scholarly journals NUMERICAL INVESTIGATION OF THE OCCURRENCE OF A CONCENTRATION-POLARIZATION LAYER

2021 ◽  
Vol 18 (2) ◽  
pp. 56-59
Author(s):  
R.K. Manatbayev ◽  
Keyword(s):  
Boundary Layer ◽  
Particle Deposition ◽  
Concentration Polarization ◽  
Membrane Surface ◽  
Porous Wall ◽  
Numerical Approach ◽  
Co2 Gas ◽  
Mixture Concentration ◽  
Lower Permeability ◽  
Concentration Polarization Layer

This work describes the appearance of a concentration polarizing boundary layer on the membrane surface during the separation of the H2/CO2 gas mixture. Concentration polarization occurs when the rejection solution accumulates near the surface of the membrane, forming a boundary layer. The inclusion of concentration polarization effects in the processing of porous walls creates additional difficulties. The boundary layer formed by concentration polarization can be considered as a type of a second porous wall with a lower permeability than the membrane. The main difficulty in modeling this situation is to determine the appropriate boundary conditions for the concentration on the wall, since the concentrations on the wall will constantly change, and the wall geometry itself may change over time due to particle deposition. To account for this effect, a numerical approach was developed, which is discussed in this work

scholarly journals The Effect of the Concentration Polarization and the Membrane Layer Mass Transport on the Membrane Separation

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Endre Nagy ◽  
Gábor Borbély
Keyword(s):  
Boundary Layer ◽  
Mass Transport ◽  
Concentration Polarization ◽  
Membrane Separation ◽  
Separation Efficiency ◽  
Enrichment Factors ◽  
Transport Parameters ◽  
Membrane Layer ◽  
Negative Effect ◽  
Concentration Polarization Layer

The negative effect of the concentration polarization layer on the membrane separation is well known. How the mass transport parameters of the membrane matrix, e.g. the solubility coefficient, membrane Peclet number, can affect the concentration profile of the boundary layer, and consequently, the separation efficiency is not investigated in detail yet. This paper gives the suitable mathematical expressions, in order to predict the well known parameters as polarization modulus, enrichment factors, etc., taking into account the transport parameters for both the concentration boundary and the membrane layers, and analyses the concentration distribution and the polarization modulus. It has been shown that the transport properties of the membrane layer have significant effect on the concentration profiles of the boundary layer and thus, on the polarization modulus, enrichment factors, etc., as well. Thus, the well known equations, e.g. the polarization modulus, enrichment factor given in the literature [see e.g. Equations (2) and (3)], could be considered as approaches.

The Fluid Mechanics of Membrane Filtration

2007 ◽  
Author(s):  
Jack S. Hale ◽  
Alison Harris ◽  
Qilin Li ◽  
Brent C. Houchens
Keyword(s):  
Membrane Filtration ◽  
Concentration Polarization ◽  
Membrane Surface ◽  
Convective Transport ◽  
Contaminated Water ◽  
Permeate Flux ◽  
Large Pressure ◽  
Cake Layer ◽  
Large Pressure Gradient ◽  
Concentration Polarization Layer

Reverse osmosis and nanofiltration membranes remove colloids, macromolecules, salts, bacteria and even some viruses from water. In crossflow filtration, contaminated water is driven parallel to the membrane, and clean permeate passes through. A large pressure gradient exists across the membrane, with permeate flow rates two to three orders of magnitude smaller than that of the crossflow. Membrane filtration is hindered by two mechanisms, concentration polarization and caking. During filtration, the concentration of rejected particles increases near the membrane surface, forming a concentration polarization layer. Both diffusive and convective transport drive particles back into the bulk flow. However, the increase of the apparent viscosity in the concentration polarization layer hinders diffusion of particles back into the bulk and results in a small reduction in permeate flux. Depending on the number and type of particles present in the contaminated water, the concentration polarization will either reach a quasi-steady state or particles will begin to deposit onto the membrane. In the later case, a cake layer eventually forms on the membrane, significantly reducing the permeate flux. Contradictive theories suggest that the cake layer is either a porous solid or a very viscous (yield stress) fluid. New and refined models that shed light on these theories are presented.

Arsenic removal by MF membrane with chemical sludge adsorption and NF membrane equipped with vibratory shear enhanced process

2003 ◽  
Vol 3 (5-6) ◽  
pp. 303-310 ◽  
Author(s):  
S.-H. Yi ◽  
S. Ahmed ◽  
Y. Watanabe ◽  
K. Watari
Keyword(s):  
Arsenic Removal ◽  
Membrane Surface ◽  
Membrane Process ◽  
Low Concentrations ◽  
Strong Shear ◽  
Low Levels ◽  
Removal Processes ◽  
Removal Of Arsenic ◽  
Concentration Polarization Layer ◽  
Chemical Sludge

