Influence of Membrane Vibration on Particles Rejection Using a Slotted Pore Membrane Microfiltration.

A new method is proposed to increase the rejection in microfiltration by applying membrane oscillation, using a new type of microfiltration membrane with slotted pores. The oscillations applied to the membrane surface result in reduced membrane fouling and increased separation efficiency. An exact mathematical solution of the flow in the surrounding solution outside the oscillating membrane is developed. The oscillation results in the appearance of a lift velocity, which moves oil particles away from the membrane. The latter results in both reduced membrane fouling and increased oil droplet rejection. This developed model was supported by the experimental results for oil water separation in the produced water treatment. It was proven that the oil droplet concentration was reduced notably in the permeate, due to the membrane oscillation, and that the applied shear rate caused by the membrane oscillation also reduced pore blockage. A four-times lower oil concentration was recorded in the permeate when the membrane vibration frequency was 25 Hz, compared to without membrane vibration. Newly generated microfiltration membranes with slotted pores were used in the experiments.

Foam drainage placed on a thin porous layer.

Drainage of foams placed on porous substrates has only recently been theoretically investigated (O. Arjmandi-Tash, N. Kovalchuk, A. Trybala, V. Starov, Foam Drainage Placed on a Porous Substrate, Soft Matter, 2015, 11(18), 3643-3652), where an equation describing foam drainage (with non-slip boundary conditions on the liquid-air interfaces) was combined with that of imbibition of liquid into the thick porous substrate. Foam-based applications have been used as a method of drug delivery, which is a recent and promising area of research related to application of medicinal products onto the skin or hair, which are both thin porous layers. A theory of foam drainage (taking into account surface viscosity) placed on a completely wettable thin porous layer is developed: the rate of foam drainage and imbibition inside the porous layer and other characteristics of the process are predicted. The "effective slip" caused by the surface viscosity increased a movement of the top boundary of the foam. The theoretical predictions are compared with experimental observations of foam drainage placed on thin porous layers. The comparison showed a reasonable agreement between the theoretical predictions and experimental observations. One of the phenomena during foam application is the possibility of a build-up of a free liquid layer on the foam/porous layer interface, which can be very useful for applications. Three different regimes of spreading/imbibition process have been predicted. Conditions and durations of free liquid layer formation have been theoretically predicted and compared with experimental observations.

Equilibrium Droplets on Deformable Substrates: Equilibrium Conditions.

Equilibrium conditions of droplets on deformable substrates are investigated, and it is proven using Jacobi's sufficient condition that the obtained solutions really provide equilibrium profiles of both the droplet and the deformed support. At the equilibrium, the excess free energy of the system should have a minimum value, which means that both necessary and sufficient conditions of the minimum should be fulfilled. Only in this case, the obtained profiles provide the minimum of the excess free energy. The necessary condition of the equilibrium means that the first variation of the excess free energy should vanish, and the second variation should be positive. Unfortunately, the mentioned two conditions are not the proof that the obtained profiles correspond to the minimum of the excess free energy and they could not be. It is necessary to check whether the sufficient condition of the equilibrium (Jacobi's condition) is satisfied. To the best of our knowledge Jacobi's condition has never been verified for any already published equilibrium profiles of both the droplet and the deformable substrate. A simple model of the equilibrium droplet on the deformable substrate is considered, and it is shown that the deduced profiles of the equilibrium droplet and deformable substrate satisfy the Jacobi's condition, that is, really provide the minimum to the excess free energy of the system. To simplify calculations, a simplified linear disjoining/conjoining pressure isotherm is adopted for the calculations. It is shown that both necessary and sufficient conditions for equilibrium are satisfied. For the first time, validity of the Jacobi's condition is verified. The latter proves that the developed model really provides (i) the minimum of the excess free energy of the system droplet/deformable substrate and (ii) equilibrium profiles of both the droplet and the deformable substrate.

Hysteresis of the Contact Angle of a Meniscus Inside a Capillary with Smooth, Homogeneous Solid Walls.

