Simulation of the motion of two elastic membranes in Poiseuille shear flow via a combined immersed boundary-lattice Boltzmann method

• The motion of two elastic membranes in a Poiseuille shear flow is simulated utilizing a combined LBM–IBM.
• Two geometrically different channels, namely, a simple channel and a channel with a groove are considered.
• In the simple channel case, when the membranes are located off the symmetry axis, they migrate toward the center of the channel.
• In the case of channel with a groove, when the membrane tensile modulus is reduced it moves out of the groove.
• The results of the present simulation are in good accordance with the existing numerical and experimental results.

In this study, the motion, deformation and rotation of two elastic membranes in a viscous shear flow in a microchannel with and without a groove are simulated utilizing a combined LBM–IBM. The membranes are considered as immersed elastic boundaries in the fluid flow. The membranes are represented in Lagrangian coordinates, while the fluid flow field is discretized by a uniform and fixed Eulerian mesh. The interaction of the fluid and membranes is modeled using an appropriate form of the Dirac delta function. Two geometrically different channels, namely, a simple channel and a channel with a groove are considered. In the simple channel case, when the membranes are placed on the symmetry axis of the channel, they continue to move and deform without any lift force and rotation induced. However, when the membranes are located off the symmetry axis, the pressure difference produced in the flow around the membranes would apply lift forces on them and expel them toward the center of the channel. In the case of channel with a groove, it was found that when a membrane tensile modulus was reduced its flexibility as well as rotational speed would increase. This would, in turn, result in a pressure difference in the flow around the membrane. The pressure difference would apply a lift force on the membrane and move it out of the groove. It is worth mentioning that the results of the present simulation have a good agreement with the available numerical and experimental results.