Capillary suspensions: Particle networks formed through the capillary force

The addition of small amounts of a secondary fluid to a suspension can, through the attractive capillary force, lead to particle bridging and network formation. The capillary bridging phenomenon can be used to stabilize particle suspensions and precisely tune their rheological properties. This effect can even occur when the secondary fluid wets the particles less well than the bulk fluid. These materials, so-called capillary suspensions, have been the subject of recent research studying the mechanism for network formation, the properties of these suspensions, and how the material properties can be modified. Recent work in colloidal clusters is summarized and the relationship to capillary suspensions is discussed. Capillary suspensions can also be used as a pathway for new material design and some of these applications are highlighted. Results obtained to date are summarized and central questions that remain to be answered are proposed in this review.     

Field induced rotational viscosity of ferrofluid: effect of capillary size and magnetic field direction

In the present investigation we report the effect of capillary diameter and the direction of applied magnetic field on the rotational viscosity of water and kerosene based ferrofluids. We found that changes in the field induced rotational viscosity are larger in the case of water based magnetic fluid than that of kerosene based fluid. The field induced rotational viscosity is found to be inversely proportional to the capillary diameter and it falls exponentially as a function of the angle between the direction of field and vorticity of flow. Magnetophoretic mobility and hydrodynamic volume fraction of nanomagnetic particles are determined for above cases.     

Evaluation of the use of capillary numbers for quantifying the removal of DNAPL trapped in a porous medium by surfactant and surfactant foam floods

The capillary number is used to quantify the mobilization potential of organic phases trapped within porous media. The capillary number has been defined in three different forms, according to types of flow velocity and viscosity used in its definition. This study evaluated the suitability of the capillary number definitions representing surfactant and surfactant foam floods by constructing capillary number-TCE saturation relationships. The results implied that the capillary number should be correctly employed, according to scale and fluid flow behavior. This study suggests that the pore-scale capillary number should be used only for investigating the organic-phase mobilization at the pore scale because it is defined by the pore velocity and the dynamic viscosity. The Newtonian-fluid capillary number using the Darcy velocity and the dynamic viscosity may be suitable for quantifying flood systems representing Newtonian fluid behavior. For viscous-force modified flood systems such as surfactant-foam floods, the apparent capillary number definition employing macroscopic properties (permeability and potential gradient) may be used to appropriately represent the desaturation of organic phases from porous media.     

Numerical investigation of the effect of insoluble surfactants on drop deformation and breakup in simple shear flow

The effect of insoluble surfactants on drop deformation and breakup in simple shear flow is studied using a combination of a three-dimensional boundary-integral method and a finite-volume method to solve the coupled fluid dynamics and surfactant transport problem over the evolving interface. The interfacial tension depends nonlinearly on the surfactant concentration, and is described by the equation of state for the Langmuir isotherm. Results are presented over the entire range of the viscosity's ratio lambda and the surface coverage x, as well as the capillary number Ca that spans from that for small deformation to values that are beyond the critical one Ca(cr). The values of the elasticity number E, which reflects the sensitivity of the interfacial tension to the maximum surfactant concentration, are chosen in the interval 0.1 < or = E < or = 0.4 and a convection dominated regime of surfactant transport, where the influence of the surfactant on drop deformation is the most significant, is considered. For a better understanding of the processes involved, the effect of surfactants on the drop dynamics is decoupled into three surfactant related mechanisms (dilution, Marangoni stress and stretching) and their influence is separately investigated. The dependence of the critical capillary number Ca(cr)(lambda) on the surface coverage is obtained and the boundaries between different modes of breakup (tip-streaming and drop fragmentation) in the (lambda; x) plane are searched for. The numerical results indicate that at low capillary number, even with a trace amount of surfactant, the interface is immobilized, which has also been observed by previous studies. In addition, it is shown that for large Péclet numbers the use of the small deformation theory to measure the interfacial tension in the case where surfactants are present can introduce a significant error.     

