Optohydrodynamics of soft fluid interfaces : Optical and viscous nonlinear effects

Recent experimental developments showed that the use of the radiation pressure, induced by a continuous laser wave, to control fluid-fluid interface deformations at the microscale, represents a very promising alternative to electric or magnetic actuation. In this article, we solve numerically the dynamics and steady state of the fluid interface under the effects of buoyancy, capillarity, optical radiation pressure and viscous stress. A precise quantitative validation is shown by comparison with experimental data. New results due to the nonlinear dependence of the optical pressure on the angle of incidence are presented, showing different morphologies of the deformed interface going from needle-like to finger-like shapes, depending on the refractive index contrast. In the transient regime, we show that the viscosity ratio influences the time taken for the deformation to reach steady state

Critical slowing down and fading away of the piston effect in porous media

We investigate the critical speeding up of heat equilibration by the piston effect (PE) in a nearly supercritical van der Waals (vdW) fluid confined in a homogeneous porous medium. We perform an asymptotic analysis of the averaged linearized mass, momentum and energy equations to describe the response of the medium to a boundary heat flux. While nearing the critical point (CP), we find two universal crossovers depending on porosity, intrinsic permeability and viscosity. Closer to the CP than the first crossover, a pressure gradient appears in the bulk due to viscous effects, the PE characteristic time scale stops decreasing and tends to a constant. In infinitly long samples the temperature penetration depth is larger than the diffusion one indicating that the PE in porous media is not a finite size effect as it is in pure fluids. Closer to the CP, a second cross over appears which is characterized by a pressure gradient in the thermal boundary layer (BL). Beyond this second crossover, the PE time remains constant, the expansion of the fluid in the BL drops down and the PE ultimately fades away

Eddies and interface deformations induced by optical streaming

We study flows and interface deformations produced by the scattering of a laser beam propagating through non-absorbing turbid fluids. Light scattering produces a force density resulting from the transfer of linear momentum from the laser to the scatterers. The flow induced in the direction of the beam propagation, called 'optical streaming', is also able to deform the interface separating the two liquid phases and to produce wide humps. The viscous flow taking place in these two liquid layers is solved analytically, in one of the two liquid layers with a stream function formulation, as well as numerically in both fluids using a boundary integral element method. Quantitative comparisons are shown between the numerical and analytical flow patterns. Moreover, we present predictive simulations regarding the effects of the geometry, of the scattering strength and of the viscosities, on both the flow pattern and the deformation of the interface. Finally, theoretical arguments are put forth to explain the robustness of the emergence of secondary flows in a two-layer fluid system

Transport of species in a fibrous media during tissue growth

Tissue engineering is of major importance in biomedical transplantation techniques. However, some questions subsist as for example the mass transport between each pahse (cell, fluide and solid). In a previous paper, a one-equation model was developed in order to model mass transport during in vitro tissue growth using the volume averaging method. Using a dimensionless form of the model and a convenient formulation of the effective dispersion tensor, a numerical resolution of the closure problem is proposed. Some results allowing to validate the numerical tool are presented. This validation is carried out using results available in the literature for 2-D unit cells and under-classes of our model (namely diffusion, diffusion/reaction and diffusion/advection problems). Finally, we provide some results for the complete model taking into account diffusion, reaction and advection in the three phase system

Résolution numérique de l’écoulement diphasique en milieu poreux hétérogène incluant les effets inertiels

La mise en place d'un outil numérique 3D de simulation d'écoulement diphasique hors régime de Darcy basé sur le modèle de Darcy-Forchheimer généralisé est présentée. L'outil est tout d’abord validé à l’aide d'une solution semi analytique 1D de type Buckley-Leverett. Des résultats obtenus dans différentes configurations homogène et hétérogènes 1D et 2D mettent en évidence l'importance des termes inertiels en fonction d'un nombre de Reynolds de l'écoulement

