Stick-slip squirmers: slip asymmetry can qualitatively change self-swimming characteristics of squirmers

Abstract

A slip asymmetry can break the fore–aft symmetry of the local hydrodynamic force distribution on the surface of an otherwise no-slip or uniform-slip particle. Here, we use the Lorentz reciprocal theorem to demonstrate that such asymmetry, even in a fractional amount, can qualitatively alter the swimming characteristics of a self-propelled spherical squirmer, markedly different from those of no-slip or uniform-slip squirmers. Unlike the usual tangential squirming by the thrust-providing B1 mode and the type-determining B2 mode, we discover two unique features for a stick-slip squirmer. First, the squirmer can acquire a swimming velocity U without the B1 mode but simply by a symmetric extensile/contractile squirming from the B2 mode, which is able to reverse the swimming direction of the squirmer. Second, a stresslet $\boldsymbol{\mathsf{S}}$ can also be induced by a unidirectional squirming from the B1 mode, capable of inverting the squirmer's stresslet from extensile type to contractile type or vice versa to change the squirmer from puller to pusher or in a reverse manner. We further show that the two squirming modes can reinforce or compete with each other to enhance or diminish U and $\boldsymbol{\mathsf{S}}$ due to interplays between the asymmetric squirming forces on the stick and the slip faces. A phase diagram is also established to categorize a variety of newly emerging swimming states, such as an enhanced/degraded puller/pusher and a backward puller/pusher, depending on the relative strength of the squirming modes β = B2/B1, the direction of the stick-slip polarity and the degree of the slip disparity. As a result of such cooperative and competitive natures, a stick-slip squirmer can swim more or less efficiently than no-slip and uniform-slip ones. These distinctive features arising from stick-slip disparity can not only be made geometrically tuneable for steering the motion of a squirmer, but also provide new means for making efficient artificial microswimmers using amphiphilic Janus particles.