PREFERENTIAL ADHESION OF MICRO-PARTICLES ONTO A FILTRATION MEMBRANE UNDER TURBULENT FLOW CONDITIONS Riccardo Maniero, Eric Climent and Patrice Bacchin Laboratoire de Génie Chimique, CNRS-INPT-UPS 5, Rue Paulin Talabot, F-31106 Toulouse University of Toulouse, France Abstract – We investigate numerically the deposition and resuspension of colloidal particles on a filtrating membrane. Physical phenomena such as flow transport, deposition, detachment and re-entrainment have been considered. The turbulent fluid flow has been obtained using Direct Numerical Simulations of the Navier-Stokes equations and the resulting velocity field has been coupled to the Lagrangian tracking of individual particles. Brownian diffusion has also been included and combined with the Lagrangian approach resulting in a stochastic process. Particular attention has been paid to describe and model hydrodynamics and chemical-physics. Interactions between the particles and the membrane have been modelled using sophisticated models for adhesion and detachment. Validations with analytical solutions related to simplified cases and comparisons with are presented as well. Results have been discussed focusing on mechanisms involved in the fouling of filtration membranes. Keywords: filtration, membrane, colloidal particles, numerical simulation, turbulent flow. 1. INTRODUCTION The Physics of transport, deposition, detachment and re-entrainment of colloidal particles suspended in a fluid are of great interest in many areas of fluids Engineering: fouling of heat exchangers, contamination of nuclear reactors, plugging of filtration membranes, occlusion of human veins, deposits in microelectronics and paper industry. Even though many models have been developed to predict these phenomena we are still far from a complete understanding. Indeed there is a lack of predictive models able to consider simultaneously all the phenomena and their interactions. We aim at simulating the convection-diffusion of colloidal particles based on an Eulerian- Lagrangian approach including deposition, detachment and re-entrainment of the particles suspended in a fluid flowing in a turbulent regime. Compared to practical applications, simplified assumptions have been considered (i.e. dilute particle dispersion, absence of electric double layer repulsion, simple geometry…) based on an analysis of critical phenomena. Some fundamental aspects of the Physics are accurately modelled (i.e. Direct Numerical Simulation (DNS) technique to determine the flow field and the wall shear stress. “Optimal stopping” technique is used for the Lagrangian tracking near the wall, JKR model of attachment). 2. DESCRIPTION OF THE PHYSICAL PROPERTIES The reference flow configuration corresponds to cross-flow filtration in tubular or plane ceramic or polymeric membrane (where the distance between filtering surface is classiclay 1 mm ÷ 1 cm). Fundamental aspects of the filtration process have been investigated in the simulations using a simplified geometry as shown in Fig. 1 (parallel porous plate channel with uniform flux across the walls). These simplifications of the geometry have been introduced in order to use periodic boundary conditions (and mass conservation) in the DNS calculations aiming at reducing the computational cost of the simulations. The actual particle diameter is 1 m while the flow Reynolds number is 4000 based on the average flow velocity (1.85m/s) and channel height is 2.2 mm (the wall Reynolds number Re τ = (τ/ρ) 1/2 h/ν =135 where τ is the mean wall shear stress, h the half height of the channel and ν,ρ the kinematic viscosity and density of the fluid); this ensures that the flow is turbulent. The particulate relaxation time (τ p = m p /6πρνr p 2245 1.11 10 -7 s with m p and r p being the mass and radius of the particle) and also the Stokes number (St 2245 4.53 10 -4 which compares the particulate response time to the fluid velocity scale) are small so we can claim that the dispersed phase behave as non-inertial particles. It is important to note that the thickness of the viscous sublayer (δ v 2245 9 10 -6 m) is significantly larger than the particle diameter. Therefore particles are completely embedded in the viscous sublayer. This validates the assumption of point particles. Close to the wall, particles approaching the membrane experience a laminar flow field related to a