A theory of contact angle hysteresis of a meniscus inside thin capillaries with smooth, homogeneous solid walls is developed in terms of surface forces (disjoining/conjoining pressure isotherm) using a quasi-equilibrium approach. The disjoining/conjoining pressure isotherm includes electrostatic, intermolecular, and structural components. The values of the static receding θr, advancing θa, and equilibrium θe contact angles in thin capillaries were calculated on the basis of the shape of the disjoining/conjoining pressure isotherm. It was shown that both advancing and receding contact angles depend on the capillary radius. The suggested mechanism of the contact angle hysteresis has a direct experimental confirmation: the process of receding is accompanied by the formation of thick ß-films on the capillary walls. The effect of the transition from partial to complete wetting in thin capillaries is predicted and analyzed. This effect takes place in very thin capillaries, when the receding contact angle decreases to zero.

Spreading of a Lidocaine Formulation on Microneedle-Treated Skin.

The spreadability of a liquid drug formulation on skin is an indication of it either remaining stationary or distributing (spreading) as a droplet. Factors determining droplet spreadability of the formulation are spreading area, diameter of the droplet base, viscosity of the liquid, contact angle, volume of droplet on skin and any others. The creation of microcavities from the application of microneedle (MN) has the potential to control droplet spreading, and hence, target specific areas of skin for drug delivery. However, there is little work that demonstrates spreading of liquid drug formulation on MN-treated skin. Below, spreading of a lidocaine hydrogel formulation and lidocaine solution (reference liquid) on porcine skin is investigated over MN-treated skin. Controlled spreadability was achieved with the lidocaine hydrogel on MN-treated skin as compared with lidocaine solution. It was observed that the droplet spreading parameters such as spreading radius, droplet height and dynamic contact angle were slightly lower for the lidocaine hydrogel than the lidocaine solution on skin. Also, the lidocaine hydrogel on MN-treated skin resulted in slower dynamic reduction of droplet height, contact angle and reduced time taken in attaining static advancing droplets because of the MN microcavities.

Spreading of blood drops over dry porous substrate: complete wetting case.

HYPOTHESIS: The process of dried blood spot sampling involves simultaneous spreading and penetration of blood into a porous filter paper with subsequent evaporation and drying. Spreading of small drops of blood, which is a non-Newtonian liquid, over a dry porous layer is investigated from both theoretical and experimental points of view. EXPERIMENTS AND THEORY: A system of two differential equations is derived, which describes the time evolution of radii of both the drop base and the wetted region inside the porous medium. The system of equations does not include any fitting parameters. The predicted time evolutions of both radii are compared with experimental data published earlier. FINDINGS: For a given power law dependency of viscosity of blood with different hematocrit level, radii of both drop base and wetted region, and contact angle fell on three universal curves if appropriate scales are used with a plot of the dimensionless radii of the drop base and the wetted region inside the porous layer and dynamic contact angle on dimensionless time. The predicted theoretical relationships are three universal curves accounting satisfactorily for the experimental data.

Modeling the effect of surface forces on the equilibrium liquid profile of a capillary meniscus.

The equilibrium profile of a capillary meniscus formed under combined action of disjoining/conjoining and capillarity pressures is investigated. Attention is focused on the shape of a transition zone between a spherical meniscus and a thin liquid film in front of the meniscus. The Poisson-Boltzmann equation is used for calculations of electrostatic contribution to the disjoining/conjoining pressure and the liquid shape inside the transition zone. Both complete and partial wetting conditions are investigated.

Particle laden fluid interfaces: dynamics and interfacial rheology.

We review the dynamics of particle laden interfaces, both particle monolayers and particle+surfactant monolayers. We also discuss the use of the Brownian motion of microparticles trapped at fluid interfaces for measuring the shear rheology of surfactant and polymer monolayers. We describe the basic concepts of interfacial rheology and the different experimental methods for measuring both dilational and shear surface complex moduli over a broad range of frequencies, with emphasis in the micro-rheology methods. In the case of particles trapped at interfaces the calculation of the diffusion coefficient from the Brownian trajectories of the particles is calculated as a function of particle surface concentration. We describe in detail the calculation in the case of subdiffusive particle dynamics. A comprehensive review of dilational and shear rheology of particle monolayers and particle+surfactant monolayers is presented. Finally the advantages and current open problems of the use of the Brownian motion of microparticles for calculating the shear complex modulus of monolayers are described in detail.

Evaporation of droplets of surfactant solutions.

