Advances in Water Treatment and Enviromental Management

176 WATER TREATMENTIn this preliminary approach, we are especially interested in the aggregation of a large numberof solid particles from a suspension on a filter surface, encountered in cross-flow ultrafiltrationconditions. Assuming a low concentration of particles in the fluid, we consider that thoseparticles, driven by the flow, appear one by one near the wall. We will suppose the particles tobe spherical and monodispersed.Trajectories of such single particles flowing in the wall region have been precedently determinedby Schmitz et al(1989). taking into account hydrodynamical and physico-chemical forces. Ithas been shown that, in a first order approximation, such trajectories can be consideredlinear, having an incidence angle with the horizontal porous plane surface.Hydrodynamical conditions, physico-chemical and double layer forces, brownian motion,concentration, density and particles shape effects are globally considered in a statisticalsimulation program which is able to perform and furthermore to visualize the deposition ofmicronic particles on a flat porous plate.3.1 Statistical ModelIn a rectangular 2D domain, we inject solid circular particles, one by one, following lineartrajectories from a random initial location far from the wall. They move towards the filter surfacerepresented by a flat plate with rectangular holes. Special moving and sticking rules are proposedto define the behaviour of particles in the flow and when they make contact with the filter orwith another particle already sticking to the wall. Those empirical rules are given to characterizethe respective importance of the different phenomena which occur in the filtration zone.Fig. 3: Particle-particle adhesion rulesAdhesion rulesA particle of center A is immediately stopped when it makes contact with the filter wall. Whenit touches a previously aggregated particle of center B, it is also captured provided that thecenterline (AB) is inside the circular sector defined by the sticking angle 6 as shown in Fig. 3.We then obtain two parameters θ i and θ v which determine respectively adhesion in incidentand vertical directions.Displacement rulesA linear incident way is given to each particle A launched from its initial point, characterizedby the incidence angle a, another parameter of the model. After making contact with a particleof center B, it turns left or right around this particle until reaching a vertical or a new incidenttrajectory and so on. The type of this new direction followed depends on the number ofreentrainment permitted. The number of reentrainments is a parameter which can be choosenfreely and accounts for the maximum number of possible “contacts” before a particle is finallycaptured. The different cases which occurs are detailed in Fig. 4.Filter surfaceThe geometrical characteristics of the filter are taken into account by the porosity parameter Pand by the diameter ratio R d defining the pore size over the particle size. Of course, particles arenot always captured as they can pass the filter if their diameter is smaller than the pore diameter.A realistic deposit on a porous surface is obtained when a multitude of particles move one byone from their initial location to the dynamical collector composed of the filter and the previouslycaptured particles. In this dynamical simulation, the trajectory incidence represents suctionintensity over parallel flow. The magnitudes of the two sticking angles θ i and θ v characterizethe respective importance of perpendicular attractive forces compared to parallelhydrodynamical and perpendicular repulsive forces. The number of reentrainments enhances