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 Primary Electroviscous Effect: Thin Double Layers (akappa>1) and a Stern Layer

The primary electroviscous effect due to the charge clouds surrounding spherical charged particles suspended in an electrolyte was studied by Hinch and Sherwood (J. Fluid Mech. 132, 337 (1983)) in the limit of double layers thin compared to the particle radius a. Here we introduce the effect of a dynamic Stern layer into that analysis, in order to explain the numerical results of Rubio-Hernández et al. (J. Colloid Interface Sci. 206, 334 (1998)) in terms of the ratio of the tangential ionic fluxes within the charge cloud to those within the Stern layer. The predictions of the asymptotic analysis are compared with those of numerical computations. The thickness of the charge cloud is characterized by the Debye length kappa(-1). If akappa>10 the predictions of the asymptotic analysis exhibit the same qualitative behavior as the numerical results, but akappa>1000 is required to achieve quantitative agreement to within 2.5%. Copyright 2000 Academic Press.     

Co- and counter-current spontaneous imbibition into groups of capillary tubes with lateral connections permitting cross-flow

A model for co- and counter-current imbibition through independent capillaries has already been developed and experiments conducted to verify the theory [E. Unsal, G. Mason, N.R. Morrow, D.W. Ruth, J. Colloid Interface Sci. 306 (2007) 105]. In this paper, the work is extended to capillaries which are connected laterally and in which cross-flow can take place. The fundamental pore geometry is a rod in an angled round-bottomed slot with a gap between the rod and a capping glass plate. The surfaces of the slot, rod and plate form capillaries and interconnecting passages which have non-axisymmetric cross-sections. Depending on the gap size either (i) a large single meniscus, (ii) two menisci one on each side of the rod, or (iii) three menisci, one between the rod and the glass additional to the ones on each side can be formed. A viscous refined oil was applied to one end of the capillaries and co-current and counter-current spontaneous imbibition experiments were performed. The opposite end was left open to the atmosphere for co-current experiments. When the gap between the rod and the plate was large, the imbibing oil advanced into the tubes with the meniscus in the largest capillary always lagging behind the two menisci in the other two smaller capillaries. For counter-current imbibition experiments the open end was sealed and connected to a sensitive pressure transducer. In some experiments, the oil imbibed into the smaller capillaries and expelled air as a series of bubbles from the end of the largest capillary. In other experiments, the oil was allowed to imbibe part way into the tubes before counter-current imbibition was started. The meniscus curvatures of the capillaries have been calculated using the Mayer and Stowe-Princen method for different cell slot angles and gap sizes using a value of zero for the contact angle. These values have been compared with actual values by measuring the capillary rise in the tubes; agreement was very close. A model for co-current and counter-current imbibition has also been developed. The significance of this model is that some hydraulic/capillary properties are common for both co-current and counter-current imbibition. The experiments give an illustration of behavior expected in a real porous material and verify the importance of the 'perfect cross-flow' modification to the 'bundle of parallel tubes' model.     

