Philippe Schmitz

A new Navier-Stokes and Darcy's law combined model for fluid flow in crossflow filtration tubular membranes

Numerical simulations were performed for laminar fluid flow in a porous tube with variable wall suction, a model of a crossflow filtration tubular membrane. The variable wall suction is described by Darcys law, which relates the pressure gradient within a flow stream to the flow rates through the permeable wall. The feed stream in the tube, which flows mainly tangentially to the porous wall, is modelled by the Navier-Stokes equations. A method of coupling the Navier-Stokes and the Darcy equations in a solution scheme was considered to develop a fluid dynamic model of crossflow filtration. The governing equations were solved numerically using a finite difference scheme. The solution depends on both the Reynolds axial and filtration number. Some assumptions adopted in simplified models are discussed.

Hydrodynamic aspects of filtration antifouling by helically corrugated membranes

Abstract The important problem of fouling encountered in micro- and ultrafiltration can be drastically reduced by promoting turbulence close to the surface of the membrane. To this purpose, we have developed a new ceramic tubular membrane geometry with a helical relief stamp at the membrane surface in order to maintain a high level of turbulence close to the surface during filtration. Microfiltration tests showed the efficiency of these new membranes and the effect of the stamp features. However, the actual mechanisms involved by this helical relief are still unclear. Therefore, this hydrodynamic study was carried out to improve our knowledge both on antifouling phenomenon and on the effect of the helical relief stamp on turbulence. The flow structure along a regular helical roughness and the flow disturbance induced by an inversion of the helix direction were characterized by flow visualization and laser Doppler anemometry measurements.

Particle Deposition in Porous Media: Analysis of Hydrodynamic and Weak Inertial Effects

We have studied the transport and capture of non-Brownian particles in porous media, when the particles are mainly submitted to hydrodynamic and weak inertial effects. Visualization experiments have been performed using several models of porous media which consist of transparent etched networks of interconnected channels. Typical particle deposits have been observed at the corners of the grains of the porous medium. Their shape and their orientation were dependent on flow rate and on the anisotropy of the flow field. A trajectory analysis model has been applied to a porous medium made of a doubly periodic array of rectangular grains very close to the experimental model. This numerical model has been used to localize particle deposits and to determine particle capture efficiency on the grains over a range of low Stokes numbers, grain aspect ratios and flow-field anisotropy ratios. The results have been interpreted in terms of shape of particle deposits and compared successfully to experimental observations.

Particle transport and capture at the membrane surface in cross-flow microfiltration

The behavior of suspended particles at the proximity of the membrane in cross-flow microfiltration is studied to better understand how the first layer of particle deposit is built at the membrane surface. The membrane model is a 3D spatially bi-periodic porous surface with circular holes of finite thickness. A semi-analytical model based on a thin screen assumption for fluid flow calculation and on correction factors to Stokes law for drag force is used to compute the particle trajectory. First, the trajectories given by this simplified model compare favorably to trajectories obtained using a complete model based on a boundary element method to compute the Stokes flow in the domain in the presence of the particle at each time step. Second the simplified model is applied to determine the capture probability density function at the membrane surface from trajectory impact points. The effect of membrane porosity, capture distance and wall shear rate are then discussed. Finally the trajectories of one single particle and a couple of particles given by the complete model are analyzed.

Particle aggregation at the membrane surface in crossflow microfiltration

Abstract We present a theoretical model which describes particle accumulation at a membrane surface during a crossflow microfiltration operation. We define empirical but realistic mechanisms for the motion and adhesion of suspended particles. These mechanisms take into account the complex balance of forces to which all particles are subjected in the proximity of the membrane. The model proposed here allows us to generate particle aggregates by a statistical method. We first characterize the influence of the model parameters on the morphology of the aggregates. Then we assign the appropriate values to simulate aggregates analogous to those occurring in crossflow microfiltration. Furthermore we perform a comparison with experimental measurements.

