Stokes flow past an array of circular cylinders through slip-patterned microchannel using boundary element method

Abstract

Two-dimensional viscous incompressible, pressure-driven, creeping flow at low Reynold's number (Re ≪ 1) around a series of circular cylinders in a slip-patterned rectangular microchannel is investigated numerically by using the boundary element method (BEM) based on a non-primitive variables approach. The non-primitive variables approach refers to the combination of stream function and vorticity variables. The Stokes equations are used to govern the flow of creeping fluid through a microchannel. We consider the alteration of the slip on both the upper and lower surfaces of the microchannel maintain the same phase (i.e., in-phase configuration). Here, the slip boundary condition refers to Navier's slip boundary condition. We considered both small as well as large patterned slip on both surfaces of the microchannel. Moreover, we have assumed that a number of cylinders of equal diameter are present in the in-line configuration in the path of flow. We studied streamlines, velocity profiles, pressure gradients, and the shear stresses with varied slip-length, and the radius of the cylinder, to get a complete comprehension of flow dynamics. We observed that the velocity and shear stress profiles exhibit significant variability in the case of fine slip patterning. Additionally, the proposed investigation holds several potential applications, such as drug capsule delivery systems, hemodynamics, bio-MEMS technology, and so forth.