Streaming potential generated by a long viscous drop in a capillary

The streaming potential generated by motion of a long drop of viscosity mu(d) = lambdamu in a uniform circular capillary filled with fluid of viscosity mu is investigated by means of a model previously used to study electrophoresis of a charged mercury drop in water. The capillary wall is at potential zeta c relative to the bulk fluid within it, and the surface of the drop is at potential zeta(d). Potentials are assumed to be sufficiently small so that the charge cloud is described by the linearized Poisson-Boltzmann equation, and the Debye length characterizing the thickness of the charge cloud is assumed to be thin compared with the gap h(0) between the drop and the capillary wall. Ions in the external fluid are not allowed to discharge at the surface of the drop, and the wall of the capillary has a nonzero surface conductivity sigma c. The drop is assumed to be sufficiently long so that end effects can be neglected. Recirculation of fluid within the drop gives rise to an enhanced streaming current when zeta(d) is nonzero, leading to an anomalously high streaming potential. This vanishes as the drop viscosity becomes large. If V is the velocity of the drop and gamma is the coefficient of interfacial tension between the two fluids, then the capillary number is Ca = mu V/gamma, and the gap varies as h(0)planck'sCa(2/3). When Ca is small, the gap h(0) is small and electrical conduction along the narrow gap is dominated by the surface conductivity sigma(c) of the capillary wall, which is constant. The electrical current convected by flowing fluid is proportional to Ca, as is the change in streaming potential caused by the presence of the drop. If sigma(c) = 0, then the electrical conductance of the gap depends on its width h(0) and on the bulk fluid conductivity sigma and becomes small as h(0) approximately equal to Ca(2/3) --> 0. The streaming potential required to cancel the O(Ca) convection current therefore varies as Ca(1/3). If sigma(c) = 0 and the drop is rigid (lambda --> infinity), then the change in streaming potential over and above that expected due to the change in pressure gradient is proportional to the difference in potentials zeta(c)-zeta(d).     

Interactions between particles with an undulated contact line at a fluid interface: capillary multipoles of arbitrary order

A colloidal particle adsorbed at a fluid interface could have an undulated, or irregular contact line in the presence of surface roughness and/or chemical inhomogeneity. The contact-line undulations produce distortions in the surrounding liquid interface, whose overlap engenders capillary interaction between the particles. The convex and concave local deviations of the meniscus shape from planarity can be formally treated as positive and negative "capillary charges," which form "capillary multipoles." Here, we derive theoretical expressions for the interaction between two capillary multipoles of arbitrary order. Depending on the angle of mutual orientation, the interaction energy could exhibit a minimum, or it could represent a monotonic attraction. For undulation amplitudes larger than 5 nm, the interaction energy is typically much greater than the thermal energy kT. As a consequence, a monolayer from capillary multipoles exhibits considerable shear elasticity, and such monolayer is expected to behave as a two-dimensional elastic solid. These theoretical results could be helpful for the understanding of phenomena related to aggregation and ordering of particles adsorbed at a fluid interface, and for the interpretation of rheological properties of particulate monolayers. Related research fields are the particle-stabilized (Pickering) emulsions and the two-dimensional self-assembly of microscopic particles.     

Hydrodynamically limited precision of gradient techniques in flow injection analysis

Based on the law of error propagation, a general expression is derived to study theoretically the hydrodynamically limited precision associated with each single element of fluid in a concentration profile in flow injection analysis. Convolution of the injection and residence time distribution functions is used to obtain response functions for a homogeneously stirred mixing chamber and for a straight capillary tube. The effects of stochastic variations on overall precision by sample introduction, pumping and timing are elucidated and compared with experimental findings. Resulting practical implications for the use of these two dispersing elements are outlined.     

Behaviour of substituted aminomethylphenol dyes in capillary isoelectric focusing with electroosmotic zone displacement

The behaviour of six substituted aminomethylphenol dyes, having pI values between 5.3 and 10.4, in capillary isoelectric focusing with electroosmotic zone displacement is described. Using untreated fused-silica capillaries and different neutral capillary conditioners in the catholyte, the low-molecular-mass dyes are shown to focus and elute reproducibly in the order of decreasing pI values. In the absence of proteins, the detection times of the dyes are independent of the sampled amount. Hence these substances permit the characterization of the pH gradient produced in this capillary isoelectric focusing method. With concurrent focusing of dyes and test proteins, a macromolecular impact on detection times (reduction of electroosmosis)‘ is revealed. The effect is shown to be dependent on the type and amount of proteins applied and has been observed with three different capillary conditioners. Nevertheless, mapping of the pH gradient with these dyes and determining the pI values of known proteins is shown to provide values in agreement with those in the literature. Hence the substituted aminomethylphenol dyes can be employed as pI markers in capillary isoelectric focusing with electroosmotic zone displacement. Further, focusing and separation of two of the six dyes by preparative recycling free fluid isoelectric focusing is described, illustrating that the substituted aminomethylphenol dyes are also applicable to other free fluid focusing methods.     

