Mean-field Density Functional Theory of a Three-Phase Contact Line

A three-phase contact line in a three-phase fluid system is modeled by a mean-field density functional theory. We use a variational approach to find the Euler-Lagrange equations. Analytic solutions are obtained in the two-phase regions at large distances from the contact line. We employ a triangular grid and use a successive over-relaxation method to find numerical solutions in the entire domain for the special case of equal interfacial tensions for the two-phase interfaces. We use the Kerins-Boiteux formula to obtain a line tension associated with the contact line. This line tension turns out to be negative. We associate line adsorption with the change of line tension as the governing potentials change.Comment: 14 pages, 13 figures, submitted to PR

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

This paper was accepted for publication in the journal Langmuir: the ACS journal of surfaces and colloids and the definitive published version is available at http://dx.doi.org/10.1021/acs.langmuir.6b00721.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 β-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

Hysteresis of Contact Angle of Sessile Droplets on Smooth Homogeneous Solid Substrates via Disjoining/Conjoining Pressure

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Langmuir copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://dx.doi.org/10.1021/acs.langmuir.5b01075A theory of contact angle hysteresis of liquid droplets on smooth, homogeneous solid substrates is developed in terms of the shape of the disjoining/conjoining pressure isotherm and quasi-equilibrium phenomena. It is shown that all contact angles, θ, in the range θr < θ < θa, which are different from the unique equilibrium contact angle θ ≠ θe, correspond to the state of slow “microscopic” advancing or receding motion of the liquid if θe < θ < θa or θr < θ < θe, respectively. This “microscopic” motion almost abruptly becomes fast “macroscopic” advancing or receding motion after the contact angle reaches the critical values θa or θr, correspondingly. The values of the static receding, θr, and static advancing, θa, contact angles in cylindrical capillaries were calculated earlier, based on the shape of disjoining/conjoining pressure isotherm. It is shown now that (i) both advancing and receding contact angles of a droplet on a on smooth, homogeneous solid substrate can be calculated based on shape of disjoining/conjoining pressure isotherm, and (ii) both advancing and receding contact angles depend on the drop volume and are not unique characteristics of the liquid–solid system. The latter is different from advancing/receding contact angles in thin capillaries. It is shown also that the receding contact angle is much closer to the equilibrium contact angle than the advancing contact angle. The latter conclusion is unexpected and is in a contradiction with the commonly accepted view that the advancing contact angle can be taken as the first approximation for the equilibrium contact angle. The dependency of hysteresis contact angles on the drop volume has a direct experimental confirmation

Concentration polarization effect at the deposition of charged Langmuir monolayers

The review summarizes the results of the recent studies of the electrokinetic relaxation process within the meniscus region during the deposition of charged Langmuir monolayers. Such electrokinetic relaxation is the consequence of the initial misbalance of partial ion fluxes within a small region near the contact line, where the diffuse parts of electric double layers, formed at the monolayer and the substrate surface, overlap. The concentration polarization within the solution near the three-phase contact line should lead to long-term relaxations of the meniscus after beginning and stopping the deposition process, to changes of the ionic composition within the deposited films, to change of the interaction of the monolayer with the substrate, and to dependence of the maximum deposition rate on the subphase composition

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