Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N11/00—Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties
  • G01N11/02—Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties by measuring flow of the material
  • G01N11/04—Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties by measuring flow of the material through a restricted passage, e.g. tube, aperture
  • G01N11/08—Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties by measuring flow of the material through a restricted passage, e.g. tube, aperture by measuring pressure required to produce a known flow
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N13/00—Investigating surface or boundary effects, e.g. wetting power; Investigating diffusion effects; Analysing materials by determining surface, boundary, or diffusion effects
  • G01N13/02—Investigating surface tension of liquids

Definitions

• the present invention relates to a device and a method to characterize a capillary system in terms of wettability and geometry by determining the liquid pressure, from which the capillary and/or viscous pressure can be deduced.
• capillary system is generally defined as a system, which features, when in contact with a liquid, a meniscus or curved liquid/air interface. The curvature of this interface determines the pressure inside the liquid.
• Typical examples comprise capillaries, thin tubings, slits, microfmidic devices, powders and porous systems.
• the capillary pressure is related to the presence of a meniscus (i.e. a liquid/gas or liquid/liquid interface) inside a capillary system. It refers to the pressure drop across this curved liquid interface.
• a meniscus i.e. a liquid/gas or liquid/liquid interface
• this curvature is not only closely related to the geometry of the capillary system, but also to the wettability of the surface at the border where the liquid and the solid meet (i.e. at the 3- phase contact line).
• the viscous pressure refers to the pressure drop inside a flowing liquid due to viscous dissipation. For a capillary system completely or partially filled with a moving liquid, it is closely related to the geometry of the capillary system.
• the measurement of the liquid pressure can be performed under static as well as under dynamic conditions. Under dynamic conditions, the liquid slowly flows in a controlled matter through the capillary system and displaces a gas or another non-miscible liquid. Depending on the measurement conditions, the capillary and viscous pressure can be obtained from the liquid pressure.
• the spatial resolved wetting properties of the inner surfaces and/or the geometrical dimensions of the capillary system can be determined with high resolution.
• the geometrical dimensions of the capillary system can be investigated.
• the wettability of a solid is characterized by the contact angle which the liquid makes with the solid (measured through the liquid).
• Different angles can be experimentally obtained: i) static angles measured after advancing or receding the liquid front and ii) dynamic angles measured during the displacement of the liquid front.
• the advancing and the receding static angles usually differ.
• a variety of possible causes may explain this contact angle hysteresis, a.o. chemical or surface composition heterogeneity.
• the contact angle is usually measured by optical imaging of a sessile drop on the surface.
• the static contact angles may be obtained by measuring the equilibrium height and/or dynamics of the capillary rise (or depression). Also optical imaging of the meniscus inside capillaries can be used to determine the meniscus curvature, from which the contact angle can be deduced.
• a major disadvantage of all known techniques to determine contact angles and surface wettability is their lack of spatial resolution.
• the contact angle only characterizes the surface wettability at the border, where the liquid front and the solid meet.
• Static methods like the sessile drop and the capillary rise method probe therefore only very small portions of the surface area, since they do not allow systematic scanning of the surface area due to experimental or physical reasons.
• This is a serious drawback, since the quality and the applicability of many technical surfaces are often primarily determined by the degree of homogeneity of the surface and the lack of local defects and/or contamination. Consequently, non-destructive techniques to characterize the spatial resolved wettability of a surface and its heterogeneity are desired.
• surface heterogeneity is defined when the local equilibrium contact angle ⁇ is not everywhere the same.
• Dynamic methods with moving liquid fronts which scan across the surface can be used to obtain information on the spatial resolved wettability.
• Many dynamic wetting methods have been published, but they all (having different objectives) do not provide this spatial information. Examples of such methods are for example given by
• Hoffmann determines the shape of the meniscus by optical imaging to obtain the dynamic contact angle when the liquid advances slowly through a capillary and displaces a gas.
• this method could be extended to obtain spatial resolved information as well.
• Such an extended method would however suffer from many drawbacks, a.o. the method would only be suitable for transparent capillaries and it would require complex data analysis.
• the most important drawback is based on the imaging principle, i.e. by using 2-D pictures of the 3-D meniscus. If the meniscus shape deviates from a spherical surface, this conversion leads to a loss of information.
• capillary pressures and/or changes thereof can be very low ( ⁇ 100 Pa). Small surface defects or contamination may even cause much smaller pressure changes ( ⁇ 5 Pa). Consequently, by measuring these very small pressure changes as a function of the position of the meniscus inside the capillary system, a non-destructive technique to characterize the spatial resolved wettability of the capillary surface and its heterogeneity can be developed.