A macroscopic model for immiscible two-phase flow in porous media

This work provides the derivation of a closed macroscopic model for immiscible two-phase, incompressible, Newtonian and isothermal creeping steady flow in a rigid and homogeneous porous medium without considering three-phase contact. The mass and momentum upscaled equations are obtained from the pore-scale Stokes equations, adopting a two-domain approach where the two fluid phases are separated by an interface. The average mass equations result from using the classical volume averaging method. A Green's formula and the adjoint Green's function velocity pair problems are used to obtain the pore-scale velocity solutions that are averaged to obtain the upscaled momentum balance equations. The macroscopic model is based on the assumptions of scale separation and the existence of a periodic representative elementary volume allowing a local description as usually postulated for upscaling. The macroscopic momentum equation in each phase includes the generalized Darcy-like dominant and viscous coupling terms and, importantly, an additional compensation term that accounts for surface tension effects to momentum transfer that is, otherwise, incompletely captured by the Darcy terms. This interfacial term, as well as the dominant and viscous coupling permeability tensors, can be predicted from the solutions of two associated closure problems that coincide with those reported in the literature. The relevance of the compensation term and the upscaled model validity are assessed by comparisons with direct numerical simulations in a model two-dimensional periodic structure. Upscaled model predictions are found to be in excellent agreement with direct numerical simulations

An investigation of inertial one-phase flow in homogeneous model porous media

Our interest in this work is the stationary one-phase Newtonian flow in a class of homogeneous porous media at large enough flow rates requiring the introduction of the inertial forces at the pore-scale. At the macroscale, this implies a nonlinear correction to Darcy's law i.e. a nonlinear between the filtration velocity and the pressure gradient. The objective here is to analyze the nonlinear correction on some periodic models of porous media with respect to the Reynolds number and the pressure gradients orientation relative to the principal axes of the periodic unit cell

An investigation of inertial one-phase flow in homogeneous model porous media

Our interest in this work is the stationary one-phase Newtonian flow in a class of homogeneous porous media at large enough flow rates requiring the introduction of the inertial forces at the pore-scale. At the macroscale, this implies a nonlinear correction to Darcy's law i.e. a nonlinear between the filtration velocity and the pressure gradient. The objective here is to analyze the nonlinear correction on some periodic models of porous media with respect to the Reynolds number and the pressure gradients orientation relative to the principal axes of the periodic unit cell

One-phase flow in porous media: is the Forchheimer correction relevant?

Our interest in this work is dedicated to the dependence upon the filtration velocity (or Reynolds number) of the inertial correction to Darcy's law for one-phase flow in homogeneous porous media. The starting point of our analysis is the averaged flow model operating at Darcy's scale. It shows that the inertial correction to Darcy's law involves a second order tensor that can be determined from the solution of the associated closure problem requiring the microscopic (pore-scale) velocity field. Numerical solutions achieved on 2D model structures are presented. The accent is laid upon the role of the Reynolds number, pressure gradient orientation and structural parameters such as porosity and structural disorder. The Forchheimer type of correction, exhibiting a quadratic dependence upon the filtration velocity, is discussed in different situations

Numerical tools for the simulation of enzymatic bio porous-electrodes operating in DET mode

Modeling of diffusion/enzymatic reaction in porous electrodes operating in direct electron transfer mode is developed. The solution at the pore-scale is extremely cumbersome due to the complex geometry of the porous material. The upscaled model is much easier to solve, while keeping the essential of the physico-chemical behavior. The method to carry out the solution can be described as follows • The effective diffusion coefficient involved in the macroscopic equations is accurately computed by solving a closure problem in a representative elementary volume. • Electrochemical parameters are identified by a direct resolution of the macroscopic model solved with a COMSOL Multiphysics code coupled to a curve fit procedure carried out on voltammetry experimental results using a Matlab code. Electrodes with different thicknesses may be considered in the fitting procedure to improve accuracy. An alternative use of the COMSOL Multiphysics code is to predict the electrode behavior and further optimize its design, if all the electrochemical parameters are identified. • To validate the upscaled model, the pore scale model may be solved with direct numerical simulations carried out in a 3D microstructure using another COMSOL Multiphysics code to compare with the solution of the upscaled model in the 1D-reduced geometry.Modélisation d'électrodes poreuses pour leur conception optimisé