power supply.

8. Microelectrorheometer according to any one of the preceding claims, further comprising a microscope.

9. Microelectrorheometer according to any one of claims 1 to 4, wherein the main microchannel (1) and the auxiliary microchannels (2) are embedded in a PDMS chip (11) and closed with a substrate (12).

10. Microelectrorheometer according to the preceding claim, wherein the substrate (12) is a glass slide.

11. Microelectrorheometer according to any one of claims 1 to 4, wherein the main microchannel (1) and the auxiliary microchannels (2) are embedded in a PDMS chip (11) and closed with another PDMS chip (13).

12. Microelectrorheometer according to any one of claims 1 to 4, wherein the main microchannel (1) and the auxiliary microchannels (2) are embedded in a single chip (14).

13. Microelectrorheometer according to the preceding claim, wherein the single chip (14) is made of fused silica, PMMA, COC, COP, PC, PSU or PI.