The simultaneous spreading and evaporation of droplets of aqueous trisiloxane (superspreader) solutions onto a hydrophobic substrate has been studied both experimentally, using a video-microscopy technique, and theoretically. The experiments have been carried out over a wide range of surfactant concentration, temperature, and relative humidity. Similar to pure liquids, four different stages have been observed: the initial one corresponds to spreading until the contact angle, θ, reaches the value of the static advancing contact angle, θad. Duration of this stage is rather short, and the evaporation during this stage can be neglected. The evaporation is essential during the next three stages. The next stage after the spreading, which is referred to herein as the first stage, takes place at constant perimeter and ends when θ reaches the static receding contact angle, θr. During the next, second stage, the perimeter decreases at constant contact angle θ = θr for surfactant concentration above the critical wetting concentration (CWC). The static receding contact angle decreases during the second stage for concentrations below CWC because the concentration increases due to the evaporation. During the final stage both the perimeter and the contact angle decrease. In what follows, we consider only the longest stages I and II. The developed theory predicts universal curves for the contact angle dependency on time during the first stage, and for the droplet perimeter on time during the second stage. A very good agreement between theory and experimental data has been found for the first stage of evaporation, and for the second stage for concentrations above CWC; however, some deviations were found for concentrations below CWC.

Evaporation kinetics of sessile droplets of aqueous suspensions of inorganic nanoparticles.

Evaporation kinetics of sessile droplets of aqueous suspension of inorganic nanoparticles on solid substrates of various wettabilities is investigated from both experimental and theoretical points of view. Experimental results on evaporation of various kinds of inorganic nanosuspensions on solid surfaces of different hydrophobicities/hydrophilicities are compared with our theoretical predictions of diffusion limited evaporation of sessile droplets in the presence of contact angle hysteresis. The theory describes two main stages of evaporation process: (I) evaporation with a constant radius of the droplet base when the contact angle decreases from static advancing contact angle down to static receding contact angle and (II) evaporation with constant contact angle equal to the static receding contact angle when the radius of the droplet base decreases. Theoretically predicted universal dependences for both evaporation stages are compared with experimental data, and a very good agreement is found.

Computer simulations of evaporation of pinned sessile droplets: influence of kinetic effects.

The aim of the current work is to present results of computer simulations, which show the influence of kinetic effects on evaporation of pinned sessile water droplets of submicrometer size placed on a heat conductive substrate. The computer simulation model also takes into account the following phenomena: influence of curvature of the droplet's surface on saturated vapor pressure above the surface (Kelvin's equation), the effect of latent heat of vaporization, thermal Marangoni convection, and Stefan flow inside an air domain above the droplet. The suggested model combines both diffusive and kinetic models of evaporation. The obtained results allow the characteristic droplet sizes to be estimated, where each of the mentioned above phenomena becomes important or can be neglected.

Influence of the molecular architecture on the adsorption onto solid surfaces: comb-like polymers.

The processes of adsorption of grafted copolymers onto negatively charged surfaces were studied using a dissipative quartz crystal microbalance (D-QCM) and ellipsometry. The control parameters in the study of the adsorption are the existence or absence on the molecular architecture of grafted polyethyleneglycol (PEG) chains with different lengths and the chemical nature of the main chain, poly(allylamine) (PAH) or poly(L-lysine) (PLL). It was found out that the adsorption kinetics of the polymers showed a complex behavior. The total adsorbed amount depends on the architecture of the polymer chains (length of the PEG chains), on the polymer concentration and on the chemical nature of the main chain. The comparison of the thicknesses of the adsorbed layers obtained from D-QCM and from ellipsometry allowed calculation of the water content of the layers that is intimately related to the grafting length. The analysis of D-QCM results also provides information about the shear modulus of the layers, whose values have been found to be typical of a rubber-like polymer system. It is shown that the adsorption of polymers with a charged backbone is not driven exclusively by the electrostatic interactions, but the entropic contributions as a result of the trapping of water in the layer structure are of fundamental importance.

Surface forces action in a vicinity of three phase contact line and other current problems in kinetics of wetting and spreading.

The most important problem in kinetics of wetting and spreading from the author's point of view is a consideration of combined surface forces and capillary action in a vicinity of the apparent three phase contact line. The latter is equally important at the consideration of static or dynamics. Other current trends in kinetics of wetting and spreading are also briefly reviewed. It is impossible to cover the whole literature on the subject: it was around 5000 publications on that subject in 2009 only and the total number of publication in the area is 65,917 (according to Science Direct). The problems to be solved in the area are marked in italic bold and underlined.

