Forced imbibition-a tool for separate determination of Laplace pressure and drag force in capillary filling experiments

When a very thin capillary is inserted into a liquid, the liquid is sucked into it: this imbibition process is controlled by a balance of capillary and drag forces which are hard to quantify experimentally, particularly considering flow on the nanoscale. By computer experiments using a generic coarse-grained model, it is shown that an analysis of imbibition forced by a controllable external pressure independently quantifies the Laplace pressure and Darcy's permeability as relevant physical parameters governing the imbibition process. From the latter one may then compute the effective pore radius, effective viscosity, dynamic contact angle and slip length of the fluid flowing into the pore. In determining all these parameters independently, the consistency of our analysis of such forced imbibition processes is demonstrated.     

Effect of capillary element aspect ratio on the dynamic imbibition within porous networks

The Washburn equation is widely accepted for describing capillary imbibition. It has, however, been shown to be insufficient at very short times due partly to the lack of inertial terms. Bosanquet (C. H. Bosanquet, Philos. Mag. ser. 645, 525 (1923)) applied an inertial term via momentum, Szekely et al. (J. Szekely, A. W. Neumann, and Y. K. Chang, J. Colloid Interface Sci.35, 273 (1971)) examined single capillaries based on a revised boundary-condition model, and Sorbie et al. (K. S. Sorbie, Y. Z. Wu, and S. R. McDougall, J. Colloid Interface Sci. 289 (1995)) reviewed and applied Szekely's work to examine the effects of comparative imbibition into a parallel pore doublet. The study here extends the work of Sorbie et al. by applying the equation of Bosanquet to a three-dimensional network model, Pore-Cor. All authors agree that, with the inclusion of inertial terms at short times, smaller radius capillaries will initially fill faster than larger radius capillaries which disagrees with the Washburn equation. It is shown that the aspect ratio of a capillary, defined as its length divided by its radius, plays an important role, in combination with the capillary radii themselves, in determining the filling rate of individual elements. The distribution of this ratio associated with the capillary throat elements within a network structure is investigated. The result is that a preferred pathway of permeation is observed under supersource imbibition conditions in the case where a broad size distribution of capillary elements occurs within a network structure.     

Modeling of spontaneous penetration of viscoelastic fluids and biofluids into capillaries

A theoretical model was developed to describe the dynamics of spontaneous penetration of viscoelastic fluids into capillaries. The model agrees quantitatively with recent experiments on absorption of droplets of polymer solutions by glass capillaries [A.V. Bazilevsky, K.G. Kornev, A.N. Rozhkov, A.V. Neimark, J. Colloid Interface Sci. (2003)]. The rate of penetration progressively reduces with the increase in fluid elasticity. Analysis revealed two main contributions to the viscoelastic drag of the liquid column: (i) viscous resistance, which is independent of fluid elasticity, and (ii) viscoelastic resistance, known as the Weissenberg effect. We analytically derived an augmented Bosanquet equation for the maximal velocity of penetration by balancing capillary, inertia, and viscoelastic forces. For slow creep of a liquid column, the Lucas-Washburn equation was modified by accounting for the Weissenberg effect. A series of numerical calculations were performed to demonstrate characteristic features of absorption of fluids at different conditions. This article also discusses some problems specific to absorption of biofluids. We show that deformations of cell membranes in the external converging flow may cause their rupture at the pore entrance.     

The possibility of different time scales in the dynamics of pore imbibition

To model the imbibition of liquids into porous solids, use is often made of the Lucas-Washburn equation, which relates the distance of penetration of a liquid at a given time to the pore radius, the viscosity and surface tension of the liquid, and the effective contact angle between the liquid and the solid. In this paper, we extend previous large-scale molecular dynamics simulations to show how this tool can be used to study the details of liquid imbibition, including the impact of the contact angle on the dynamics of penetration and the evolution of the internal flow field. In particular, we show that the asymptotic behavior of the contact angle versus time for a completely wetting liquid is given by approximately t(-1/4).     

