Abstract
We illustrate a concept for shape-changing microswimmers, which exploits the hysteresis of a shape transition of an elastic object, by an elastic disk undergoing cyclic localized swelling. Driving the control parameter of a hysteretic shape transition in a completely time-reversible manner gives rise to a non-time-reversible shape sequence and a net swimming motion if the elastic object is immersed into a viscous fluid. We prove this concept with a microswimmer which is a flat circular elastic disk that undergoes a transition into a dome-like shape by localized swelling of an inner disk. The control parameter of this shape transition is a scalar swelling factor of the disk material. With a fixed outer frame with an additional attractive interaction in the central region, the shape transition between flat and dome-like shape becomes hysteretic and resembles a hysteretic opening and closing of a scallop. Employing Stokesian dynamics simulations of a discretized version of the disk we show that the swimmer is effectively moving into the direction of the opening of the dome in a viscous fluid if the swelling parameter is changed in a time-reversible manner. The swimming mechanism can be qualitatively reproduced by a simple 9-bead model.
Highlights
Swimming on the microscale at low Reynolds numbers requires special propulsion mechanisms which are effective in the presence of dominating viscous forces
Phoretic swimmers create gradients in external fields such as concentration or temperature which in turn give rise to symmetry-breaking interfacial forces leading to propulsion if they overcome the friction force of the microswimmer
At low Reynolds numbers, the cyclic deformation pattern must not be invariant under timereversal: the scallop theorem formulated by Purcell states that periodic reciprocal patterns of deformation can not lead to an effective net motion on the microscale because of the linearity of the Stokes equation
Summary
Swimming on the microscale at low Reynolds numbers requires special propulsion mechanisms which are effective in the presence of dominating viscous forces. Flagella employ a periodic forcing but overcome the scallop theorem by exploiting friction along the elastic flagellum to break time-reversibility This requires a matching of driving and frictional damping time scales for efficient propulsion. This makes this concept hard to reproduce or imitate in a controlled fashion in an artificial system.9,10 Another basic strategy to overcome the scallop theorem are deformation cycles that involve at least two control parameters and drive the swimmer periodically along a closed contour in this at least two-dimensional parameter space. By further enhancing the elastic disk with a fixed frame with attractive interactions we can endow this transition with genuine hysteretic effects These hysteresis effects allow us to break the reciprocity of the shape cycle we employ simple cyclic and fully time-reversible oscillations of the swelling factor as single global and scalar control parameter. A simplified 9-bead model is presented that mimics the essence of the underlying swimming mechanism and is able to qualitatively reproduce and explain its main characteristics
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