Buckling Instability Causes Inertial Thrust for Spherical Swimmers at All Scales

Abstract

Microswimmers, and among them aspirant microrobots, generally have to cope with flows where viscous forces are dominant, characterized by a low Reynolds number (Re). This implies constraints on the possible sequences of body motion, which have to be nonreciprocal. Furthermore, the presence of a strong drag limits the range of resulting velocities. Here, we propose a swimming mechanism, which uses the buckling instability triggered by pressure waves to propel a spherical, hollow shell. With a macroscopic experimental model, we show that a net displacement is produced at all Re regimes. An optimal displacement caused by non-trivial history effects is reached at intermediate Re. We show that, due to the fast activation induced by the instability, this regime is reachable by microscopic shells. The rapid dynamics would also allow high frequency excitation with standard traveling ultrasonic waves. Scale considerations predict a swimming velocity of order 1 cm/s for a remote-controlled microrobot, a suitable value for biological applications such as drug delivery.Besides their playful aspect, artificial microswimmers present undeniable fundamental and practical interests, mostly driven by a constant race toward increasing miniaturization with potential applications such as targeted drug delivery. Comprehensive studies aim to identify the efficient strategies for small scale displacement in liquids [1][2][3][4][5][6][7], which can possibly be exploited for the conception of synthetic microswimmers. Sticking to the strict definition of swimming as performing a displacement induced by body deformation, quite a few realizations of synthetic microswimmers can be found in literature [8][9][10][11][12]. A growing attention toward the simplicity of their fabrication [13][14][15] opens possibilities for transfer in the industrial arena. The two main external sources of power are magnetic [10,11,13] and acoustic [12,14,15] fields, which are probably more suitable for medical applications and less expensive. The major conceptual difficulty lies in the low Reynolds flows usually associated with microscopic scales; the scallop theorem [16] then imposes that a non zero displacement may only occur via a nonreciprocal succession of shapes. Except in chiral systems [10,11], this necessary condition requires at least two degrees of freedom, which commonly implies two control parameters. Such heavy double steering could indeed be bypassed if flow rates can be rendered high enough so that inertia cannot be neglected anymore, or if any hysteresis in the deformation "naturally" prevents reciprocity.We suggest fulfilling these two conditions together with simple spherical colloidal shells full of air that are microscopic objects quite easy to manufacture [17,18]. Deflation from a spherical geometry occurs via buckling, which is a subcritical instability, likely to provide both swiftness and hysteresis during a deflation-re-inflation cycle driven by a single scalar control parameter : pressure. We investigate the swimming that results from t...

Let’s deflate that beach ball

“…These results are compared to what is known from thin shell theory, which allows to discuss its validity range. Our low-cost experimental set-up was conceived as an efficient and versatile tool for exploring with students instability issues and bifurcations diagrams under several conditions (volume or pressure imposed), and for characterizing shells before using them in a more complex environment [15]. Yet, it provides for the first time an experimental characterization of the relationship between pre-buckling and post-buckling states.…”

An ALE method for simulations of axisymmetric elastic surfaces in flow

“…While 20 such a high computational speed is not required in most typical applications, it does enable otherwise unfeasible simulations as soon as the problems involve a high number of grid points or rich dynamics demanding many time steps. As examples, we present first simulations of the observed shape oscillations of novel microswimming shells [11] and the uniaxial compression of biological cells filled with cytoplasm [42]. In collaboration with (bio)physicists, the method is currently used to get more insight into the dynamics of microswimming shells and the cellular cortex.…”

“…If the outer pressure is increased, the air inside the shell will be compressed such that the shell shrinks but remains spherical. When the pressure difference exceeds a shell-specific threshold, the shell will buckle at the weak spot [11], which is a very rapid process accompanied by rapid elastic surface oscillations. Decreasing the outer pressure again leads to inflation of the shell and debuckling.…”

“…The dynamics of elastic membranes, shells and capsules in fluid flow has become an active research area in computational physics and computational biology. Example systems include vesicle membranes immersed in fluids [1,2,3,4], red and white blood cells transported with the blood plasma [5,6,7,8], general biological cells including cytoplasmic flows [9,10], or even man-made elastic thin shells to deliver cargo though a fluid [11]. Therefore, there exists a broad interest in advanced modeling and simulation technologies that enable the understanding of such systems.…”

Elasticity and stability of shape-shifting structures

“…Buckling bilayer plates can be utilized to generate shape-shifting structures [40] that may be used as soft grippers [140]. Buckling of shells has provided an intriguing way to control global shape [141,142,12] and local patterning [143,144,145,146], reduce aerodynamic drag [147,148], generate lock-and-key colloids that can selectively aggregate [149], form liquid crystal shell actuators [150], and pave the way for buckling microswimmers [151].…”