Shape Factor Correlations of Hydraulic Conductance in Noncircular Capillaries

In Part I of this paper, we introduced the Mason-Morrow shape factor and the corner half-angles to capture the part of geometry of angular capillaries essential in pore network calculations of single- and two-phase flow in drainage and imbibition. We then used this shape factor to obtain simple expressions for the hydraulic conductance in single-phase flow through triangular, rectangular, and oval capillaries. In Part II, we study two-phase fluid flow along angular capillaries. The nonwetting fluid occupies the central part of the capillary, whereas the wetting liquid fills the corners. First, we verify the numerical solution obtained by Ransohoff-Radke for concave corner menisci by using a high-resolution finite element method with zero and infinite surface shear viscosity. We present new numerical results for corner flow domains bounded by convex menisci, i.e., for pinned contact lines and forced imbibition. We also present numerical solutions for two-phase flow with momentum transfer across the interface. We introduce a dimensionless hydraulic conductance of wetting fluid in the corners and correlate it with the corner filament shape factor, corner half-angle, and contact angle. By appropriate scaling, we obtain an accurate universal curve for flow conductance in the corners of an arbitrary angular capillary and for arbitrary contact angles. We give error estimates of the Ransohoff-Radke flow resistance factors, of the Zhou et al. analytical expressions for the resistance factors, and of our universal curves for the hydraulic conductance with no-slip and perfect-slip boundary conditions at the interface. Our expressions for the hydraulic conductance in corner flow of wetting liquid not only are valid for both concave and convex fluid interfaces but also are more accurate than any other published correlation. Copyright 2001 Academic Press.     

Experimental study of the immiscible displacement of shear-thinning fluids in pore networks

The pore scale mechanisms and network scale transient pattern of the immiscible displacement of a shear-thinning nonwetting oil phase (NWP) by a Newtonian wetting aqueous phase (WP) are investigated. Visualization imbibition experiments are performed on transparent glass-etched pore networks at a constant unfavorable viscosity ratio and varying values of the capillary number (Ca), and equilibrium contact angle (theta(e)). Dispersions of ozokerite in paraffin oil are used as the shear-thinning NWP, and aqueous solutions of PEG colored with methylene blue are used as the Newtonian WP. At high Ca values, the tip splitting and lateral spreading of WP viscous fingers are suppressed; at intermediate Ca values, the primary viscous fingers expand laterally with the growth of smaller capillary fingers; at low Ca values, network spanning clusters of capillary fingers separated by hydraulically conductive noninvaded zones of NWP arise. The spatial distribution of the mobility of shear-thinning NWP over the pore network is very broad. Pore network regions of low NWP mobility are invaded through a precursor advancement/swelling mechanism even at relatively high Ca and theta(e) values; this mechanism leads to irregular interfacial configurations and retention of a substantial amount of NWP along pore walls; it becomes the dominant mechanism in displacements performed at low Ca and theta(e) values. The residual NWP saturation increases and the end WP relative permeability decreases as Ca increases and both become more sensitive to this parameter as the shear-thinning behavior strengthens. The shear-thinning NWP is primarily entrapped in individual pores of the network rather than in clusters of pores bypassed by the WP. At relatively high flow rates, the amplitude of the variations of pressure drop, caused by fluid redistribution in the pore network, increase with shear-thinning strengthening, whereas at low flow rates, the motion of stable and unstable menisci in pores is reflected in strong pressure drop fluctuations.     

Prediction of imbibition in unconsolidated granular materials

A new way of modeling imbibition is proposed in this paper. It combines two elements. One is a physically consistent, dynamic criterion for the imbibition of an individual pore originally suggested by Melrose (SPEJ (November 1965) 259-271). The other is the use of a simple but physically representative model of porous media: a dense random packing of spheres that is geometrically predetermined. This approach allows truly a priori predictions of imbibition curves (saturation vs capillary pressure) for different values of contact angle, different initial conditions (e.g., different drainage endpoints), and different macroscopic sample geometries (the ratio of external to internal pores). It also provides a mechanistic basis for understanding the influence of pore-scale phenomena such as "snap-off" of nonwetting phase in the pore throats due to the coalescence of pendular rings. The simulations show that the capillary pressure curve for this unconsolidated packing is very sensitive to the wettability parameters (such as contact angle), whereas the influence of different initial conditions and snap-off is almost negligible. Predicted capillary pressure curves are compared to experimental data presented in the literature, and are consistent with them.     

