The mechanism of propulsion of a model microswimmer in a viscoelastic fluid next to a solid boundary

Abstract

In this paper we study swimming of a model organism, the so-called Taylor's swimming sheet, in a viscoelastic fluid close to a solid boundary. This situation comprises natural habitats of many swimming microorganisms, and while previous investigations have considered the effects of both swimming next to a boundary and swimming in a viscoelastic fluid, seldom have both effects been considered simultaneously. We re-visit the small wave amplitude result obtained by Elfring and Lauga (Gwynn J. Elfring and Eric Lauga, in Saverio E. Spagnolie, editor, Complex Fluids in Biological Systems, Springer New York, New York, NY, 2015), and give a mechanistic explanation to the decoupling of the effects of viscoelasticity, which tend to slow the sheet, and the presence of the boundary, which tends to speed up the sheet. We also develop a numerical spectral method capable of finding the swimming speed of a waving sheet with an arbitrary amplitude and waveform.We use it to show that the decoupling mentioned above does not hold at finite wave amplitudes and that for some parameters the presence of a boundary can cause the viscoelastic effects to increase the swimming speed of microorganisms.

Mechanical effects of complex rheological liquid on a microorganism propelling through a rigid cervical canal: swimming at low Reynolds number

“…Swimming of microorganism next to solid boundary was thoroughly analyzed by Balmforth et al [23] for Bingham plastic fluid. A similar problem was recently attempted by Ives and Morozov [24] for viscoelastic Oldroyd-B fluid where the authors presented extensive parametric analysis of swimming speed and flow field generated by the organism computed through spectral numerical method. Lauga [25] extended Taylor's problem for variety of non-Newtonian models to estimate the effects of the rheology of surrounding unbounded fluid on swimming speed and rate of work done by the organism.…”

Biological interactions between Carreau fluid and microswimmers in a complex wavy canal with MHD effects

“…The Bingham model was integrated by Balmforth et al [21] to study the swimming of microorganism near to a rigid wall. More recently, Ives and Morozov [22] presented an analysis of swimming in a viscoelastic Oldroyd-B fluid in the presence of a solid wall. The computations were carried out by an efficient spectral method.…”

Swimming sheet near a plane surfactant-laden interface

“…It was later extended by Blake [26] who allowed the passage of both longitudinal and transverse waves along the sheet to represent the almost flat ciliated organisms such as Paramecium or Opalina. Due to the mathematical simplicity associated with this model, it has been used to study the locomotion (i) in a complex fluid [27][28][29][30][31][32][33][34], (ii) in a gel [35,36], (iii) in a liquid crystal [37], (iv) in a porous media [38], (v) under confinement [2][3][4][39][40][41][42][43][44][45], (vi) at finite inertia of the fluid or the organism [2,[46][47][48] and (vii) under transient effects [49]. The research on the locomotion under confinement has been restricted to the confinements caused by a rigid or soft wall [2,3,[39][40][41][42]45], a plane clean interface [4], a deforming membrane [43] or a gel [44] with a Newtonian or a non-Newtonian suspending fluid.…”