Experimental validation of plugging during drop formation in a T-junction

At low capillary number, drop formation in a T-junction is dominated by interfacial effects: as the dispersed fluid flows into the drop maker nozzle, it blocks the path of the continuous fluid; this leads to a pressure rise in the continuous fluid that, in turn, squeezes on the dispersed fluid, inducing pinch-off of a drop. While the resulting drop volume predicted by this "squeezing" mechanism has been validated for a range of systems, as of yet, the pressure rise responsible for the actual pinch-off has not been observed experimentally. This is due to the challenge of measuring the pressures in a T-junction with the requisite speed, accuracy, and localization. Here, we present an empirical study of the pressures in a T-junction during drop formation. Using Laplace sensors, pressure probes we have developed, we confirm the central ideas of the squeezing mechanism; however, we also uncover other findings, including that the pressure of the dispersed fluid is not constant but rather oscillates in anti-phase with that of the continuous fluid. In addition, even at the highest capillary number for which monodisperse drops can be formed, pressure oscillations persist, indicating that drop formation in confined geometries does not transition to an entirely shear-driven mechanism, but to a mechanism combining squeezing and shearing.     

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.     

矩形截面毛细管电泳和二维分离

在石英单晶表面制成矩矩截面毛细管柱中进行电泳实验。由于矩形柱比圆形柱有更大散热侧面积且石英单晶的导热性能远无于熔融石英，所以可施加较高的场强，不仅提高了柱效，而且缩矩了分离时间。两相交的通道之间形成自然连接，可实现二维分离，并消除死体积。     

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.     

Mean field kinetic theory for a lattice gas model of fluids confined in porous materials

We consider the mean field kinetic equations describing the relaxation dynamics of a lattice model of a fluid confined in a porous material. The dynamical theory embodied in these equations can be viewed as a mean field approximation to a Kawasaki dynamics Monte Carlo simulation of the system, as a theory of diffusion, or as a dynamical density functional theory. The solutions of the kinetic equations for long times coincide with the solutions of the static mean field equations for the inhomogeneous lattice gas. The approach is applied to a lattice gas model of a fluid confined in a finite length slit pore open at both ends and is in contact with the bulk fluid at a temperature where capillary condensation and hysteresis occur. The states emerging dynamically during irreversible changes in the chemical potential are compared with those obtained from the static mean field equations for states associated with a quasistatic progression up and down the adsorption/desorption isotherm. In the capillary transition region, the dynamics involves the appearance of undulates (adsorption) and liquid bridges (adsorption and desorption) which are unstable in the static mean field theory in the grand ensemble for the open pore but which are stable in the static mean field theory in the canonical ensemble for an infinite pore.     

Geometry-driven wetting transition

Wetting states are quantitatively described by the number of inflection points on the liquid-vapor interface and by the macroscopic contact angle. The number of inflection points required for complete, partial, and pseudopartial wetting is determined for geometries with positive, zero, and negative capillary pressures. The wetting state of a material system is not always independent of the magnitude of the capillary pressure; for example, the wetting state of a fluid inside a capillary tube may depend on the capillary radius. In particular, a fluid that pseudopartially wets the inside of a tube exhibits a transition to partial wetting (or complete wetting) as the capillary radius is decreased.     

Double-emulsion drops with ultra-thin shells for capsule templates

We introduce an emulsification technique that creates monodisperse double-emulsion drops with a core-shell geometry having an ultra-thin wall as a middle layer. We create a biphasic flow in a microfluidic capillary device by forming a sheath flow consisting of a thin layer of a fluid with high affinity to the capillary wall flowing along the inner wall of the capillary, surrounding the innermost fluid. This creates double-emulsion drops, using a single-step emulsification, having a very thin fluid shell. If the shell is solidified, its thickness can be small as a hundred nanometres or even less. Despite the small thickness of this shell, these structures are nevertheless very stable, giving them great potential for encapsulation. We demonstrate this by creating biodegradable microcapsules of poly(lactic acid) with a shell thickness of a few tens of nanometres, which are potentially useful for encapsulation and delivery of drugs, cosmetics, and nutrients.     

Thermally controlled fluidic self-assembly

A novel approach for the fluidic self-assembly (FSA) of microparts in a multibatch process utilizing the thermal behavior of the carrier fluid as a means for selecting binding sites is presented. In the system studied, fluidic assembly takes place due to a capillary bridge between hexadecane deposited on a hydrophobic patch on a substrate and a hydrophobic surface on a micropart suspended in a carrier fluid. When desired, FSA of microparts is prevented by causing the surrounding carrier fluid to form a gel when heated, offering a method for directing self-assembly to sites that are not heated. It is shown that a suitable carrier fluid is 15 wt % Pluronic F127, which gels at about 40 degrees C when tested in the geometry used to demonstrate the concept. Experimental results demonstrating FSA and thermally controlled fluidic assembly (TCFSA) of plastic microparts dispersed in Pluronic F127 solution are presented. Potentially, TCFSA offers a general method for directed assembly as it relies on restricting the transport of microparts to a site rather than interfering with the fundamental attractive forces responsible for self-assembly.     