Forced impregnation of a capillary tube with drop impact

We experimentally investigate how the impregnation of porous media can be forced using the initial kinetic energy of an impacting drop. We focus on the scale of a single pore – either hydrophilic or hydrophobic – and thus study the impact of a single drop falling on vertical cylindrical capillary tubes. This experimental configuration therefore differs from the impregnation of a porous media because of the finite volume of the drop and its initial kinetic energy. We observe different limit regimes: at low impact velocity, we recover the classical results for impregnation. The liquid does not impregnate the hydrophobic pore while it is totally sucked into the hydrophilic one. At high impact velocities, the drop is broken in two parts: one part spreads at the top of the surface while an isolated slug is trapped within the pore. We determine the critical speeds for these regimes and obtain a full phase-diagram for our observations. We also stress the characteristics of impregnating slugs namely their volume and their motion within the pores.     

Short timescale inkjet ink component diffusion: an active part of the absorption mechanism into inkjet coatings

The structures of inkjet coatings commonly contain a high concentration of fine diameter pores together with a large pore volume capacity. To clarify the interactive role of the porous structure and the coincidentally occurring swelling of binder during inkjet ink vehicle imbibition, coating structures were studied in respect to their absorption behaviour for polar and non-polar liquid. The absorption measurement was performed using compressed pigment tablets, based on a range of pigment types and surface charge polarity, containing either polyvinyl alcohol (PVOH) or styrene acrylic latex (SA) as the binder, by recording the liquid uptake with a microbalance. The results indicate that, at the beginning of liquid uptake, at times less than 2 s, the small pores play the dominant role with respect to the inkjet ink vehicle imbibition. Simultaneously, water molecules diffuse into and within the hydrophilic PVOH binder causing binder swelling, which diminishes the number of active small pores and reduces the diameter of remaining pores, thus slowing the capillary flow as a function of time. The SA latex does not absorb the vehicle, and therefore the dominating phenomenon is then capillary absorption. However, the diffusion coefficient of the water vapour across separately prepared PVOH and SA latex films seems to be quite similar. In the PVOH, the polar liquid diffuses into the polymer network, whereas in the SA latex the hydrophobic nature prevents the diffusion into the polymer matrix and there exists surface diffusion. At longer timescale, permeation flow into the porous coating dominates as the resistive term controlling the capillary driven liquid imbibition rate.     

Capillary imbibition of surfactant solutions in porous media and thin capillaries: partial wetting case

The capillary imbibition of aqueous surfactant solutions into dry porous substrates is investigated from both theoretical and experimental points of view in the case of partial wetting. Cylindrical capillaries are used as a model of porous media to study the problem. It is shown that if the mean pore size is below a critical value, then the permeability of the porous medium is not influenced by the presence of surfactants whatever the value of the concentration: the imbibition front moves exactly in the same way as in the case of the imbibition of pure water. The critical radius is determined by the adsorption of the surfactant molecules onto the inner surface of the pores. If the mean pore size is larger than the critical value, then the permeability increases with increasing surfactant concentration. These theoretical conclusions are in agreement with the experimental observations.     