• Kumar et al. investigated the capillary pressure related to a moving meniscus inside a cylindrical capillary. However, they only developed a technique to measure the first and second derivative of the pressure with respect to the velocity of the meniscus, not to measure the capillary pressure itself (neither under the static or dynamic conditions). Moreover, their technique does not provide any spatial re- solution. Despite previous attempts of Kumar et al. and others, a method for the direct measurement of the capillary pressure in a liquid has now been found.
• the problem of the invention is to provide a device and a method for the characterization of a capillary system in terms of wettability and geometry by determining the liquid pressure and changes thereof with high resolution, from which the capillary and/or viscous pressure can be deduced.
• a further problem is to provide a special resolved characterization of small tubes or capillaries.
• the solution of this problem according to the invention is a pressure measuring device for characterizing the capillary pressure and/or wettability of a capillary system in terms of wettability at a resolution of at least 100 Pa, preferably at least 10 Pa, comprising
• a prefe ⁇ ed measuring liquid is selected from water, alcohols, hydrocarbon, halogenated hydrocarbons or silicon oil.
• the measuring liquid is free from surface active compounds.
• the liquid pump is a hydrostatic pump.
• a hydrostatic pump allows a precise regulation of the fluid flow in either direction, e.g. a perfect constant rate of displacement of the meniscus inside the capillary system.
• the hydrostatic pump preferably comprises of a hydrostatic column in combination with a flow valve and a flow regulator.
• the flow regulator provides a viscous resistance, which determines the fluid flow for given hydrostatic column of height h (relative to the position of the capillary system).
• the fluid flow rate D can be precisely controlled, if the pressure drop ⁇ P (fr) across the flow regulator is much larger than the sum of the absolute capillary pressure
• the viscous resistance across the connecting tubing is much smaller than that across the capillary system. Therefore, the length and inner diameter of the connecting tubing should be chosen as small as possible but such that preferably 7 y j . y i .y
• a differential pressure sensor is usually used for the measurements, although any other type of pressure sensors may be used as well. Pressures sensors with very high sensitivity are required. Such sensors for liquids are commercially not available, only for gases. Consequently, in order to enable an accurate measurement, a gas/liquid- interface has to be introduced into the system. This interface is positioned inside the sensor cell and determines the design of the sensor cell.
• the differential sensor is used to measure the pressure difference ⁇ R between the air pressure ⁇ Rs* inside the sensor cell and the atmospheric pressure ⁇ P atm .
• Preferred is a pressure measuring device, characterised in that the pressure sensor is connected via a air tight pressure sensor cell to the tubing between flow regulator and capillary system.
• a further preferred embodiment of the pressure measuring device is characterized in that pressure sensor measures the difference between the sensor cell pressure and the atmospheric pressure.
• the sensor cell has to be designed as such that
• This uncontrolled liquid flow causes positioning e ⁇ ors of the air/liquid interface inside the capillary system.
• Criterion 1 can be fulfilled by optimizing the surface properties of the inner walls of the sensor cell and by carefully choosing the radius of the sensor cell.
• both static contact angle and sensor cell dimensions can be adjusted.
• the static contact angle of the measuring liquid with the sensor cell inner wall preferably approaches 90°.
• the radius of the sensor cell should be preferably
• K -xj ⁇ /p -g
• y and p are the surface tension and the density of the measuring liquid, respectively, and g the gravity constant (or more precisely, the standard acceleration of free fall).
• a cdl > K more preferred a cell > 3 • and even more preferred a cell > 5 • K .
• the maximum radius a cell is limited due to criterion 2.
• Criterion 2 can be fulfilled by choosing conditions that minimize displacement of the meniscus inside the sensor cell due to pressure and temperature changes. This can be achieved by i) by working under thermostated conditions and by ii) reducing the air volume V atr inside the sensor cell.
• Thermostating the air inside the sensor cell has shown to be essential for correct and precise measurement.
• the temperature change AT during measurement should be as small as possible, preferably AT ⁇ 0,5K , more preferred AT ⁇ 0,2K , and even more preferred AT ⁇ 0,05K .