Fluid mechanics of electroosmotic flow and its effect on band broadening in capillary electrophoresis

Electroosmotic flow (EOF) usually accompanies electrophoretic migration of charged species in capillary electrophoresis unless special precautions are taken to suppress it. The presence of the EOF provides certain advantages in separations. It is an alternative to mechanical pumps, which are inefficient and difficult to build at small scales, for transporting reagents and analytes on microfluidic chips. The downside is that any imperfection that distorts the EOF profile reduces the separation efficiency. In this paper, the basic facts about EOF are reviewed from the perspective of fluid mechanics and its effect on separations in free solution capillary zone electrophoresis is discussed in the light of recent advances.     

Electrokinetic flow in a capillary with a charge-regulating surface polymer layer

An analytical study of the steady electrokinetic flow in a long uniform capillary tube or slit is presented. The inside wall of the capillary is covered by a layer of adsorbed or covalently bound charge-regulating polymer in equilibrium with the ambient electrolyte solution. In this solvent-permeable and ion-penetrable surface polyelectrolyte layer, ionogenic functional groups and frictional segments are assumed to distribute at uniform densities. The electrical potential and space charge density distributions in the cross section of the capillary are obtained by solving the linearized Poisson-Boltzmann equation. The fluid velocity profile due to the application of an electric field and a pressure gradient through the capillary is obtained from the analytical solution of a modified Navier-Stokes/Brinkman equation. Explicit formulas for the electroosmotic velocity, the average fluid velocity and electric current density on the cross section, and the streaming potential in the capillary are also derived. The results demonstrate that the direction of the electroosmotic flow and the magnitudes of the fluid velocity and electric current density are dominated by the fixed charge density inside the surface polymer layer, which is determined by the regulation characteristics such as the dissociation equilibrium constants of the ionogenic functional groups in the surface layer and the concentration of the potential-determining ions in the bulk solution.     

Analytical study of Joule heating effects on electrokinetic transportation in capillary electrophoresis

Electric fields are often used to transport fluids (by electroosmosis) and separate charged samples (by electrophoresis) in microfluidic devices. However, there exists inevitable Joule heating when electric currents are passing through electrolyte solutions. Joule heating not only increases the fluid temperature, but also produces temperature gradients in cross-stream and axial directions. These temperature effects make fluid properties non-uniform, and hence alter the applied electric potential field and the flow field. The mass species transport is also influenced. In this paper we develop an analytical model to study Joule heating effects on the transport of heat, electricity, momentum and mass species in capillary-based electrophoresis. Close-form formulae are derived for the temperature, applied electrical potential, velocity, and pressure fields at steady state, and the transient concentration field as well. Also available are the compact formulae for the electric current and the volume flow rate through the capillary. It is shown that, due to the thermal end effect, sharp temperature drops appear close to capillary ends, where sharp rises of electric field are required to meet the current continuity. In order to satisfy the mass continuity, pressure gradients have to be induced along the capillary. The resultant curved fluid velocity profile and the increase of molecular diffusion both contribute to the dispersion of samples. However, Joule heating effects enhance the sample transport velocity, reducing the analysis time in capillary electrophoretic separations.     

Electrokinetic coupling in unsaturated porous media

We consider a charged porous material that is saturated by two fluid phases that are immiscible and continuous on the scale of a representative elementary volume. The wetting phase for the grains is water and the nonwetting phase is assumed to be an electrically insulating viscous fluid. We use a volume-averaging approach to derive the linear constitutive equations for the electrical current density as well as the seepage velocities of the wetting and nonwetting phases on the scale of a representative elementary volume. These macroscopic constitutive equations are obtained by volume-averaging Ampère's law together with the Nernst-Planck equation and the Stokes equations. The material properties entering the macroscopic constitutive equations are explicitly described as functions of the saturation of the water phase, the electrical formation factor, and parameters that describe the capillary pressure function, the relative permeability functions, and the variation of electrical conductivity with saturation. New equations are derived for the streaming potential and electro-osmosis coupling coefficients. A primary drainage and imbibition experiment is simulated numerically to demonstrate that the relative streaming potential coupling coefficient depends not only on the water saturation, but also on the material properties of the sample, as well as the saturation history. We also compare the predicted streaming potential coupling coefficients with experimental data from four dolomite core samples. Measurements on these samples include electrical conductivity, capillary pressure, the streaming potential coupling coefficient at various levels of saturation, and the permeability at saturation of the rock samples. We found very good agreement between these experimental data and the model predictions.