Surfactant solutions and porous substrates: spreading and imbibition

In Section 1, spreading of small liquid drops over thin dry porous layers is investigated from both theoretical and experimental points of view [V.M. Starov, S.R. Kosvintsev, V.D. Sobolev, M.G. Velarde, S.A. Zhdanov, J. Colloid Interface Sci. 252 (2002) 397]. Drop motion over a porous layer is caused by an interplay of two processes: (a) the spreading of the drop over already saturated parts of the porous layer, which results in an expanding of the drop base, and (b) the imbibition of the liquid from the drop into the porous substrate, which results in a shrinkage of the drop base and an expanding of the wetted region inside the porous layer. As a result of these two competing processes, the radius of the drop goes through a maximum value over time. A system of two differential equations has been derived to describe the evolution with time of radii of both the drop base and the wetted region inside the porous layer. This system includes two parameters, one accounts for the effective lubrication coefficient of the liquid over the wetted porous substrate, and the other is a combination of permeability and effective capillary pressure inside the porous layer. Two additional experiments were used for an independent determination of these two parameters. The system of differential equations does not include any fitting parameter after these two parameters are determined. Experiments were carried out on the spreading of silicone oil drops over various dry microfiltration membranes (permeable in both normal and tangential directions). The time evolution of the radii of both the drop base and the wetted region inside the porous layer were monitored. All experimental data fell on two universal curves if appropriate scales are used with a plot of the dimensionless radii of the drop base and of the wetted region inside the porous layer on dimensionless time. The predicted theoretical relationships are two universal curves accounting quite satisfactory for the experimental data. According to theory predictions [1]: (i) the dynamic contact angle dependence on the same dimensionless time as before should be a universal function, and (ii) the dynamic contact angle should change rapidly over an initial short stage of spreading and should remain a constant value over the duration of the rest of the spreading process. The constancy of the contact angle on this stage has nothing to do with hysteresis of the contact angle: there is no hysteresis in the system under investigation. These conclusions again are in good agreement with experimental observations [V.M. Starov, S.R. Kosvintsev, V.D. Sobolev, M.G. Velarde, S.A. Zhdanov, J. Colloid Interface Sci. 252 (2002) 397]. In Section 2, experimental investigations are reviewed on the spreading of small drops of aqueous SDS solutions over dry thin porous substrates (nitrocellulose membranes) in the case of partial wetting [S. Zhdanov, V. Starov, V. Sobolev, M. Velarde, Spreading of aqueous SDS solutions over nitrocellulose membranes. J. Colloid Interface Sci. 264 (2003) 481-489]. The time evolution was monitored of the radii of both the drop base and the wetted area inside the porous substrate. The total duration of the spreading process was subdivided into three stages-the first stage: the drop base expands until the maximum value of the drop base is reached; the contact angle rapidly decreases during this stage; the second stage: the radius of the drop base remains constant and the contact angle decreases linearly with time; the third stage: the drop base shrinks and the contact angle remains constant. The wetted area inside the porous substrate expends during the whole spreading process. Appropriate scales were used with a plot of the dimensionless radii of the drop base, of the wetted area inside the porous substrate, and the dynamic contact angle on the dimensionless time. Experimental data showed [S. Zhdanov, V. Starov, V. Sobolev, M. Velarde, Spreading of aqueous SDS solutions over nitrocellulose membranes. J. Colloid Interface Sci. 264 (2003) 481-489]: the overall time of the spreading of drops of SDS solution over dry thin porous substrates decreases with the increase of surfactant concentration; the difference between advancing and hydrodynamic receding contact angles decreases with the surfactant concentration increase; the constancy of the contact angle during the third stage of spreading has nothing to do with the hysteresis of contact angle, but determined by the hydrodynamic reasons. It is shown using independent spreading experiments of the same drops on nonporous nitrocellulose substrate that the static receding contact angle is equal to zero, which supports the conclusion on the hydrodynamic nature of the hydrodynamic receding contact angle on porous substrates. In Section 3, a theory is developed to describe a spontaneous imbibition of surfactant solutions into hydrophobic capillaries, which takes into account the micelle disintegration and the concentration decreasing close to the moving meniscus as a result of adsorption, as well as the surface diffusion of surfactant molecules [N.V. Churaev, G.A. Martynov, V.M. Starov, Z.M. Zorin, Colloid Polym. Sci. 259 (1981) 747]. The theory predictions are in good agreement with the experimental investigations on the spontaneous imbibition of the nonionic aqueous surfactant solution, Syntamide-5, into hydrophobized quartz capillaries. A theory of the spontaneous capillary rise of surfactant solutions in hydrophobic capillaries is presented, which connects the experimental observations with the adsorption of surfactant molecules in front of the moving meniscus on the bare hydrophobic interface [V.J. Starov, Colloid Interface Sci. 270 (2003)]. In Section 4, 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 [V. Straov, S. Zhdanov, M. Velarde, J. Colloid Interface Sci. 273 (2004) 589]. Cylindrical capillaries are used as a model of porous media for theoretical treatment of the problem. It is shown that if an averaged pore size of the porous medium is below a critical value, then the permeability of the porous medium is not influenced by the presence of surfactants at any concentration: the imbibition front moves exactly in the same way as in the case of the imbibition of the pure water. The critical radius is determined by the adsorption of the surfactant molecules on the inner surface of the pores. If an averaged pore size is bigger than the critical value, then the permeability increases with surfactant concentration. These theoretical conclusions are in agreement with experimental observations. In Section 5, the spreading of surfactant solutions over hydrophobic surfaces is considered from both theoretical and experimental points of view [V.M. Starov, S.R. Kosvintsev, M.G. Velarde, J. Colloid Interface Sci. 227 (2000) 185]. Water droplets do not wet a virgin solid hydrophobic substrate. It is shown that the transfer of surfactant molecules from the water droplet onto the hydrophobic surface changes the wetting characteristics in front of the drop on the three-phase contact line. The surfactant molecules increase the solid-vapor interfacial tension and hydrophilise the initially hydrophobic solid substrate just in front of the spreading drop. This process causes water drops to spread over time. The time of evolution of the spreading of a water droplet is predicted and compared with experimental observations. The assumption that surfactant transfer from the drop surface onto the solid hydrophobic substrate controls the rate of spreading is confirmed by experimental observations. In Section 6, the process of the spontaneous spreading of a droplet of a polar liquid over solid substrate is analyzed in the case when amphiphilic molecules (or their amphiphilic fragments) of the substrate surface layer are capable of overturning, resulting in a partial hydrophilisation of the surface [V.M. Starov, V.M. Rudoy, V.I. Ivanov, Colloid J. (Russian Academy of Sciences English Transaction) 61 (3) (1999) 374]. Such a situation may take place, for example, during contact of an aqueous droplet with the surface of a polymer whose macromolecules have hydrophilic side groups capable of rotating around the backbone and during the wetting of polymers containing surface-active additives or Langmuir-Blodgett films composed of amphiphilic molecules. It was shown that droplet spreading is possible only if the lateral interaction between neighbouring amphiphilic molecules (or groups) takes place. This interaction results in the tangential transfer of "the overturning state" to some distance in front of the advancing three-phase contact line making it partially hydrophilic. The quantitative theory describing the kinetics of droplet spreading is developed with allowance for this mechanism of self-organization of the surface layer of a substrate in the contact with a droplet.     