Some mechanisms of immiscible fluid displacement in small networks

We report experimental observations on immiscible displacement in two small networks using three different pairs of fluids, air-oil, air-water, and oil-water, to vary the wettability. The experiments were run for a wide range of capillary number, from 10⁻⁷ to 10⁻³. Various mechanisms are observed. These are film spreading and drainage, Haines' jump, free slip and stick-slip meniscus motion, contact angle hysteresis, snap-off, coalescence, and blocking of film and bubble. For the air-oil case, oil is perfectly wetting in the network. In imbibition, the displacement occurs first via thin film spreading, followed by snap-off of menisci, and then by piston-like displacement at low flow rates. As the flow rate increases, piston-like displacement dominates because film spreading is comparatively slow. Snap-off of menisci in the throats is a necessary condition for air trapping. In drainage, meniscus snap-off and coalescence are observed in one network. For both imbibition and drainage, during each snap-off or piston-like displacement event, all menisci move freely along the channels to adjust their curvatures, due to the lubrication of the wetting film. For the other two fluid pairs at low flow rates, this curvature readjustment through free slipping of meniscus is not observed, presumably due to the absence of wetting film during the displacement. At high flow rate, oscillation of menisci due to volumetric competition is observed. Neither wetting film spreading nor throat snap-off is observed. Stick and slip motion of meniscus is observed, probably due to the roughness and/or heterogeneous wettability of the solid surface. For the oil-water system the wettability seems to be time dependent. Coalescence between two menisci can occur in the throat, in the pore, or at the pore-throat boundary during displacement. Trapping of the displaced phase is due to its being bypassed or snapped off in the throat.     

Crystallization mechanisms in convective particle assembly

Colloidal particles are continuously assembled into crystalline particle coatings using convective fluid flows. Assembly takes place inside a meniscus on a wetting reservoir. The shape of the meniscus defines the profile of the convective flow and the motion of the particles. We use optical interference microscopy, particle image velocimetry, and particle tracking to analyze the particles' trajectory from the liquid reservoir to the film growth front and inside the deposited film as a function of temperature. Our results indicate a transition from assembly at a static film growth front at high deposition temperatures to assembly in a precursor film with high particle mobility at low deposition temperatures. A simple model that compares the convective drag on the particles to the thermal agitation explains this behavior. Convective assembly mechanisms exhibit a pronounced temperature dependency and require a temperature that provides sufficient evaporation. Capillary mechanisms are nearly temperature independent and govern assembly at lower temperatures. The model fits the experimental data with temperature and particle size as variable parameters and allows prediction of the transition temperatures. While the two mechanisms are markedly different, dried particle films from both assembly regimes exhibit hexagonal particle packings. We show that films assembled by convective mechanisms exhibit greater regularity than those assembled by capillary mechanisms.     

Dissolutive Capillary Penetration with Expanding Pores and Transient Contact Angles

The penetration kinetics of a cylindrical capillary and a capillary porous body with a temporally expanding capillary radius due to reactive dissolution ahead of the liquid front is modeled under conditions where the equilibrium contact angle is not attained during at least part of the penetration process. These effects cause deviations from the predictions of the Washburn equation, with the actual penetration kinetics depending upon the rate processes involved. Copyright 2000 Academic Press.     

Electroosmotically driven capillary transport of typical non-Newtonian biofluids in rectangular microchannels

In this paper, a detailed theoretical model is developed for studying the capillary filling dynamics of a non-Newtonian power-law obeying fluid in a microchannel subject to electrokinetic effects. Special attention is devoted to model the effects of the electroosmotic influences in the capillary advancement process, variable resistive forces acting over different flow regimes, and the dynamically evolving contact line forces, in mathematically closed forms. As an illustrative case study, in which the flow parameters are modeled as functions of the hematocrit fraction in the sample, the capillary dynamics of a blood sample are analyzed. Flow characteristics depicting advancement of the fluid within the microfluidic channel turn out to be typically non-linear, as per the relative instantaneous strengths of the capillary forces, electroosmotic forces and viscous resistances. Non-trivial implications of the blood hematocrit level and the imposed electric field on the progression of the capillary front are highlighted, which are expected to be of significant consequence towards the dynamics of electroosmotically aided capillary filling processes of biofluidic samples.     

