Fouling layer growth and distribution at the interface of pressure-driven membranes

Migration of settling particles in a horizontal viscous flow through a vertical slot with porous walls

“…However, v l is nearly constant for the walls of low permeability (Bentrcia and Drew, 1990). In this case the fluid velocity v à ¼ ðu à ; v à ; w Ã Þ in a channel is sought in the form (Berman, 1953):…”

“…In many applications, e.g., cross-flow membrane filtration (Altena and Belfort, 1984;Bentrcia and Drew, 1990;Drew et al, 1991), a transport of proppant particles in a hydraulic fracture (Hammond, 1995), the flow is bounded by permeable walls, and the migration occurs also due to fluid leak-off through the walls. The relative importance of inertial lift and drag due to leak-off was studied for the lateral migration of inertialess neutrally-buoyant particles in the channel flows with one (Altena and Belfort, 1984) and two (Drew et al, 1991) porous walls.…”

Mathematical Modeling of the Flow of a Multiphase Heterogeneous Medium in a Permeable Tube

“…The hydrodynamics of such flows has been studied in a large number of theoretical and experimental works. In some of them [1], ideas of hydraulics were used, while, in others [2][3][4][5][6][7][8][9], a sought function was expanded in a series in powers of a small parameter in order to solve the Navier-Stokes equation. This equation was also solved by the Laplace integral transform method [5], which was then developed further [10,11].…”

“…This equation was also solved by the Laplace integral transform method [5], which was then developed further [10,11]. In addition, the problem under consideration has also been solved using the method of integral relations [7,12,13], grid methods [14], the energy equation [15], transformation to self-similar variables [16], etc.…”

“…The results of numerous works were generalized in a monograph [10]. The formation and growth of a deposit layer and its effect on the dynamic characteristics of the flow were also studied [7,13,17]. In all the above works [1][2][3][4][5][6][7][8][10][11][12][13][14][15][16][17], the rheological state of the liquid medium is supposed to be linear.…”