Capillary Rise in Granitic Rocks: Interpretation of Kinetics on the Basis of Pore Structure

The capillary transport of water into granitic rocks has been interpreted on the basis of the structure of its porous network. An effective pore radius has been calculated from a three-sized single-pore model proposed by F. A. L. Dullien, El-Sayed, and V. K. Batra (J. Colloid Interface Sci. 60, 497, 1977) Considering the porous network of granites as consisting of fissures grouped in two size types, macro- and microfissures, an effective radius was found from the characteristic radii for each type and the average of these two values. Good agreement between the effective radius calculated and the radius estimated using a capillary rate value measured experimentally provides a suitable basis for identifying interrelationships between the pore structure and moisture capillary rise. In fact, it is possible to predict the process rate from only two characteristic pore sizes, corresponding to the radii of macrofissures and microfissures. The abnormally low rate of capillary rise observed in one of the granites studied could be easily interpreted as due to the involvement exclusively of the macrofissures of its porous network in capillary transport. Copyright 2000 Academic Press.     

Effect of molecular weight on the capillary absorption of polymer droplets

We study capillary absorption of small polymer droplets into nonwettable capillaries using coarse-grained molecular dynamics simulations and a simple analytical model. Studies of droplets of simple fluids have revealed that the capillary process depends on the ratio of tube-to-droplet radii [Willmott Faraday Discuss., 2010, 146, 233; Marmur J. Colloid Interface Sci. 1988, 122, 209]. Here we consider the absorption of droplets of polymers and study the effect of polymer chain length on the capillary absorption process. Our simulations reveal that for droplets of the same size (radius), the critical tube radius, below which there is no absorption, increases with the length of the polymer chains that constitute the droplets. We propose a model to explain this effect, which incorporates an entropic penalty for polymer confinement and find that this model agrees quantitatively with the simulations. We also find that the absorption dynamics is sensitive to the polymer chain length. In some cases during the capillary uptake transient partial absorption states, where the droplet is partially in and partially out of the tube, were observed. Such dynamics cannot be explained by a generalized Lucas-Washburn approach.     

Diffuse Double-Layer Interaction between Two Identical Spherical Colloidal Particles

A simple method is given for calculating the potential energy of the diffuse double-layer interaction between two identical spherical colloidal particles in a symmetrical electrolyte solution with the help of Derjaguin's approximation. This method uses accurate analytic expressions for the corresponding interaction energy between two parallel similar plates obtained previously (Colloids Surf. A Physicochem. Eng. Asp. 146, 213 (1999); J. Colloid Interface Sci. 212, 130 (1999)). Agreement with numerical data provided by Honig and Mul (J. Colloid Interface Sci. 36, 258 (1971)) is excellent particularly for small particle separations. Copyright 2000 Academic Press.     

