Nanofiltration Mass Transfer at the Entrance Region of a Slit Laminar Flow

Abstract

A numerical model to predict laminar flows hydrodynamics and concentration polarization of salt aqueous solutions in a slit is proposed and experimentally validated. Physical modeling for the flow and for the mass transfer process is incorporated, in association with the osmotic pressure constitutive equation and a variation law for the membrane intrinsic rejection coefficient. The finite volume formulation is used with the SIMPLE algorithm to solve the discretized equations derived from the partial nonlinear differential equations of the mathematical model. The convection terms of the transport equations are discretized by the second-order hybrid central differences/upwind scheme. The experimental cell is a slit 200 mm × 30 mm × 2 mm that simulates the two-dimensional hydrodynamic flow conditions of the open feed channel of a spiral wound module. The predicted values at the hydrodynamic entrance region for different permeation velocities and rejection coefficients for sodium sulfate solutions, and for a single Schmidt number of 850, are compared against the corresponding experimental values and exhibit an excellent agreement. A new mass transfer correlation St p = 1 + 3.68 × 10-4(x/h)-1.11 Re 0.95 Re p -1.79 is proposed.

Effects of ultrafiltration permeation rates on the hydrodynamics of a minichannel/slit laminar flow

“…8b) and for the permeation flux v p = 1.5×10 −5 m/s. Once the permeation flux is kept unchanged for both cases, the flow develops more slowly, as expected, for the largest value of the circulating Reynolds number, Re = 1000, similarly to what occurred in NF systems described by Geraldes et al (1998). Fig.…”

“…They concluded that, for typical UF permeation velocities ranging from 10 −6 to 10 −5 m/s, suction has no significant effects and the hydrodynamic entrance length is practically invariant. Geraldes et al (1998) and performed a set of numerical simulations for the asymmetric nanofiltration (NF) in a slit, in order to evaluate the effect of permeation rates on the hydrodynamic entrance length and on the momentum and concentration boundary layer growth. They concluded that the typical permeation velocities encountered in NF do not affect the hydrodynamic boundary layer development, i.e., the entrance length does not vary with the permeation velocity, although it may affect the onset of the concentration boundary layer.…”

Tailoring the enzymatic synthesis and nanofiltration fractionation of galacto-oligosaccharides

“…The tangential flow filtrations were performed in a cell unit described previously [23] with a slit-type (20 cm × 3 cm × 0.2 cm) feed channel and an effective membrane area of 60 cm 2 . The membranes were first compacted through pure water recirculation at a pressure of 30 bar for 3 h and characterized through the determination of the hydraulic permeabilities, observed retentions to reference solutes, R obs, and MWCO.…”

The role of adsorption on nanofiltration of azo dyes

“…The Grober equation is an empirical correlation, but it can also be obtained from the boundary layer model that assumes an impermeable wall and low mass transfer rates. Geraldes et al [25,26], have shown that the momentum boundary layer growth is independent of the permeation fluxes in the range of interest of nanofiltration (0.2 × 10 −5 m/s < J v < 3 × 10 −5 m/s). Therefore, those assumptions do not influence the hydrodynamics boundary layer, and Eq.…”