Gaussian memory in kinematic matrix theory for self-propellers

Nourhani, Amir; Crespi, Vincent H.; Lammert, Paul E.

doi:10.1103/physreve.90.062304

Cited by 12 publications

(7 citation statements)

References 79 publications

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“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14] Self-locomotion at low Reynolds number has been studied for many years in biological systems. [15][16][17][18][19] New artificial nanomotors exhibit linear [20][21][22][23][24][25][26] and rotational motion [27][28][29][30][31][32][33][34][35][36] in abiotic systems without external driving forces. To assist experimental e↵orts in developing faster [22][23][24] and more functional 37,38 nanomotors, mathematical models of motor function [39][40][41][42][43][44] have been developed to relate the velocity and performance of motors to the physical parameters of the nanomotor and its environment.…”

Section: Introductionmentioning

confidence: 99%

A general flux-based analysis for spherical electrocatalytic nanomotors

et al. 2015

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We present a flux-based analysis of the motion of spherical electrocatalytic nanomotors based on an electrokinetic model with general distribution of cation flux over the motor surface. Using the method of matched asymptotic expansions, we find a general expression for the motor velocity to leading order in the Debye length in the limit of weak surface cation flux. The nanomotor velocity is proportional to the first Legendre coe cient of surface cation flux and depends non-linearly on the interfacial potential at the particle surface, inversely on the fluid viscosity and background ion concentration in the electrolyte. The results are consistent with previous experimental observations and numerical calculations. We also provide a scaling analysis that portrays the physical picture of self-electrophoresis at the molecular level based on migration of ions and transfer of their momentum to fluid.

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Section: Introductionmentioning

confidence: 99%

A general flux-based analysis for spherical electrocatalytic nanomotors

et al. 2015

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“…To study the dynamics of these particles we use the kinematrix theory [19,20], that we recently developed as an alternative to Langevin and Fokker-Planck formalisms. In the limit of short noise correlation and momentum relaxation times, the self-propeller's kinematic properties such as orientational diffusion, angular speed and flipping rate can be packaged into a 3 × 3 kinematrix K. The dynamics of the body frame is governed by…”

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confidence: 99%

Spiral diffusion of rotating self-propellers with stochastic perturbation

et al. 2016

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Translationally diffusive behavior arising from the combination of orientational diffusion and powered motion at microscopic scales is a known phenomenon, but the peculiarities of the evolution of expected position conditioned on initial position and orientation have been neglected. A theory is given of the spiral motion of the mean trajectory depending upon propulsion speed, angular velocity, orientational diffusion and rate of random chirality reversal. We demonstrate the experimental accessibility of this effect using both tadpole-like and Janus sphere dimer rotating motors. Sensitivity of the mean trajectory to the kinematic parameters suggest that it may be a useful way to determine those parameters.Active colloids such as microswimmers and nanomotors are a class of non-equilibrium systems which has been the subject of intense research in recent years [1][2][3]. At the sub-micron length scale, stochastic effects significantly perturb a self-propeller's deterministic motion, and the coupling of such noise to a steady motion can lead to unexpected emergent phenomena such as motilityinduced phase separation [4], chiral diffusion [5], and phenomena with biological relevance [6] which can now be modelled by artificial active colloids. In the absence of noise a circle swimmer, confined to a plane with a strong rotational component to its powered motion, travels on a fixed circle with a steady clockwise or counterclockwise chirality [7]. Artificial swimmers of this sort have been fabricated in a variety of forms such as tadpoles [8,9], Janus sphere dimers [10,11], nanorods [12,13], and acoustically-activated swimmers [14]. Stochastic perturbations in the form of unbiased orientational diffusion or random chirality-reversal resulting from flipping about the direction of motion have significant effects on the long term motion: an effective translational diffusion is generated [15][16][17], the infinite-time limit of the mean position conditioned on the initial position and velocity is non-zero and chirality-dependent [5], and the mean approach to the limit is a logarithmic spiral [17,18].In this Letter, we experimentally and theoretically demonstrate "spiral diffusion" as a general finite-time behavior of the conditional mean position in circle swimmers. First, we expose the phenomenon in experimental data for both tadpole-like [9] and Janus-sphere dimer [10] rotary microswimmers (see Fig. 1), and present fits to the model. Then, we explain the theory for spiral diffusion of circle swimmers subjected to both orientational diffusion and flipping (change of chirality). The expected position of the swimmer, conditioned on its initial position, velocity direction and chirality, evolves along a converging spiral. The theory serves as a sensitive and accurate utility for determining kinematic parameters such as angular velocity and orientational diffusivity. Supplementary Material contains the details of fabrication and experimental protocols, as well as movies of simulated ensembles of swimmers for a variety of noise par...

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“…The development of electrocatalytic nanomotors over the past decade has opened a new area in colloid science focused on artificial self-propelling particles at the microand nanoscales [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. These artificial swimmers can mimic the self-locomotion of small-Reynolds-number biological swimmers [17][18][19][20][21] by harvesting energy from their local environments to power rectilinear [22][23][24][25][26][27] or rotational [28][29][30][31][32][33][34][35][36] motion.…”

Section: Introductionmentioning

confidence: 99%

Self-consistent nonlocal feedback theory for electrocatalytic swimmers with heterogeneous surface chemical kinetics

2015

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We present a self-consistent nonlocal feedback theory for the phoretic propulsion mechanisms of electrocatalytic micromotors or nanomotors. These swimmers, such as bimetallic platinum and gold rods catalyzing decomposition of hydrogen peroxide in aqueous solution, have received considerable theoretical attention. In contrast, the heterogeneous electrochemical processes with nonlocal feedback that are the actual "engines" of such motors are relatively neglected. We present a flexible approach to these processes using bias potential as a control parameter field and a locally-open-circuit reference state, carried through in detail for a spherical motor. While the phenomenological flavor makes meaningful contact with experiment easier, required inputs can also conceivably come from, e.g., Frumkin-Butler-Volmer kinetics. Previously obtained results are recovered in the weak-heterogeneity limit and improved small-basis approximations tailored to structural heterogeneity are presented. Under the assumption of weak inhomogeneity, a scaling form is deduced for motor speed as a function of fuel concentration and swimmer size. We argue that this form should be robust and demonstrate a good fit to experimental data.

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Gaussian memory in kinematic matrix theory for self-propellers

Cited by 12 publications

References 79 publications

A general flux-based analysis for spherical electrocatalytic nanomotors

A general flux-based analysis for spherical electrocatalytic nanomotors

Spiral diffusion of rotating self-propellers with stochastic perturbation

Self-consistent nonlocal feedback theory for electrocatalytic swimmers with heterogeneous surface chemical kinetics

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