An implicit finite difference analysis of magnetic swimmers propelling through non-Newtonian liquid in a complex wavy channel

There are many unicellular tiny organisms which can self-propel collectively through non-Newtonian fluids by means of producing undulating deformation. Example includes nematodes, rod shaped bacteria and spermatozoa. Here we use Taylor's swimming sheet model, with non-Newtonian fluid bounded with in a complex wavy walls of a two-dimensional channel. Oldroyd-4 constant fluid is approximated as cervical mucus and MHD effects are also considered. After utilizing lubrication and creeping flow assumption the reduced non-linear differential equation is solved (by implicit finite difference technique) so that it will satisfy the dynamic equilibrium condition for steady propulsion. For a special (Newtonian) case the expressions of swimming speed and flow rate are also presented. We also demonstrate that the rheological properties of non-Newtonian fluid can assist or resist the pack of micro-organisms (swimming sheet), while the larger undulation amplitude in swimmer's body and magnetic field in downward direction can enhance the propulsion speed. The solution obtained via implicit finite difference method is also validated by a built in MATLAB routine bvp-4c. This built in function is based on collocation technique. Moreover an excellent correlation is achieved for both numerical methods. (C) 2019 Elsevier Ltd. All rights reserved.