• the volume V air depends on the size of the sensor cell and the position of the meniscus inside this cell. It has to be adjusted depending on the dimensions of the capillary system and the desired spatial resolution Ax of the spatial resolved wetting properties, as defined above. Therefore, we define a critical air volume V° lr
• V air ⁇ 5 • V ⁇ ir , more preferred V air ⁇ 1 • V_ , and even more preferred rC
• the pressure sensor cell with attached pressure sensor preferably should be air tight and positioned between the flow regulator and the capillary system according to Figure 1.
• pressure sensor resolution should be preferably 1 Pa or less.
• the flow can be stopped by closing a flow valve, which can preferably be introduced e.g. between hydrostatic pump and flow regulator according to Figure 1.
• Additional valves, tubings, connectors, height detectors or other functional units may be used to regulate the fluid flow and to calibrate the equipment.
• Another object of the invention is a method for characterizing a capillary system concerning capillary pressure and/or wettability comprising the steps providing a pressure measuring device described above by,
• a second phase e.g. air
• the device In order to perform a measurement, the device is completely or partially filled with the measuring liquid, which can be pumped into or out of the capillary system, displacing a gas or another non-miscible liquid.
• the pressure difference ⁇ R can be measured both under static (no fluid flow) or under dynamic (finite fluid flow) conditions.
• the pressure R 2 inside the second phase should be known and preferably constant. If the second phase is air of atmospheric pressure, R 2 equals P atm , which can be considered constant. If the second phase is a liquid, the pressure inside this liquid should be kept constant, e.g. by attaching a liquid reservoir at the back end of the capillary system. Preferably, this reservoir is open, i.e. in contact with the atmosphere.
• the (effective) radius a r of this reservoir should be preferably a r > 3 -K , more preferred a r > 5 - ⁇ and even more preferred a r > 10 - J .
• the known height h r of this reservoir should be preferably sufficiently large, so that i) it is much larger than the effective radius of the capillary system and ii) it does not significantly change during the measurement
• this pressure difference ⁇ R can be written as a sum of capillary pressure AP L and a hydrostatic contribution ⁇ R / ,.
• the hydrostatic pressure contribution ⁇ R / can be quantified by measuring the hydrostatic offset h ⁇ et , defined as the height difference between the interface inside the sensor cell and the one inside the capillary system by any appropriate means.
• ⁇ R ⁇ p • g • h ⁇ et , where h ⁇ et is taken positive if the height of the meniscus inside the capillary system is higher than that of the meniscus inside the sensor cell.
• Any appropriate height measurement device with a height resolution « 0,1 mm can be used.
• the hydrostatic contribution ⁇ R / can also be quantified through an internal calibration method. Internal calibration methods may for example be based on incorporating a capillary system with well-defined geometrical, viscous resistance and/or wetting properties into the hydraulic system of the measuring device at defined height. Also the phenomenon of maximum bubble pressure can be applied.
• the hydrostatic contribution can then be obtained directly from the sensor output ⁇ R adjusted as such, that the viscous pressure drop ⁇ R V across the hydrodynamic resistance is much larger than that of the capillary pressure ⁇ R £ .
• the capillary pressure ⁇ R £ and changes thereof can not only be measured under static, but also under dynamic conditions when a liquid meniscus slowly moves (i.e. advances or recedes) through the capillary system and displaces the second phase, i.e. a gas or another non-miscible liquid.
• the sensor output contains in principle also a pressure contribution ⁇ R V due to viscous stresses inside the capillary system, which are not associated to the presence of the meniscus inside the capillary system. This contribution can be made negligible by reducing the fluid flow D sufficiently. Therefore, we define a critical volume flow rate D c
• this critical flow rate D c determines the desired flow rate D during measurement.
• the viscous pressure contribution ⁇ R V can be experimentally determined by performing a dynamic measurement (flow rate D known) with a completely filled capillary system attached at the back end to an open liquid reservoir with a (effective) radius a r and filled to a defined liquid level.
• more prefe ⁇ ed consider > 5 • ⁇ and even more prefe ⁇ ed a r > 10 • K is effectively eliminated.
• the inventive method for characterizing a capillary system in terms of wettability and geometry is related to the measurement of liquid pressures and changes thereof.
• the liquid pressure is related to the surface properties and/or to the geometry of the capillary system.
• the method for characterization of the surface wettability has a spatial resolution and is therefore suitable to quantify the homogeneity of surfaces inside capillary systems and to characterize the inner geometry of these systems.
• the invention is also suitable for detection of defects and contamination of surfaces inside capillary systems. These defects and contamination can be localized.