Conventional arsenic removal processes have difficulty removing low concentrations of arsenic ion from water. Therefore, it is very hard to comply with stringent low levels of arsenic, such as below 10 μg/L. So, we have developed two arsenic removal processes which are able to comply with more stringent arsenic regulations. They are the MF membrane process combined with chemical sludge adsorption and NF membrane process equipped with the vibratory shear enhanced process (VSEP). In this paper, we examine the performance of these new processes for the removal of arsenic ion of a low concentration from water. We found that chemical sludge produced in the conventional rapid sand filtration plants can effectively remove As (V) ions of H2AsO4- and HAsO42- through anion exchange reaction. The removal efficiency of MF membrane process combined with chemical sludge adsorption increased to about 36%, compared to MF membrane alone. The strong shear force on the NF membrane surface produced by vibration on the VSEP causes the concentration polarization layer to thin through increased back transport velocity of particles. So, it can remove even dissolved constituents effectively. Therefore, As (V) ions such as H2AsO4- and HAsO42- can be removed. The concentration of As (V) ions decreased from 50 μg/L to below 10 μg/L and condensation factor in recirculating water increased up to 7 times by using NF membrane equipped with VSEP.

Rotationally symmetric flow of Reiner-Rivlin fluid over a heated porous wall using numerical approach

2021 ◽  
pp. 095440622110342
Author(s):  
Talat Rafiq ◽  
M Mustafa ◽  
Junaid Ahmad Khan
Keyword(s):  
Boundary Layer ◽  
Layer Structure ◽  
Full Range ◽  
Porous Wall ◽  
Symmetric Flow ◽  
Axial Velocity Component ◽  
Suction Velocity ◽  
Rotationally Symmetric ◽  
Non Linear System ◽  
Rotationally Symmetric Flow

This research features one parameter family of solutions representing rotationally symmetric flow of non-Newtonian fluid obeying Reiner-Rivlin model. Such flows take place over a revolving plane permeable surface through origin such that fluid at infinity also undergoes uniform rotation about the vertical axis. Heat transfer accompanied with viscous heating effect is also analyzed. A similarity solution is proposed that results into a coupled non-linear system with four unknowns. Boundary layer structure is characterized by a parameter [Formula: see text] that compares angular velocity of external flow with that of the rotating surface. Solutions are developed by a well-known package bvp4c of MATLAB for full range of [Formula: see text]. Flow pattern for different choices of [Formula: see text] is scrutinized by computing both 2 D and 3 D streamlines. It is further noted that value of suction velocity is important with regards to the sign of axial velocity component. Boundary layer suppresses considerably whenever the surface is permeable. For sufficiently high suction velocity with [Formula: see text], entire fluid undergoes rigid body rotation. In no suction case, axially upward flow accelerates for increasing values of parameter [Formula: see text] in the range [Formula: see text], whereas opposite trend is apparent in the case [Formula: see text]. Results for normalized wall shear and Nusselt number are scrutinized for various choices of embedded parameters.

scholarly journals A Numerically Supported Investigation of the 3D Flow in Centrifugal Impellers: Part I — The Validation Base

1996 ◽  
Author(s):  
Ch. Hirsch ◽  
S. Kang ◽  
G. Pointel
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Boundary Layer Separation ◽  
Numerical Approach ◽  
Secondary Flows ◽  
Pump Impeller ◽  
High Loss ◽  
Leakage Flows ◽  
Fine Mesh ◽  
Radial Pump

The three-dimensional flow in centrifugal impellers is investigated on the basis of a detailed analysis of the results of numerical simulations. In order to gain confidence in this process, an in-depth validation is performed, based on computations of Krain’s centrifugal compressor and of a radial pump impeller, both with vaneless diffusers. Detailed comparisons with available experimental data provide high confidence in the numerical tools and results. The appearance of a high loss ‘wake’ region results from the transport of boundary layer material from the blade surfaces to the shroud region and its location depends on the balance between secondary and tip leakage flows and is not necessarily connected to 3D boundary layer separation. Although the low momentum spots near the shroud can interfere with 3D separated regions, the main outcome of the present analysis is that these are two distinct phenomena. Part I of this paper focuses on the validation base of the numerical approach, based on fine mesh simulations, while Part II presents an analysis of the different contributions to the secondary flows and attempts to estimate their effect on the overall flow pattern.

Some Boundary Layer-Porous Wall Coupling Effects in Laminar Flows With Surface Injection

1970 ◽  
Vol 92 (3) ◽  
pp. 257-266
Author(s):  
D. A. Nealy ◽  
P. W. McFadden
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Balance ◽  
Transfer Problem ◽  
Porous Wall ◽  
Laminar Flows ◽  
Stream Velocity ◽  
Axial Conduction ◽  
Boundary Layer Development ◽  
Layer Development

Using the integral form of the laminar boundary layer thermal energy equation, a method is developed which permits calculation of thermal boundary layer development under more general conditions than heretofore treated in the literature. The local Stanton number is expressed in terms of the thermal convection thickness which reflects the cumulative effects of variable free stream velocity, surface temperature, and injection rate on boundary layer development. The boundary layer calculation is combined with the wall heat transfer problem through a coolant heat balance which includes the effect of axial conduction in the wall. The highly coupled boundary layer and wall heat balance equations are solved simultaneously using relatively straightforward numerical integration techniques. Calculated results exhibit good agreement with existing analytical and experimental results. The present results indicate that nonisothermal wall and axial conduction effects significantly affect local heat transfer rates.

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