Asymmetry of diffusion permeability of bi-layer membranes.

To reveal the reason of asymmetry of the diffusion permeability of bi-layer electrodialysis membranes the following problems have been solved using the model of "homogeneous porous membrane": - diffusion of non-electrolyte solutions across a bi-layer membrane; - diffusion of electrolyte solutions across a non-charged bi-layer membrane; - diffusion of electrolyte solutions across a charged single layer membrane; - diffusion of electrolyte solutions across a charged bi-layer membrane. It is shown that the main factor responsible for the asymmetry is the difference between absolute values of densities of fixed charges (or so called "exchange capacities") of different layers of a membrane under investigation. Only in this case the ratio of the thickness of the membrane layers as well as the ratio of ion diffusivities contributes also to the asymmetry of the diffusion permeability. In the present review we survey and generalize our previous investigations and propose a new theory of asymmetry of diffusion permeability of bi-layer membranes. We have deduced explicit algebraic formulas for the degree of asymmetry of diffusion permeability of bi-layer membranes under consideration.

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.

Spontaneous rise of surfactant solutions into vertical hydrophobic capillaries.

It has been found earlier (N.V. Churaev, G.A. Martynov, V.M. Starov, Z.M. Zorin, Colloid Polym. Sci. 259 (1981) 747) that aqueous surfactant solutions spontaneously rise in vertical hydrophobized quartz capillaries. A theory of this phenomenon is presented, which connects the experimental observations with the adsorption of surfactant molecules in front of the moving meniscus on the bare hydrophobic interface.

Nonflat equilibrium liquid shapes on flat surfaces.

The hydrostatic pressure in thin liquid layers differs from the pressure in the ambient air. This difference is caused by the actions of surface forces and capillary pressure. The manifestation of the surface force action is the disjoining pressure, which has a very special S-shaped form in the case of partial wetting (aqueous thin films and thin films of aqueous electrolyte and surfactant solutions, both free films and films on solid substrates). In thin flat liquid films the disjoining pressure acts alone and determines their thickness. However, if the film surface is curved then both the disjoining and the capillary pressures act simultaneously. In the case of partial wetting their simultaneous action results in the existence of nonflat equilibrium liquid shapes. It is shown that in the case of S-shaped disjoining pressure isotherm microdrops, microdepressions, and equilibrium periodic films exist on flat solid substrates. Criteria are found for both the existence and the stability of these nonflat equilibrium liquid shapes. It is shown that a transition from thick films to thinner films can go via intermediate nonflat states, microdepressions and periodic films, which both can be more stable than flat films within some range of hydrostatic pressure. Experimental investigations of shapes of the predicted nonflat layers can open new possibilities of determination of disjoining pressure in the range of thickness in which flat films are unstable.

Viscosity of emulsions: influence of flocculation.

A model has been suggested by Raijinder Pal (J. Colloid Interface Sci. 231 (2000) 168) that describes experimental data on the viscosity of concentrated emulsions reasonably well. To deduce the final equation the author assumed that droplets are covered with a layer of surfactant molecules. This means that the effective volume of a single emulsion droplet is increased by a factor K>1. It has been found that K should vary between 1.166 and 2.070 to fit the experimental data. If the drop radii are around 1 microm (for an estimate) then the drops would be covered with a layer which thickness should range from 550 A (which is 10 times of the size of SDS micelles) to 3570 A. No doubt adsorption of surfactant molecules results in an increase of the effective drop radius but not by that much. We present an alternative theoretical model for description of the viscosity-volume fraction of droplets behavior of emulsions. The model is based on the assumption that clusters of drops (doublets, triplets, and so on) are formed under the influence of colloidal, hydrodynamic interactions and/or applied shear. According to the proposed model clustering determines the volume fraction dependency of the effective viscosity of emulsions. Two limiting cases are considered: a developed flocculation and a low-flocculated emulsion. In the first case the final equation is close to that deduced by Pal; however, the physical meaning of the equation is substantially different. Comparison with available experimental data shows good agreement with the equations deduced in both the cases of a developed flocculation and a low-flocculated emulsion.