David Jacqmin

Contact-line dynamics of a diffuse fluid interface

An investigation is made into the moving contact line dynamics of a Cahn–Hilliard–van 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 e 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.

Combined field-induced dielectrophoresis and phase separation for manipulating particles in microfluidics

Experiments were conducted in microfluidics equipped with dielectrophoretic gates arranged perpendicular to the flow. Under the action of a high-gradient ac field and shear, flowing suspensions were found to undergo a phase separation and to form a distinct front between the regions enriched with and depleted of particles. We demonstrate that this many-body phenomenon, which originates from interparticle electrical interactions, provides a method for concentrating particles in focused regions and for separating biological and nonbiological materials. The evolution of the particle patterns formation is well described by a proposed electrohydrodynamic model.

Onset of wetting failure in liquid–liquid systems

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

Non-parallel effects in the instability of Long's vortex

As shown in Foster & Smith (1989), at large flow force M , Longs self-similar vortex is in the form of a swirling ring-jet, whose axial velocity profile is of sech 2 form. At azimuthal wavenumber n of comparable order to the axial wavenumber, linear helical modes of instability are essentially those of the Bickley jet varicose and sinuous modes. However, at small axial wavenumbers, the three-dimensionality of the vortex is important, and the instabilities depend heavily on the effects of the swirl. We explore here the effects of finite Reynolds number Re on these long-wave inertial modes. It is shown that, because the radial velocity scales with Re −1 M , the non-parallelism of the flow is more important than the viscous terms in determining the finite- Re behaviour. The three-layer structure of the parallel-flow instability modes remains, but with a critical layer considerably modified by radial velocity. In investigating the critical range Re = O ( M 3 ), we find the following: for n > 1, the non-parallelism stabilizes the unstable inertial modes, leading to determination of neutral curves; for n n > 1 case requires a computational scheme that accounts for the presence of viscosity. It turns out that the n n > − 1) modes are prograde (retrograde) with respect to the rotation of the main vortex.

Very, very fast wetting

Just after formation, optical fibers are wetted stably with acrylate at capillary numbers routinely exceeding 1000. It is hypothesized that this is possible because of dissolution of air into the liquid coating. A lubrication/boundary integral analysis that includes gas diffusion and solubility is developed. It is applied using conservatively estimated solubility and diffusivity coefficients and solutions are found that are consistent with industry practice and with the hypothesis. The results also agree with the claim of Deneka, Kar & Mensah (1988) that the use of high solubility gases to bathe a wetting line allows significantly greater wetting speeds. The solutions indicate a maximum speed of wetting which increases with gas solubility and with reduction in wetting-channel diameter.

Instabilities caused by oscillating accelerations normal to a viscous fluid-fluid interface

Two incompressible viscous fluids with different densities meet at a planar interface. The fluids are subject to an externally imposed oscillating acceleration directed normal to the interface. The resulting basic-state flow is motionless with an internal pressure oscillation. We discuss the linear evolution of perturbations to this basic state. General viscosities and densities for the two fluids are considered but a Boussinesq equal-viscosity approximation is discussed in particular detail. For this case we show that the linear evolution of a perturbation to the interface subject to an arbitrary oscillating acceleration is governed by a single integro-differential equation. We apply a Floquet analysis to the fluid system for the case of sinusoidal forcing. Parameter regions of subharmonic, harmonic, and untuned modes are delineated. The critical Stokes-Reynolds number is found as a function of the surface tension and the difference in density and viscosity between the two fluids. The most unstable perturbation wavelengths are determined. For zero surface tension these are found to be short, on the order of a small multiple of the Stokes viscous lengthscale. The critical Stokes-Reynolds number and the most unstable perturbation wavelengths are found to be insensitive to the degree of density and viscosity differences between the two fluids.

Stability of an oscillated fluid with a uniform density gradient

We consider instabilities in a fluid with a constant density gradient that is subject to arbitrarily oriented oscillatory accelerations. With the Boussinesq approximation and for the case of an unbounded fluid, transformation to Lagrangian coordinates allows the reduction of the problem to an ordinary differential equation for each three-dimensional wavenumber. The problem has three parameters: the non-dimensional amplitude R of the base-state oscillation, the non-dimensional level of background steady acceleration, which for some cases can be represented in terms of a local (in time) Richardson number Ri , and the Prandtl number Pr. Some general bounds on stability are derived. For Pr = 1 closed-form solutions are found for impulse (delta function) accelerations and a general asymptotic solution is constructed for large R and general imposed accelerations. The asymptotic solution takes advantage of the fact that at large R wave growth is concentrated at ‘zero points’. These are times when the effective vertical wavenumber passes through zero. Kelvin–Helmholtz instabilities are found to dominate at low R while Rayleigh–Taylor instabilities dominate at high. At high R , the uniform shear of the Kelvin–Helmholtz case tends to distort and weaken instability waves. With unsteady flows, Ri = ¼ is no longer an instability limit. Significant instabilities have been found for sinusoidal forcing for Ri up to 0.6.

Frontogenesis driven by horizontally quadratic distributions of density

Attention is given to the quadratic density distribution in a channel, which has been established by Simpson and Linden to be the simplest case of the horizontally nonlinear distribution of fluid density required for the production of frontogenesis. The porous-media and Boussinesq flow models are examined, and their evolution equations are reduced to one-dimensional systems. While both the porous-media and the inviscid/nondiffusive Boussinesq systems exhibit classic frontogenesis behavior, the viscous Boussinesq system exhibits a more complex behavior: boundary-layer effects force frontogenesis away from the lower boundary, and at late times the steepest density gradients are close to mid-channel.

Conveyor-belt method for assembling microparticles into large-scale structures using electric fields

The authors propose and experimentally demonstrate a conveyor-belt method appropriate for building large-scale microparticle structures by sequentially energizing electrodes to aggregate the particles into predetermined locations and then to translate them collectively to a work area for final assembly. This approach employs collective phenomena in a negatively polarized suspension exposed to a high-gradient strong ac electric field.

Very Fast Wetting In The Presence Of Soluble Gases

An integro-differential equation is derived that describes the flow of a soluble gas in the half cusp formed at a 1800 high-speed wetting line. Calculations made using this equation show that diffusion of the gas into the liquid is a significant mechanism for alleviating stresses. The ameliorating effects of slip and Knudsen diffusion are also considered. Results suggest that bathing a wetting line with high-solubility gas will allow significantly faster wetting speeds.