Numerical Analysis of a Planar Wave Propagation Based Micro Propulsion System

Micro-propulsion mechanisms differ from macro scale counterparts owing to the domination of viscous forces in microflows. In essence, propulsion mechanisms such as cilia and flagella of single celled organisms can be deemed as nature’s solution to a challenging problem, and taken as a basis for the design of an artificial micro-propulsion system. In this paper we present numerical analysis of the flow due to oscillatory planar waves propagating on micro strips. The time-dependent three-dimensional flow due to moving boundaries of the strip is governed by incompressible Navier-Stokes equations in a domain with moving boundaries, which is modeled by means of an arbitrary Lagrangian-Eulerian formulation. The fluid medium surrounding the actuator boundaries is bounded by a channel, and neutral boundary conditions are used in the upstream and downstream. Effects of actuation parameters such as amplitude, excitation frequency, wavelength of the planar waves are demonstrated with numerical simulations that are carried out by third party software, COMSOL. Functional-dependencies with respect to the actuation parameters are obtained for the average velocity of the strip and the efficiency of the mechanism. INTRODUCTION Propulsion mechanisms of microswimmers can be imitated artificial artificial propulsion systems to operate in low Reynolds number environments. A series of theoretical work focus on natural microswimmers and their actuation principles [1-6]. It was shown that inside highly viscous fluids with low Reynolds number, a conventional time reversible swimming action can not yield desired propulsive effect due to ‘scallop theorem’ [1]. Microswimmers, which usually are single celled organisms like spermatozoa, employ planar or helical wave propagation via their flagellum and cilia called organelles [2,3]. Periodic traveling-wave deformations on the biopolymer tail of the microorganism are the result of the balance between the bending stresses of the structure and the total stress in the fluid [4]. Sir Taylor presented asymptotic solutions of the flow for a sinusoidal wave propagating on an infinite inextensible sheet immersed in a viscous fluid [5]. Later, Katz presented an asymptotic solution for the infinite sheet placed inside a channel [6]. Childress [7] expanded the study to extensible sheet propulsion. Our previous work verifies asymptotic results of Taylor [5] and Katz [6] by means of numerical solution of the two-dimensional time-dependent Stokes flow due to plane waves traveling on a finite-length thin membrane inside a channel [8]. Although time irreversible wave propulsion is the method utilized by natural microswimmers, efficiency of these swimmers is found to be very low due to high shear losses [9]. Recent, theoretical and experimental studies on the propulsion of autonomous swimming robots utilize the biological mechanisms [10,11,12]. The mechanism is replicated artificially by wave propagation on an artificial tail made from magnetic filaments attached to blood-cells and driven by alternating external magnetic fields [13]. Traveling wave propagation on an electrically driven Nafion based tail in centimeter scale proved to be viable as a propulsion system [14] at low frequencies. Similarly, three-dimensional numerical investigation of surface acoustic waves created by interdigital transducers on a thin membrane was carried out as an actuation method at large frequencies despite the small amplitude of the acoustic waves [15]. Further-