TY - JOUR
T1 - Can phoretic particles swim in two dimensions?
AU - Sondak, David
AU - Hawley, Cory
AU - Heng, Siyu
AU - Vinsonhaler, Rebecca
AU - Lauga, Eric
AU - Thiffeault, Jean Luc
N1 - Publisher Copyright:
© 2016 American Physical Society.
PY - 2016/12/16
Y1 - 2016/12/16
N2 - Artificial phoretic particles swim using self-generated gradients in chemical species (self-diffusiophoresis) or charges and currents (self-electrophoresis). These particles can be used to study the physics of collective motion in active matter and might have promising applications in bioengineering. In the case of self-diffusiophoresis, the classical physical model relies on a steady solution of the diffusion equation, from which chemical gradients, phoretic flows, and ultimately the swimming velocity may be derived. Motivated by disk-shaped particles in thin films and under confinement, we examine the extension to two dimensions. Because the two-dimensional diffusion equation lacks a steady state with the correct boundary conditions, Laplace transforms must be used to study the long-time behavior of the problem and determine the swimming velocity. For fixed chemical fluxes on the particle surface, we find that the swimming velocity ultimately always decays logarithmically in time. In the case of finite Péclet numbers, we solve the full advection-diffusion equation numerically and show that this decay can be avoided by the particle moving to regions of unconsumed reactant. Finite advection thus regularizes the two-dimensional phoretic problem.
AB - Artificial phoretic particles swim using self-generated gradients in chemical species (self-diffusiophoresis) or charges and currents (self-electrophoresis). These particles can be used to study the physics of collective motion in active matter and might have promising applications in bioengineering. In the case of self-diffusiophoresis, the classical physical model relies on a steady solution of the diffusion equation, from which chemical gradients, phoretic flows, and ultimately the swimming velocity may be derived. Motivated by disk-shaped particles in thin films and under confinement, we examine the extension to two dimensions. Because the two-dimensional diffusion equation lacks a steady state with the correct boundary conditions, Laplace transforms must be used to study the long-time behavior of the problem and determine the swimming velocity. For fixed chemical fluxes on the particle surface, we find that the swimming velocity ultimately always decays logarithmically in time. In the case of finite Péclet numbers, we solve the full advection-diffusion equation numerically and show that this decay can be avoided by the particle moving to regions of unconsumed reactant. Finite advection thus regularizes the two-dimensional phoretic problem.
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U2 - 10.1103/PhysRevE.94.062606
DO - 10.1103/PhysRevE.94.062606
M3 - Article
AN - SCOPUS:85006474759
SN - 2470-0045
VL - 94
JO - Physical Review E
JF - Physical Review E
IS - 6
M1 - 062606
ER -