On the apparent permeability of a porous layer backed by a perforated plate

Two-dimensional slow viscous flow from a fluid reservoir, through a porous layer and then through a perforated plate is studied assuming Stokes flow in the fluid reservoir and Darcy flow within the porous medium. It is first shown that the coupled Stokes/Darcy problem can be reduced to a Darcy problem when the various length scales are constrained such that Darcys law is appropriate to describe flow in the porous layer in the vicinity of the perforations of the plate. The apparent permeability of the porous layer is studied as a function of the (uniform) thickness of the layer, and as a function of the size and spacing of the performations in the plate. The apparent permeability is shown to be significantly lower than the intrinsic permeability of the porous layer when the layer is sufficiently thin. Closed-form expressions for the apparent permeability are derived using conformal transformation techniques. We then present a model of particle deposition onto the perforated plate. The growth of the porous layer resulting from the deposition is studied, as is the evolution of its apparent permeability.

Particle capture in porous media when physico-chemical effects dominate

The transport and capture of particles in porous media when the particles are submitted to hydrodynamics and physico-chemical effects were studied. Visualization experiments were performed using a porous media model consisting of a transparent, etched network of interconnected channels: particles were micrometric spheres of latex. Typically shaped particle deposits were observed in the pore space of the porous medium, preferentially close to the inlet. Their location depended on flow structure. Macroscopically, the kinetics of fouling were found to vary widely when the mean flow rate and ionic strength changed. The results have been intrepreted in terms of permeability and effluent concentration. In addition, a specific parameter, named apparent deposit area, was used to quantify and compare the whole images of particle deposition in the porous medium recorded during the experiments. Suprisingly, the apparent deposit area at the inlet correlates very well to the permeability.

Hydrodynamic aspects of crossflow microfiltration. Analysis of particle deposition at the membrane surface

Abstract During a crossflow microfiltration operation, particle deposition is the first, and one of the major reasons, for flux reduction and fouling. The hydrodynamic field at the proximity of the filter surface is determined and discussed under various filtration conditions. A two-dimensional finite-element model is developed in order to compute the fluid flow near one or several square pores uniformly distributed on a flat plate modelling the membrane surface. This study at pore level confirms the existence of two flow structures which determine the possibility of particle deposition. Finally a simplified model of particle trajectories is proposed. The balance of forces takes into account Van der Waals and Stokes forces. Results show the particle deposition on the membrane surface.

Mineral membranes made of sintered clay: application to crossflow microfiltration

New mineral membranes made of sintered clay were performed and characterized in terms of porosity, hydraulic resistance, pore diameter and mechanical resistance. These membranes can be used as microfiltration membranes. The variations of the filtrate flux as a function of time are measured during crossflow microfiltration operations of dilute suspensions of bentonite and talc, for different transmembrane pressure values and mean flow rates. Four membranes of different porosities are tested. Then, we show that the clay membranes can be used in different applications such as water treatment and membrane bioreactor, according to the average pore diameter.

Removal forces and adhesion properties of Saccharomyces cerevisiae on glass substrates probed by optical tweezer

In agroindustry, the hygiene of solid surfaces is of primary importance in order to ensure that products are safe for consumers. To improve safety, one of the major ways consists in identifying and understanding the mechanisms of microbial cell adhesion to nonporous solid surfaces or filtration membranes. In this paper we investigate the adhesion of the yeast cell Saccharomyces cerevisiae (about 5 mum in diameter) to a model solid surface, using well-defined hydrophilic glass substrates. An optical tweezer device developed by Piau [J. Non-Newtonian Fluid Mech. 144, 1 (2007)] was applied to yeast cells in contact with well-characterized glass surfaces. Two planes of observation were used to obtain quantitative measurements of removal forces and to characterize the corresponding mechanisms at a micrometer length scale. The results highlight various adhesion mechanisms, depending on the ionic strength, contact time, and type of yeast. The study has allowed to show a considerable increase of adhering cells with the ionic strength and has provided a quantitative measurement of the detachment forces of cultured yeast cells. Force levels are found to grow with ionic strength and differences in mobility are highlighted. The results clearly underline that a microrheological approach is essential for analyzing the adhesion mechanisms of biological systems at the relevant local scales.