Sensitivity of drainage and imbibition to pore structures as revealed by computer simulation of displacement process

This work concerns the effects of the properties of porous media on two phase fluid displacement at slow rates. These properties include the size frequency distributions, shape and connectivity of pores and throats, the size correlation of directly connected throats and pores and the spatial arrangement of pores and throats in porous media. Computer simulations using 3-dimensional networks of pores and throats were used to determine the effects of these properties on the form of primary and secondary drainage curves, imbibition curves and scanning loops of a capillary pressure diagram.The application of the results is in deriving information about the structure of a porous medium from capillary pressure curves and understanding how predictions about the form of relative permeability curves can be made from capillary pressure curves.The concepts of finite and infinite throat and pore controlled domains are applied during the filling and emptying of a network. These concepts are then combined with considerations of the accessibility of network sites to non-wetting phase or wetting phase sources and sinks to provide information about the amounts and distribution of continuous and discontinuous wetting phase (wp) and non-wetting phase (nwp) at any stage of a displacement. The distribution of fluids Is strictly controlled by the domains. It is shown that recognition of the types, abundance and distribution of domains provides a fundamental basis for understanding boundary effects, differences in tortuosity in porous systems containing two immiscible phases, breakthrough pressures, and saturations, differences in nwp withdrawal efficiency between uncorrelated and correlated pore-throat size models, differences in hysteresis between drainage and imbibition and differences in the shapes of capillary pressure and relative permeability curves for various types of porous structures.     

Integrated continuous microfluidic liquid-liquid extraction

We describe continuous flow liquid-liquid phase separation in microfluidic devices based on capillary forces and selective wetting surfaces. Effective liquid-liquid phase separation is achieved by using a thin porous fluoropolymer membrane that selectively wets non-aqueous solvents, has average pore sizes in the 0.1-1 microm range, and has a high pore density for high separation throughput. Pressure drops throughout the microfluidic network are modelled and operating regimes for the membrane phase separator are determined based on hydrodynamic pressure drops and capillary forces. A microfluidic extraction device integrating mixing and phase separation is realized by using silicon micromachining. Modeling of the phase separator establishes the operating limits. The device is capable of completely separating several organic-aqueous and fluorous-aqueous liquid-liquid systems, even with high fractions of partially miscible compounds. In each case, extraction is equivalent to one equilibrium extraction stage.     

Molecular dynamics simulations of capillary rise experiments in nanotubes coated with polymer brushes

The capillary filling of a nanotube coated with a polymer brush is studied by molecular dynamics simulations of a coarse-grained model, assuming various conditions for the fluid-wall and fluid-brush interactions. Whereas the fluid is modeled by simple point particles interacting with Lennard-Jones forces, the (end-grafted, fully flexible) polymers that form the brush coating are described by a standard bead-spring model. Our experiments reveal that capillary filling is observed even for walls that would not be wetted by the fluid, provided the polymer brush coating itself wets. Generally, it is found that the capillary rise always proceeds through a t1/2 law with time t while the underlying molecular mechanism differs for wettable and nonwettable walls. For wettable walls, fluid imbibition is compatible with the Lucas-Washburn mechanism whereby the total influx of matter drops steadily with growing chain length N and the meniscus speed goes through a minimum at intermediate chain lengths. Moreover, because of flow, the polymer brush reorganizes its structure by forming a dense plug of chain segments under the meniscus that follows the meniscus in its motion. When the tube wall does not wet, one observes no meniscus formation for short chains although the fluid seeps through the wet brush. For a brush coating with longer chains, axial segregation between the brush segments and the fluid occurs by a kind of diffusive spreading, reminiscent of invasion percolation transport in a random medium, leading to the formation of a moving meniscus. For even longer chains that reach the tube axis, the rise of a meniscus with vanishing curvature-like imbibition in a porous medium is observed to take place.     

Nonlinear penetration of liquid drops into radial capillaries

The nonlinear dynamics of the impact and penetration of a liquid droplet in a radial capillary is studied numerically. The radial capillary is formed by two parallel plates at a distance of delta(g). The top plate has an orifice at its center. A droplet impacting on the orifice-plate partly spreads over the top plate, and the rest penetrates into the capillary gap between the two plates. The rate of spread of the fluid on the orifice plate, xi(out), is governed by the contact angle, beta, between the liquid and the orifice plate and the droplet initial momentum, whereas the rate of fluid spread inside the capillary gap, xi(in), is decided by the contact angles with both plates and the plate gap, delta(g).