Axisymmetric spheroidal squirmers and self-diffusiophoretic particles

Abstract

We study, by means of an exact analytical solution, the motion of a spheroidal, axisymmetric squirmer in an unbounded fluid, as well as the low Reynolds number hydrodynamic flow associated to it. In contrast to the case of a spherical squirmer -for which, e.g., the velocity of the squirmer and the magnitude of the stresslet associated with the flow induced by the squirmer are respectively determined by the amplitudes of the first two slip ("squirming") modes -for the spheroidal squirmer each squirming mode either contributes to the velocity, or contributes to the stresslet. The results are straightforwardly extended to the self-phoresis of axisymmetric, spheroidal, chemically active particles in the case when the phoretic slip approximation holds.

Exact axisymmetric interaction of phoretically active Janus particles

“…For instance, we can similarly introduce these geometrical functions for interactions of two spheroidal particles. Given that the exact motion of a single spheroidal squirmer with a catalytic surface has been recently discussed by Pöhnl, Popescu & Uspal (2020), one can use that solution to construct a reflection-based approach for capturing the far-field behaviour of two spheroidal particles. However, studying the full behaviour of the system still requires an exact evaluation of the geometrical function for which computational approaches (such as the boundary element method Uspal 2019) should be employed.…”

Rheotaxis of spheroidal squirmers in microchannel flow: Interplay of shape, hydrodynamics, active stress, and thermal fluctuations

“…A more general representation of the flow field, including infinitely many squirming modes, is presented in Ref. [78]. As a consequence, the swim velocity and active stress of a spheroidal squirmer depend not only on B 1 and B 2 , respectively, but include contributions from further modes.…”

Enhanced velocity fluctuations in interacting swimmer suspensions

“…There also exist ellipsoidal generalizations of the squirmer model, with an expansion similar to (5.1) for the slip velocity (Toppaladoddi & Balmforth 2014; Kyoya et al. 2015; Felderhof 2016; Poehnl, Popescu & Uspal 2020).…”

“…Such a squirmer swims with a speed 2B 1 /3, while the disturbance velocity in the far-field has a dipolar character with amplitude B 2 (see, for instance, Ishikawa & Pedley (2007a)). There also exist ellipsoidal generalizations of the squirmer model, with an expansion similar to (5.1) for the slip velocity (Toppaladoddi & Balmforth 2014;Kyoya et al 2015;Felderhof 2016;Poehnl, Popescu & Uspal 2020). In light of the use of the ellipsoidal squirmer models above, it is of interest to derive scaling estimates for the tracer diffusivity when the dipole disturbance field and swimming speed may be assumed independent.…”