• the minimum size of detectable surface spots depends on i) the geometry of the capillary system (i.e. on its effective radius a cs ), ii) on local contact angles of the local spot and the su ⁇ ounding capillary wall (i.e. on ⁇ s and ⁇ cs , respectively) and iii) on the resolution of the pressure sensor AP r .
• the minimum detectable area_4 m , consult of such spots can be roughly estimated by the equation
• the very high sensitivity of the pressure measurement inside the liquid phase under static and dynamic conditions can also be used for: characterizing geometrical properties of capillary systems characterizing the surface properties inside microfluidic devices - monitoring fluid flow inside microfluidic devices characterizing the surface properties of flat surfaces monitoring fluid flow through membranes, filters and porous media determination of the specific surface area of powders determination of contact angles on powders and inside porous media (and consequently surface free energies) investigating the dynamics of wetting and spreading of simple and complex
• liquid pressures can be very precisely measured. Moreover, very small pressures and changes thereof with a resolution of ⁇ 10 Pa, preferably ⁇ 3 Pa, even more prefe ⁇ ed of ⁇ 2 Pa can be measured. This enables the measurement of capillary pressures and therefore the determination of the spatial resolved wetting properties of the inner surfaces and/or the geometrical dimensions of capillary systems with high sensitivity. With the method and device according to the invention, the axial position of liquid meniscus inside the capillary system can be controlled with a high spatial resolution of «1 OO ⁇ m.
• non-destructive capillaries may be opaque and of any form and length - only one data point/measurement (instead of complex imaging analysis) wettability scan across the capillary surface high sensitivity for local defects along meniscus perimeter high spatial resolution of wettability in axial direction detection of very small surface defects and contamination - precise adjustment of volume flow rate, independent of the capillary system properties handling with small amounts of measuring liquids possible only temperature control of small gas volume inside sensor cell is necessary commercially available pressure sensors can be used
• Figure 1 shows a schematic drawing of the measuring device.
• FIG 3 shows the investigation of a hydrophobic Teflon tubing (radius approximately 1,3 mm). Sensor output as a function of meniscus position inside the Teflon tubing.
• Experimental procedure measurement of untreated tubing (run 1); drying, rinsing with chloroform, drying lO min with N2; measurement (run 2); drying 10 min with N2; measurement (run 3).
• Sensor sensitivity 50 Pa/V. The curves have been shifted for optical purposes.
• Figure 5 shows the Investigation of a hydrophobic Teflon tubing with a dilated region (original radius approximately 1,3 mm). Sensor output as a function of meniscus position inside the Teflon tubing.
• Figure 6 shows the Characterization of capillary driven flow through a valve.
• Figure 7 shows the Characterization of blood flow through a separation pad.
• FIG. 1 A schematic drawing of the measuring device connected to the tubing is given in Figure 1. To avoid measurements artifacts, major care was taken to position the tubing perfectly horizontally (e.g. no corrugations) and to prevent electrostatic charging of the Teflon tubing and the input of external vibrations (e.g. due to closing doors).
• hydrostatic offset h 0 ff set (in mm H O). The hydrostatic offset is used to adjust the sensed pressure within the measuring range of sensor.
• the voltage/pressure conversion can be done by using the characteristic sensor properties. Since under these conditions the sensor output is dominated by the Laplace contribution, the conversion gives directly the Laplace pressure (taking the hydrostatic off set into account). This statement is co ⁇ oborated by the fact that under dynamic conditions at flow rates corresponding from 10 till 25 mm H 2 O pumping pressure (i.e. co ⁇ esponding to an average contact line velocity v c from 134 till
• this example shows that the measuring device can be used to determine advancing and receding static and dynamic contact angles inside capillary systems with homogeneous surfaces.
• This example shows that method described above can be used to obtain spatial resolved information about the wetting properties and surface contamination of a capillary system.
• example 1 is being repeated with a different tubing but of the same type as in example 1.
• the resulting spatial resolved pressure profile is depicted in Figure 3. It shows many small peaks with a typical amplitude approximately 5-10Pa. Video analysis of the meniscus movement through the tubing shows that these peaks are related to a pinning behavior of the 3-phase contact line.
• This example shows that the method sensitivity for detection and localization of surface defects can be enhanced by a suitable pretreatment of the capillary surface.
• Figure 4 shows that the rinsing step with chloroform makes surface defects visible through the occu ⁇ ence of peaks at well-defined position. These peaks are not present in the voltage/pressure profile of the original tubing in run 1. In the third run, these peaks can be reproduced with a decrease of intensity.