A theory on bubble-size dependence of the critical electrolyte concentration for inhibition of coalescence

The interaction of pairs of bubbles with equal diameters grown on adjacent capillaries in aqueous magnesium sulfate solutions is studied by varying electrolyte concentration and bubble diameter by Tsang, Koh and Koch [Y.H. Tsang, Y.-H. Koh, D.L. Koch, J. Colloid Interface Sci. 275 (2004) 290] (referred to as TKK hereafter). They find that the critical concentration to prevent coalescence, Ct, increases as the equivalent diameter, deq, decreases. In fact, Ct is found to scale as deq(-1.2). This dependence is stronger than that predicted by Prince and Blanch (Ct approximately deq(-0.5)) (referred to as PB [M.J. Prince, H.W. Blanch, AIChE J. 36 (1990) 1425] hereafter) on the basis of a postulation that lubrication pressure due to Marangoni stresses inhibit coalescence. TKK postulate instead that bubbles are stabilized by hydration structures. We further illustrate here that when hydration force term is added to the equation of motion of the film thinning process, predicted values of critical concentration are found to scale as deq(-1). The current prediction shows a much better agreement with the experimental results than that proposed by PB. This suggests previous assumption that immobility of the interface by Marangoni effect as the dominant mechanism of inhibition of coalescence in an electrolytic solution is inaccurate [M.J. Prince, H.W. Blanch, AIChE J. 36 (1990) 1425, G. Marrucci, Chem. Eng. Sci. 24 (1969) 975].     

A numerical study of the effect of insoluble surfactants on the stability of a viscous drop translating in a Hele-Shaw cell

A circular drop is a linearly stable solution for the buoyancy-driven motion of drops in a Hele-Shaw cell [Gupta et al. J. Colloid Interface Sci.218(1), 338 (1999)]. In the absence of surface-active agents, an initially prolate drop always goes to a steady circular shape while initially oblate drops exhibit complex dynamics [Gupta et al. J. Colloid Interface Sci.222, 107 (2000)]. In this study, the effect of insoluble surfactant impurities on the critical conditions for drop breakup is explored by using the Langmuir adsorption framework in conjunction with a physically based expression for the depth-averaged tangential stress exerted on a two-phase interface in a Hele-Shaw cell. It is shown that the presence of surfactants can have both a stabilizing and a destabilizing effect on the shape of the drop, depending on the Bond number, the magnitude of the initial perturbation, and the strength of surface convection. Similar to the clean drop dynamics, two marginally stable branches are found. Increasing the surface Peclet number results in the stabilization of the main branch while the secondary branch shifts to higher Bond numbers. The mode of breakup is also found to be strongly influenced by the strength of surface convection.     

Three-phase capillary entry conditions in pores of noncircular cross-section

In this work we challenge the assumption that the capillary entry pressures for displacements in three-phase flow are the same as those in two-phase flow. Using an energy balance, as derived by R.P. Mayer and R.A. Stowe (J. Colloid Interface Sci. 20 (1965) 893-911) and H.M. Princen (J. Colloid Interface Sci. 30 (1969) 69-75; 30 (1969) 359-371; 34 (1970) 171-184) for two-phase flow, we derive a general formula for determination of the capillary entry pressures for piston-like displacement of two bulk phases in a pore where a third phase may also be present. The method applies to capillaries of angular cross-section and uniform but arbitrary wettability. To use this method we have determined all possible underlying phase occupancies in cross-sections on either side of the main terminal meniscus, in particular the presence of corner arc menisci (AMs). Indeed, the capillary entry pressures for piston-like displacements depend on the pressure in the remaining third phase if the cross-sectional fluid configurations contain this phase. This dependence only vanishes when layers of the intermediate-wetting phase completely separate the wetting and the non-wetting phases. The complexity of the corresponding equations and the quantitative effects are studied using two different geometries, the equilateral triangle and the rhombus. The main difference is that the latter geometry has unequal corners, which may carry different AMs. We have carried out a limited sensitivity study with respect to the effect of wettability, the spreading coefficient of the intermediate-wetting phase, and the aspect ratio of the principal radii of the rhombus.     

