Fouling Mitigation via Chaotic Advection in a Flat Membrane Module with a Patterned Surface
Abstract
:1. Introduction
2. Problem Definition
2.1. Channel Geometry
2.2. Governing Equations and Boundary Conditions
2.3. Simulation Details
3. Results and Discussion
3.1. Convergence with Mesh Refinement
3.2. Flow Characteristics
3.3. Evolution of the Foulant Concentration
3.4. Growth Rate of the Wall Concentration
3.5. Pressure Loss in the Constant Permeate Flux Mode
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
List of Symbols
Concentration of foulant, mol/m3 | |
Concentration in the bulk, mol/m3 | |
Concentration at the inlet, mol/m3 | |
Concentration in the permeate, mol/m3 | |
Concentration on the wall (membrane surface), mol/m3 | |
Dimensionless wall concentration | |
Dimensionless line-averaged wall concentration | |
Diffusivity of foulants, m2/s | |
δ | Thickness of the concentration boundary layer (film layer), m |
Half-height of a thin slit channel, m | |
Channel height, m | |
Groove depth, m | |
Dimensionless groove depth | |
Length of a periodic unit of the channel, m | |
Unit outward normal vector | |
n | Exponent of the growth rate of the wall concentration |
Pressure, Pa | |
Péclet number | |
Reynolds number | |
Critical Reynolds number | |
Wall Reynolds number | |
Velocity vector, m/s | |
Uniform normal velocity at the inlet, m/s | |
Maximum velocity in the fully developed laminar flow through a thin slit, m/s | |
Permeate velocity, m/s | |
Dimensionless downwelling velocity magnitude | |
Channel width, m | |
Groove width, m | |
Dimensionless –coordinate | |
Greek Letters | |
Inlet boundary | |
Outlet boundary | |
Non-permeable solid boundary | |
Membrane surface | |
Concentration boundary layer thickness, m | |
Viscosity, Pa∙s | |
Groove angle, ° |
Appendix A. Back Transport of Tracer Particles
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Mesh | Number of Elements | Minimum Element Size |
---|---|---|
M1 | 8,608,896 | 0.01 |
M2 | 16,685,136 | 0.005 |
M3 | 30,380,832 | 0.0025 |
M4 | 41,685,120 | 0.00125 |
50 | 0.05 | 0.2347 |
0.10 | 0.2163 | |
0.15 | 0.2005 | |
0.20 | 0.1866 | |
0.25 | 0.1773 | |
0.30 | 0.1712 | |
100 | 0.05 | 0.2419 |
0.10 | 0.2191 | |
0.15 | 0.1916 | |
0.20 | 0.1749 | |
0.25 | 0.1668 | |
0.30 | 0.1633 | |
200 | 0.05 | 0.2524 |
0.10 | 0.2084 | |
0.15 | 0.1745 | |
0.20 | 0.1627 | |
0.25 | 0.1625 | |
0.30 | 0.1666 | |
500 | 0.05 | 0.2580 |
0.10 | 0.1577 | |
0.15 | 0.1342 | |
0.20 | 0.1411 | |
0.25 | 0.1559 | |
0.30 | 0.1771 |
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Kim, K.T.; Park, J.E.; Jung, S.Y.; Kang, T.G. Fouling Mitigation via Chaotic Advection in a Flat Membrane Module with a Patterned Surface. Membranes 2021, 11, 724. https://doi.org/10.3390/membranes11100724
Kim KT, Park JE, Jung SY, Kang TG. Fouling Mitigation via Chaotic Advection in a Flat Membrane Module with a Patterned Surface. Membranes. 2021; 11(10):724. https://doi.org/10.3390/membranes11100724
Chicago/Turabian StyleKim, Kyung Tae, Jo Eun Park, Seon Yeop Jung, and Tae Gon Kang. 2021. "Fouling Mitigation via Chaotic Advection in a Flat Membrane Module with a Patterned Surface" Membranes 11, no. 10: 724. https://doi.org/10.3390/membranes11100724