• this example shows that the measuring device can also be used to characterize the geometry of a capillary system. Therefore, the measurement described in example 2 is being repeated with a different tubing but of the same type as in example 1. Through a blow molding procedure, the radius of the tubing has been locally increased by approximately 20%. Before measurement, the tubing is cleaned in order to remove any possible surface contamination.
• the measuring liquid is preferably non- wetting and non-miscible with the wetting liquid.
• the measuring device can also be used to characterize and quantify flow behavior in capillary devices, in which the liquid flow should be driven by capillary forces.
• the resulting pressure profile in Figure 6 shows a pressure increase when the liquid is forced to enter the valve. Upon exit the valve, the pressure increases first, subsequently it decreases. This means that in absence of any external applied pressure, this valve will not fill spontaneously when it comes into in contact with water. In fact, here the capillary forces resist the filling of the valve.
• the external applied pressure which is necessary to overcome the capillary forces and to fill this valve, can be quantified. In this particular case approximately 150 Pa.
• the measuring device can also be used to characterize the liquid flow through porous systems, e.g. filters.
• porous systems e.g. filters.
• the advantages of this method lies in the fact that one can work with very small amounts of liquid/sample and that only very small pressures have to be applied to drive the liquid flow. The latter is special advantageous, since one can also work with very fragile porous systems without distorting their structure under practice relevant conditions.
• the resulting pressure profile in Figure 7 shows a slow pressure increase when the blood sample flows through the separation pad. Since the memscus penetrates nearly instantaneously through the filter after starting the fluid flow, the slow pressure increase is dominated by the viscous flow contribution. Capillary effects can be neglected in this particular case. Hence, the pressure increase indicates clogging of the pad with blood cells, since with water as sample this effect is not being observed. This clogging phenomenon was co ⁇ oborated by light microscopy.
• the spatial resolved wetting behavior of flat surfaces can be investigated with the measuring device if these surface can be introduced into a capillary system, which can be investigated according to the procedures described in the previous examples. Therefore, a slit capillary of width a, height b and length / can be used. Hence, the slit capillary contains two flat walls (1 and 2) of width a and length /.
• the construction of the slit capillary should be now designed as such, that these flat walls can be represented by the flat surface(s) to be investigated.
• the investigation can be carried out with one or two (preferably identical) surfaces. If only one flat surface has to be investigated, this surface can be split in two parts and used as wall 1 and wall 2.
• the surface is only used for one wall (say 1), the other wall (2) has to be represented by a flat homogeneous surface with known wetting properties. This holds also for the properties of the two other capillary walls (3 and 4) of width b and length /.
• An appropriate connection between slit capillary and measuring device to enable the measurement similar to example 1 has to be made.
• Equation 1 is used to interpret the pressure profile in terms of wetting behavior of the oxidized silicon surface.
• Diggins et al. (Colloids and Surfaces, 44, 1990, 299-313) describe an experimental apparatus for the determination of powder wettability. Using White's thermodynamic approach (Journal of Colloid and Interface Science, 90, 1982, 536), they obtain the macroscopic contact angle and the specific surface area of the powder.
• the principle of Diggins technique is based on the measurement of the equilibrium capillary pressure in a carefully packed bed of particles in an air tight column with a valve at the top. The liquid under study is allowed to spontaneously enter the powder bed from the bottom of the column. After some time, the top valve is closed. The liquid still continues to rise until the overpressure in the top part of the column exactly compensates the capillary pressure (taking hydrostatic contributions into account).
• a pressure transducer detects the overpressure in the top part of the column, from which the capillary pressure can be deduced.
• a column (radius 1cm) is filled with the dry quartz powder, whilst gently tapping to ensure uniformity of packing.
• the bottom part of the column which tapers to a na ⁇ ow capillary, is connected to the measurement device as described in example 1.
• One experiment is carried out with water as measuring liquid, another with cyclohexane. Different packed beds are used for the different liquids. The pressure is measured under static conditions (no fluid flow), according to the principles of the procedure described in example 1.
• the measurement are repeated at a different position of the macroscopic meniscus inside the particle bed after opening the fluid valve for a certain time and closing it again.
• the capillary pressure in the packed bed is relative large, O(0.1 bar). Therefore as differential pressure sensor, the 144SB001D-PCB of Sensortechnics is used (operating pressure 0-1 bar).
• Interpretation of the data to obtain the static (water) contact angle on and the specific surface area of the particles is carried out according to the theory of White.

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