Forces between a rigid probe particle and a liquid interface. II. The general case

The semianalytic theory developed previously (Chan, D. Y. C., Dagastine, R. R., and White, L. R., J. Colloid Interface Sci. 236, 141 (2001)) to predict the force curve of an AFM measurement at a liquid interface using a colloidal probe has been expanded to incorporate a general force law with both attractive and repulsive forces. Expressions for the gradient of the force curve are developed to calculate the point at which the probe particle on the cantilever will spontaneously jump in toward the liquid interface. The calculation of the jump instability is reduced to a straightforward embroidery of the simple algorithms presented in Chan et al. In a variety of sample calculations using force laws including van der Waals, electrostatic, and hydrophobic forces for both oil/water and bubble/water interfaces, we have duplicated the general behaviors observed in several AFM investigations at liquid interfaces. The behavior of the drop as a Hookean spring and the numerical difficulties of a full numerical calculation of F(deltaX) are also discussed.     

Molecular orbital theory study on surface complex structures of phosphates to iron hydroxides: calculation of vibrational frequencies and adsorption energies

Quantum mechanical calculations were applied to resolve controversies about phosphate surface complexes on iron hydroxides. Six possible surface complexes were modeled: deprotonated, monoprotonated, and diprotonated versions of bridging bidentate and monodentate complexes. The calculated frequencies were compared to experimental IR frequency data (Persson et al. J. Colloid Interface Sci. 1996, 177, 263-275; Arai and Sparks J. Colloid Interface Sci. 2001, 241, 317-326.). This study suggests that the surface complexes change depending on pH. Four possible species are a diprotonated bidentate complex at pH 4-6, either a deprotonated bidentate or a monoprotonated monodentate complex at pH 7.5-7.9, and a deprotonated monodentate complex at pH 12.8. In addition, reaction energies were calculated for adsorption from aqueous solution to determine relative stability to form a monoprotonated monodentate complex and a deprotonated bidentate complex. According to these results, the monoprotonated monodentate complex should be favored. Vibrational frequencies of the monoprotonated monodentate and deprotonated bidentate complexes were analyzed with electronic effects on the Fe-OP and H-OP bonds.     

Analytical expressions for the electrical potential near planar, cylindrical, and spherical surfaces for symmetric electrolytes

The conjecture of Tuinier (J. Colloid Interface Sci. 258 (2003) 45) for the electrical potentials near a cylindrical surface and near a spherical surface under the conditions of symmetric electrolyte and large scaled radius are derived by solving the corresponding Poisson-Boltzmann equation. The surface charge density-surface potential relations for these surfaces are also derived under the conditions of constant surface potential. We show that the level of surface charge density for planar, cylindrical, and spherical surfaces follows the order spherical surface > cylindrical surface > planar surface.     

Dynamics of Drop Formation in an Electric Field

The effect of an electric field on the formation of a drop of an inviscid, perfectly conducting liquid from a capillary which protrudes from the top plate of a parallel-plate capacitor into a surrounding dynamically inactive, insulating gas is studied computationally. This free boundary problem which is comprised of the surface Bernoulli equation for the transient drop shape and the Laplace equation for the velocity potential inside the drop and the electrostatic potential outside the drop is solved by a method of lines incorporating the finite element method for spatial discretization. The finite element algorithm employed relies on judicious use of remeshing and element addition to a two-region adaptive mesh to accommodate large domain deformations, and allows the computations to proceed until the thickness of the neck connecting an about to form drop to the rest of the liquid in the capillary is less than 0.1% of the capillary radius. The accuracy of the computations is demonstrated by showing that in the absence of an electric field predictions made with the new algorithm are in excellent agreement with boundary integral calculations (Schulkes, R. M. S. M. J. Fluid Mech. 278, 83 (1994)) and experimental measurements on water drops (Zhang, X., and Basaran, O. A. Phys. Fluids 7(6), 1184 (1995)). In the presence of an electric field, the algorithm predicts that as the strength of the applied field increases, the mode of drop formation changes from simple dripping to jetting to so-called microdripping, in accordance with experimental observations (Cloupeau, M., and Prunet-Foch, B. J. Aerosol Sci. 25(6), 1021 (1994); Zhang, X., and Basaran, O. A. J. Fluid Mech. 326, 239 (1996)). Computational predictions of the primary drop volume and drop length at breakup are reported over a wide range of values of the ratios of electrical, gravitational, and inertial forces to surface tension force. In contrast to previously mentioned cases where both the flow rate in the tube and the electric field strength are nonzero, situations are also considered in which the flow rate is zero and the dynamics are initiated by impulsively changing the field strength from a certain value to a larger value. When the magnitude of the step change in field strength is small, the results of the new transient calculations accord well with those of an earlier stability analysis (Basaran, O. A., and Scriven, L. E. J. Colloid Interface Sci. 140(1), 10 (1990)) and thereby provide yet another testament to the accuracy of the new algorithm. Copyright 1999 Academic Press.     

