Transition in swimming direction in a model self-propelled inertial swimmer

Abstract

We propose a reciprocal, self-propelled model swimmer at intermediate Reynolds numbers (Re). Our swimmer consists of two unequal spheres that oscillate in antiphase generating nonlinear steady streaming (SS) flows. We show computationally that the SS flows enable the swimmer to propel itself, and also switch direction as Re increases. We quantify the transition in the swimming direction by collapsing our data on a critical Re and show that the transition in swimming directions corresponds to the reversal of the SS flows. Based on our findings, we propose that SS can be an important physical mechanism for motility at intermediate Re.PACS numbers: May be entered using the \pacs{#1} command. arXiv:1801.03974v2 [physics.flu-dyn]

Scallop Theorem and Swimming at the Mesoscale

“…This is commonly achieved by the inertial dynamics of the fluid [17,18], here characterized by the Reynolds number Re f ¼ ρ f LŪ=η (ρ f and η being the fluid density and viscosity, L the swimmer body length, and U the average swimming speed). For example, the inclusion of inertia in the dynamics can be achieved by using steady streaming [19][20][21], vortex generation [22], or turbulent flows [23]. The possibilities for the exploitation of the swimmer's own inertia were first suggested a decade ago by Gonzalez-Rodriguez and Lauga [24], opening the debate on and additional investigations of swimming in this regime [20,21,25].…”

“…For example, the inclusion of inertia in the dynamics can be achieved by using steady streaming [19][20][21], vortex generation [22], or turbulent flows [23]. The possibilities for the exploitation of the swimmer's own inertia were first suggested a decade ago by Gonzalez-Rodriguez and Lauga [24], opening the debate on and additional investigations of swimming in this regime [20,21,25]. Interestingly, recent experiments and simulations have shown that mesoscopic structures, i.e., 100 μm to 1 cm in scale, display coasting effects [26][27][28] while generating fluid flows with a time-reversible behavior [29,30].…”

“…The Reynolds number Re s of such a swimmer is set by its bead density ρ s , its bead size a, and its beating frequency ω such that Re s ¼ ρ s a 2 ω=η. This design possesses only one internal degree of freedom, which leads to a reciprocal deformation, and therefore it cannot swim without the help of inertia [19,20,24]. Assuming that the Reynolds number of the fluid is Re f ≪ 1 and of the swimmer Re s ∼ 1, the flow should be dominated by the fluid viscosity while the propulsion mechanism should be related to the coasting time of the swimmer, which we define as τ ¼ m=ð6πηaÞ, with m being the bead mass.…”

“…With no fitting parameters, the agreement is excellent, with the error not exceeding 10%. The strongest deviations are found around the peak velocity, where the nonzero fluid inertia may play a small role [18,20,21]. Furthermore, from reading out the stroke amplitude obtained in experiments, the measured velocities can be compared to the model using Eq.…”

Streaming-enhanced flow-mediated transport

“…This phenomenon is well understood, both theoretically and experimentally, in the case of individual vibrating cylinders (Holtsmark et al 1954;Stuart 1966;Riley 1967;Davidson & Riley 1972;Riley 2001;Lutz, Chen & Schwartz 2005) and spheres (Lane 1955;Riley 1966;Chang & Maxey 1994), and has found application in microfluidic flow control, mixing, sorting and pumping (Liu et al 2002;Marmottant & Hilgenfeldt 2003, 2004Lutz, Chen & Schwartz 2006;Ahmed et al 2009;Ryu, Chung & Cho 2010;He et al 2011;Tovar, Patel & Lee 2011;Wang, Jalikop & Hilgenfeldt 2011;Thameem, Rallabandi & Hilgenfeldt 2016). Yet little is known in the case of complex geometries and configurations involving multiple objects (House, Lieu & Schwartz 2014;Klotsa et al 2015;Chong et al 2016;Rallabandi, Wang & Hilgenfeldt 2017;Dombrowski et al 2019).…”