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An investigation is made into the moving contact line dynamics of a Cahn-Hilliardvan der Waals (CHW) diffuse mean-field interface. The interface separates two incompressible viscous fluids and can evolve either through convection or through diffusion driven by chemical potential gradients. The purpose of this paper is to show how the CHW moving contact line compares to the classical sharp interface contact line. It therefore discusses the asymptotics of the CHW contact line velocity and chemical potential fields as the interface thickness and the mobility κ both go to zero. The CHW and classical velocity fields have the same outer behaviour but can have very different inner behaviours and physics. In the CHW model, wall-liquid bonds are broken by chemical potential gradients instead of by shear and change of material at the wall is accomplished by diffusion rather than convection. The result is, mathematically at least, that the CHW moving contact line can exist even with no-slip conditions for the velocity. The relevance and realism or lack thereof of this is considered through the course of the paper.The two contacting fluids are assumed to be Newtonian and, to a first approximation, to obey the no-slip condition. The analysis is linear. For simplicity most of the analysis and results are for a 90 • contact angle and for the fluids having equal dynamic viscosity µ and mobility κ. There are two regions of flow. To leading order the outer-region velocity field is the same as for sharp interfaces (flow field independent of r) while the chemical potential behaves like r −ξ , ξ = π/2/max{θ eq , π − θ eq }, θ eq being the equilibrium contact angle. An exception to this occurs for θ eq = 90 • , when the chemical potential behaves like ln r/r. The diffusive and viscous contact line singularities implied by these outer solutions are resolved in the inner region through chemical diffusion. The length scale of the inner region is about 10 √ µκ -typically about 0.5-5 nm. Diffusive fluxes in this region are O(1). These counterbalance the effects of the velocity, which, because of the assumed no-slip boundary condition, fluxes material through the interface in a narrow boundary layer next to the wall.The asymptotic analysis is supplemented by both linearized and nonlinear finite difference calculations. These are made at two scales, experimental and nanoscale. The first set is done to show CHW interface behaviour and to test the qualitative applicability of the CHW model and its asymptotic theory to practical computations of experimental scale, nonlinear, low capillary number flows. The nanoscale calculations are carried out with realistic interface thicknesses and diffusivities and with various assumed levels of shear-induced slip. These are discussed in an attempt to evaluate the physical relevance of the CHW diffusive model. The various asymptotic and numerical results together indicate a potential usefullness for the CHW model for calculating and modelling wetting and dewetting flows.

Some model problems are considered in order to investigate wetting failure in liquid–liquid systems. Three geometries are considered, two-dimensional two-phase shear flow, two-dimensional driven capillary rise, and both two- and three-dimensional two-phase driven cavity flow. In the first two cases, the two fluids are made equiviscous. The driven cavity flow is investigated for both equi- and non-equiviscous fluids. Three methods of analysis are used for the equiviscous case, an essentially exact Fourier series method, a quasi-parallel approximation and a phase-field model. The Fourier series validates the phase-field method in that they both give nearly identical results for onset of instability. At relatively large slip length divided by channel width ($10^{-2}$), the capillary number at which onset of wetting failure (entrainment of the receding fluid in the advancing) occurs is highly dependent on the type of flow. This dependence, however, appears to diminish rapidly as the slip length becomes smaller. The capillary number for the onset of instability is moderately dependent on gravity level.Three-dimensional phase-field calculations are then discussed that show wetting failure through tipstreaming and splitting instabilities. Spot checks indicate that the onset points of two- and three-dimensional instabilities are very close. It is hypothesized that tipstreaming can be understood in part as a quasi-two-dimensional phenomenon.

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We report observations of a new electric field-and shear-induced many-body phenomenon in the behavior of suspensions. Its origin is dielectrophoresis accompanied by the field-induced phase separation. As a result, a suspension undergoes a field-driven phase separation leading to the formation of a distinct boundary between regions enriched with and depleted of particles. The theoretical predictions are consistent with experimental data even though the model contains no fitting parameters. It is demonstrated that the field-induced dielectrophoresis accompanied by the phase separation provides a new method for concentrating particles in focused regions and for separating biological and non-biological materials, a critical step in the development of miniaturizing biological assays.