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A standard approach to propulsion velocities of autophoretic colloids with thin interaction layers uses a reciprocity relation applied to the slip velocity although the surface flux (chemical, electrical, thermal, etc.), which is the source of the field driving the slip, is often more accessible. We show how, under conditions of low Reynolds number and a field obeying the Laplace equation in the outer region, the slip velocity can be bypassed in velocity calculations. In a sense, the actual slip velocity and a normal field proportional to the flux density are equivalent for this type of calculation. Using known results for surface traction induced by rotating or translating an inert particle in a quiescent fluid, we derive simple and explicit integral formulas for translational and rotational velocities of arbitrary spheroidal and slender-body autophoretic colloids.
Self-propulsion and directed movement of nano- and micro-particles can in principle provide novel components for applications in microrobotics and MEMS. Our research involves the design of catalytic propulsion systems and the control of colloidal movement based on this principle. We have designed autonomous nanomotors that mimic biological motors by using catalytic reactions to generate forces derived from chemical gradients. Through architectural control of bimetallic catalytic particles, we have recently developed systems that undergo more complex movement. For example, we have constructed 10-micron scale rotary motors by contact lithography. In these chiral motors, bimetallic Au-Pt patterns are free-standing and move in the pattern predicted by theory. These studies demonstrate that by designing the proper architecture, one can tailor the pattern of movement to specific applications, such as changing from translational to rotational movement. The potential for elaboration of these designs to more complex micro-machine assemblies is discussed.
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