Every group of microorganism utilizes a diverse mechanical strategy to propel through complex environments. These swimming problems deal with the fluid-organism interaction at micro-scales in which Reynolds number is of the order of 10-3. By adopting the same propulsion mechanism of so-called Taylor's sheet, here we address the biomechanical principle of swimming via different wavy surfaces. The passage (containing micro-swimmers) is considered to be passive two-dimensional channel filled with viscoelastic liquid, i.e., Oldroyd-4 constant fluid. For some initial value of unknowns, i.e., cell speed and flow rate of surrounding liquid, the resulting boundary value problem is solved by robust finite difference scheme. This convergent solution is further employed in the equilibrium conditions which will obviously not be satisfied for such crude values of unknowns. These unknowns are further refined (to satisfy the equilibrium conditions) by modified Newton-Raphson algorithm. These computed pairs are also utilized to compute the energy losses. The speed of swimming sheet its power delivered and flow rate of Oldroyd-4 constant fluid are compared for different kinds of wavy sheets. These results are also useful in the manufacturing of artificial (soft) microbots and the optimization of locomotion strategies.
Keywords: Finite difference method (FDM); Micro-swimmers; Oldroyd-4 constant fluid; Reynolds number.