Bio-inspired propulsion of micro-swimmers within a passive cervix filled with couple stress mucus

BACKGROUND AND OBJECTIVE

The swimming mechanism of self-propelling organisms has been imitated by biomedical engineers to design the mechanical micro bots. The interaction of these swimmers with surrounding environment is another important aspect. The present swimming problem integrates Taylor sheet model with couple stress fluid model. The thin passage containing micro-swimmers and mucus is approximated as a rigid (passive) two-dimensional channel. The spermatozoa forms a pack quite similar as a complex wavy sheet.

METHODS

Swimming problem with couple stress cervical liquid (at low Reynolds number) leads to a linear sixth order differential equation. The boundary value problem (BVP) is solved analytically with two unknowns i.e. speed of complex wavy sheet and flow rate of couple stress mucus. After utilizing this solution into equilibrium conditions these unknowns can be computed via Newton-Raphson algorithm. Furthermore, the pairs of numerically calculated organism speed and flow rate are utilized in the expression of power dissipation.

RESULTS

This work describes that the speed of micro-swimmers can be enhanced by suitable rheology of the surrounding liquid. The usage of couple stress fluid as compared to Newtonian fluid enhances the energy dissipation and reduces the flow rate. On the other hand complex wavy surface also aids the organisms to swim faster.

Locomotion of an efficient biomechanical sperm through viscoelastic medium

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.

Mathematical modelling of ciliary propulsion of an electrically-conducting Johnson-Segalman physiological fluid in a channel with slip

Bionic systems frequently feature electromagnetic pumping and offer significant advantages over conventional designs via intelligent bio-inspired properties. Complex wall features observed in nature also provide efficient mechanisms which can be utilized in biomimetic designs. The characteristics of biological fluids are frequently non-Newtonian in nature. In many natural systems super-hydrophobic slip is witnessed. Motivated by these phenomena, in this paper, we discussed a mathematical model for the cilia-generated propulsion of an electrically-conducting viscoelastic physiological fluid in a ciliated channel under the action of magnetic field. The rheological behavior of the fluid is simulated with the Johnson-Segalman constitutive model which allows internal wall slip. The regular or coordinated movement of the ciliated edges (which line the internal walls of the channel) is represented by a metachronal wave motion in the horizontal direction which generates a two-dimensional velocity profile. This mechanism is imposed by a periodic boundary condition which generates propulsion in the channel flow. Under the classical lubrication approximation, the boundary value problem is non-dimensionalized and solved analytically with a perturbation technique. The influence of the geometric, rheological (slip and Weissenberg number) and magnetic parameters on velocity, pressure gradient and the pressure rise (evaluated via the stream function in symbolic software) are presented graphically and interpreted at length.