Frequency-dependent higher-order Stokes singularities near a planar elastic boundary: Implications for the hydrodynamics of an active microswimmer near an elastic interface

Abstract

The emerging field of self-driven active particles in fluid environments has recently created significant interest in the biophysics and bioengineering communities owing to their promising future biomedical and technological applications. These microswimmers move autonomously through aqueous media where under realistic situations they encounter a plethora of external stimuli and confining surfaces with peculiar elastic properties. Based on a farfield hydrodynamic model, we present an analytical theory to describe the physical interaction and hydrodynamic couplings between a self-propelled active microswimmer and an elastic interface that features resistance toward shear and bending. We model the active agent as a superposition of higher-order Stokes singularities and elucidate the associated translational and rotational velocities induced by the nearby elastic boundary. Our results show that the velocities can be decomposed in shear and bending related contributions which approach the velocities of active agents close to a no-slip rigid wall in the steady limit. The transient dynamics predict that contributions to the velocities of the microswimmer due to bending resistance are generally more pronounced than to shear resistance. Bending can enhance (suppress) the velocities resulting from higher-order singularities whereas the shear-related contribution decreases (increases) the velocities. Most prominently, we find that near an elastic interface of only energetic resistance toward shear deformation, such as that of an elastic capsule designed for drug delivery, a swimming bacterium undergoes rotation of the same sense as observed near a no-slip wall. In contrast to that, near an interface of only energetic resistance toward bending, such as that of a fluid vesicle or liposome, we find a reversed sense of rotation. Our results provide insight into the control and guidance of artificial and synthetic self-propelling active microswimmers near elastic confinements. arXiv:1907.09389v2 [physics.flu-dyn]

Wall-induced translation of a rotating particle in a shear-thinning fluid

“…2018 a ), which was also shown to have interesting implications on the direction of circular swimming (Daddi-Moussa-Ider et al. 2019).…”

Theoretical framework for pairwise microswimmer interactions

“…In the case of sinusoidal driving forces with a single frequency, also the ξ 3 timeaveraged flow field vanishes since it is associated to odd products of the sinusoidal stroke, which averages to zero over a stroke cycle. This explains why passive dipolar interactions therefore arise firstly at fourth order in the stroke amplitude (∼ ξ 4 /r 2 ) (12). In [34], a stroke comprising stepwise arm contractions at constant velocity [5] has been employed, associated to infinitely many harmonics of the base frequency ω in a Fourier decomposition.…”

“…Due to the dominance of viscous drag over inertia and the ensuing time-independence of the Stokes equations, a successful swimming strategy has to break the time-reversal symmetry [1]. Several theoretical models [2,3,4,5,6,7,8,9,10,11,12,13], experimental realizations [14,15,16,17,18,19,20,21,22,23] and simulations [24,25,26,27,28] have been employed to scrutinize the details of locomotion under these laws. Overall, due to the absence of inertia, the force to self-propel exerted by a microswimmer on its surrounding is balanced by friction, and force monopoles are not present.…”

Towards an analytical description of active microswimmers in clean and in surfactant-covered drops

“…The induced translational and rotational velocities resulting from the fluid-mediated hydrodynamic interactions between the microswimmer and the surface of the drop are provided by Faxén's laws as [103,199,202,203]…”