Comparing lattice Boltzmann simulations of periodic fluid flow in repeated micropore structures with longitudinal symmetry and asymmetry

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Pumping of a particulate suspension back and forth through a membrane of periodic axisymmetric pores results in no net flow of the fluid; however, the particles are transported along the pores from one side of the membrane to the other. The movement of the particles is dependent on the geometry of the pore walls. Current simulations for this problem utilise standard computational fluid dynamics techniques (e.g. finite element method, boundary element method). However, there are difficulties associated with applying these techniques to this problem, such as the requirement of many spatial periods. The lattice Boltzmann method overcomes these disadvantages by utilising periodic boundary conditions, which are straightforward to implement. Flow simulations in longitudinally symmetric and asymmetric pores with various Reynolds numbers are compared. The importance of pore shape and viscous effects is showcased through streamline plots. References P. L. Bhatnagar, E. P. Gross, and M. Krook. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94.3 (1954), p. 511. doi: 10.1103/PhysRev.94.511 W. R. Bowen and F. Jenner. Theoretical descriptions of membrane filtration of colloids and fine particles: An assessment and review. Adv. Colloid Interface Sci. 56 (1995), pp. 141–200. doi: 10.1016/0001-8686(94)00232-2 S. Chen and G. D. Doolen. Lattice Boltzmann method for fluid flows. Ann. Rev. Fluid Mech. 30 (1998), pp. 329–364. doi: 10.1146/annurev.fluid.30.1.329 R. L. C. Cisne, T. F. Vasconcelos, E. J. R. Parteli, and J. S. Andrade. Particle transport in flow through a ratchet-like channel. Microfluid. Nanofluid. 10 (2011), pp. 543–550. doi: 10.1007/s10404-010-0688-y J. A. Deiber and W. R. Schowalter. Flow through tubes with sinusoidal axial variations in diameter. AIChE J. 25.4 (1979), pp. 638–645. doi: 10.1002/aic.690250410 N. Islam. Fluid flow and particle transport through periodic capillaries. Bull. Aust. Math. Soc. 96.3 (2017), pp. 521–522. doi: 10.1017/S0004972717000739 C. Kettner, P. Reimann, P. Hänggi, and F. Müller. Drift ratchet. Phys. Rev. E 61.1 (2000), p. 312. doi: 10.1103/PhysRevE.61.312 S. H. Kim and H. Pitsch. A generalized periodic boundary condition for lattice Boltzmann method simulation of a pressure driven flow in a periodic geometry. Phys. Fluids 19.10 (2007), p. 108101. doi: 10.1063/1.2780194 T. Krüger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva, and E. M. Viggen. The lattice Boltzmann method: Principles and practice. Vol. 10. Graduate Texts in Physics. Springer International Publishing, 2017, pp. 978–3. doi: 10.1007/978-3-319-44649-3. G. Leneweit and D. Auerbach. Detachment phenomena in low Reynolds number flows through sinusoidally constricted tubes. J. Fluid Mech. 387 (1999), 129–150. doi: 10.1017/S0022112099004619 M. Sakthivel and K. Anupindi. An off-lattice Boltzmann method for blood flow simulation through a model irregular arterial stenosis: The effects of amplitude and frequency of the irregularity. Phys. Fluids 33.3 (2021), p. 031912. doi: 10.1063/5.0044948 T. Sikdar, N. J. Pinky, A. Roy, S. S. Hossain, and N. Islam. Oscillating flow of viscous incompressible fluid through sinusoidal periodic tube at low Reynolds number. Int. J. Fluid Mech. Therm. Sci. 6.1 (2020), pp. 9–18. doi: 10.11648/j.ijfmts.20200601.12 J. G. Zhou. Axisymmetric lattice Boltzmann method revised. Phys. Rev. E 84.3 (2011), p. 036704. doi: 10.1103/PhysRevE.84.036704