Electroviscous Effect in Dilute Suspensions of Alumina

A study on the electroviscous effect of alumina suspensions has been made. At the low volume fraction of the particles studied here only a first-order effect was detected. Ubbelohde-type capillary viscometers have been used. A simple method to determine the hydrodynamic constant k(1) has been proposed. The experimental primary electroviscous coefficients corresponding to different electrolyte concentrations have been compared with two different theoretical approachs (I. G. Watterson, and L. R. White, J. Chem. Soc. Faraday Trans. 2 77, 1115 (1981); F. J. Rubio-Hernández, E. Ruiz-Reina, and A. I. Gómez-Merino, J. Colloid Interface Sci. 206, 334 (1998)) and the results suggest that the presence of a dynamic Stern layer plays a certain role in this effect. Copyright 2000 Academic Press.     

FORMATION MECHANISM OF UNIFORM SPINDLE-TYPE TITANIA PARTICLES IN THE GEL-SOL PROCESS

Recently, as an application of the novel synthetic of monodisperse particies named the “gel-sol method”, uniform spindle-like titania particles of anatase type have been produced by a 2-step process, consisting of the first aging of an aqueous solution of a titanium-triethanolamine compound for 24 h at 100^°C for the formation of a rigid hydrolyzed gel and the second aging for 72 h at 140^°C for the nucleation and growth of the titania particles in the gel network (T. Sugimoto et al., J. Colloid Interface Sci., in press). In this paper, the study is focused on the characterization of the titanium-triethanolamine compound, gel. and final product titania, the formation mechanism of the titania panicles, and their size control.     

From homogeneous dispersion to micelles-a molecular dynamics simulation on the compromise of the hydrophilic and hydrophobic effects of sodium dodecyl sulfate in aqueous solution

The structural and functional diversity of surfactant systems has attracted simulation works in atomistic, coarse grain, and mesoscopic models (Bandyopadhyay, S.; et al. Langmuir 2000, 16, 942; Senapati, S.; et al. J. Phys. Chem. B 2003, 107, 12906; Maiti, P. K.; et al. Langmuir 2002, 18, 1908; Srinivas, G.; et al. J. Phys. Chem. B 2004, 108, 8153; Groot, R. D.; et al. J. Chem. Phys. 1999, 110, 9739; Rekvig, L.; et al. Langmuir 2003, 19, 8195). However, atomistic models have suffered from their tremendous computational cost and are, so far, not able to simulate the structural behaviors in sufficient spatio-temporal scales (Shelley, J. C.; Shelley, M. Y. Curr. Opin. Colloid Interface Sci. 2000, 5, 101). The other two approaches are not microscopic enough to describe the configurations of the surfactants that determine their behaviors (Shelley and Shelley). In this study, we propose to simplify atomistic models based on the observation that the compromise of the hydrophilic and hydrophobic effects (Li, J.; Kwauk, M. Chem. Eng. Sci. 2003, 58, 521-535) and molecular structures of surfactants are the dominant factors shaping their structures in the systems. With this simplification, we are able to simulate with moderate computing cost the whole process of micelle formation from an initially uniform dispersion of sodium dodecyl sulfate (SDS) in aqueous solution. The resulting micelle structures are different from those predicted by atomistic simulations that started with a predefined micelle configuration at the same surfactant concentrations. However, if we use their initial micelle configuration, micelle structures the same as theirs are obtained. Analyses show that our results are more realistic and that the results of the atomistic simulations suffer from artificial initial conditions. Therefore, our model may serve as a reasonable simplification of atomistic models in terms of the general structure of micelles.     

Contact Angle Determined by Spontaneous Imbibition in Porous Media: Experiment and Theory

In this paper, a theoretical model was established to determine the contact angle by introducing a new defined effective capillary radius into the Lucas–Washburn equation. Based on the theoretical model, capillary rise experiments of water imbibed by different glass beads were carried out to measure the contact angle; the results were similar to the available data published in the literature. In addition, the model was modified to take account of the dynamic contact angle, according to the experimental data. The influence of the dynamic contact angle on the movement of the spontaneous imbibition was studied.