Dumbbell micro-robot driven by flow oscillations

Vladimirov, V. A.

doi:10.1017/jfm.2013.30

Cited by 8 publications

(5 citation statements)

References 31 publications

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“…Methods based on electromagnetic or chemical actuation have been developed [13] and currently there is interest in using acoustic techniques to generate propulsion through the oscillation of entrapped air bubbles [20,21]. Vladimirov proposed an alternative mechanism that may lead to swimming based on a deformable object which is neutrally buoyant, but composed of coupled spheres with different sizes and densities [22]. Such an object can generate relative motion of its parts if immersed in a vibrating fluid; this motion may lead to swimming.…”

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confidence: 99%

Propulsion of a Two-Sphere Swimmer

et al. 2015

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We describe experiments and simulations demonstrating the propulsion of a neutrally-buoyant swimmer that consists of a pair of spheres attached by a spring, immersed in a vibrating fluid. The vibration of the fluid induces relative motion of the spheres which, for sufficiently large amplitudes, can lead to motion of the center of mass of the two spheres. We find that the swimming speed obtained from both experiment and simulation agree and collapse onto a single curve if plotted as a function of the streaming Reynolds number, suggesting that the propulsion is related to streaming flows. There appears to be a critical onset value of the streaming Reynolds number for swimming to occur. We observe a change in the streaming flows as the Reynolds number increases, from that generated by two independent oscillating spheres to a collective flow pattern around the swimmer as a whole. The mechanism for swimming is traced to a strengthening of a jet of fluid in the wake of the swimmer.

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confidence: 99%

Propulsion of a Two-Sphere Swimmer

et al. 2015

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“…For example, it can be several applied systems taken from Strogatz (2015), Murray (1989), after installing the time-oscillations into the coefficients. Multiple examples of two-timing equations and drifts in fluid dynamics are given by Vladimirov (2012), Vladimirov (2013a), Vladimirov (2013b), Vladimirov, Proctor and Hughes (2015). In particular, Vladimirov (2013a), Vladimirov (2013b) show that the self-propulsion of deformed bodies in micro-hydrodynamics represents a drift motion in self-generated oscillating field.…”

Section: Discussionmentioning

confidence: 99%

Distinguished Limits and Drifts: between Nonuniqueness and Universality

Vladimirov¹

2021

Preprint

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This paper deals with a version of the two-timing method which describes various 'slow' effects caused by externally imposed 'fast' oscillations. Such small oscillations are often called vibrations and the research area can be referred as vibrodynamics. The basic small parameter represents the ratio of two time-scales; it appears in equations as a regular perturbation. We focus our study on the usually hidden aspects of the two-timing method such as the uniqueness or multiplicity of distinguished limits (DLs) and universal structures of averaged equations. The equations considered represent a generic system of first order ODEs, containing a prescribed oscillating velocity u, given as a function of a general analytic form. The derived dimensionless form of these equations contains two scaling parameters, and proper connections between them lead to the existence of asymptotic solutions. The main result is the demonstration that there are two (and only two) different DLs called DL-1 and DL-2. Calculations show the existence of the closed systems of equations for the first three successive approximations, and indicate that an infinite number of such closed equations are available. It is remarkable that these equations possess universal structures, containing a quadratic in u averaged function called the drift velocity V 2 , which we require to be not nonzero. DL-2 produces a closed averaged system of equations in the zeroth approximation that always represents the main aim in applications. In DL-1, the averaged equations of the zeroth approximation formally coincide with the original system, while the first approximation exhibits a similarity with a linearized version of the previous equation; however it is drastically different, since V 2 appears as its nonhomogeneous 'driving' term. Possible generalizations and interpretations of drift velocities are briefly discussed. To illustrate the broadness of our study, two examples from mathematical biology are shown. The paper is accessible for students in applied mathematics and physics.

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“…Dynamics of microparticles in a viscous fluid play important roles in many applications in medicine and technology, such as minimising surgical invasion and controlling drug delivery, see, e.g., [1] and [2]. e study of the motion of small particles in suspension has been of interest to scientists for many years and is still an active area of research, see, e.g., [3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

“…Substituting ( 8)-( 10) into (7), and after simplification, yields the dimensionless form (all asterisks are omitted for brevity) of the equation…”

mentioning

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On the Motion of Two Microspheres in a Stokes Flow Driven by an External Oscillator Field

Al-Hatmi

Purnama

2021

International Journal of Mathematics and Mathematical Sciences

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Hydrodynamic interactions of a two-solid microspheres system in a viscous incompressible fluid at low Reynolds number is investigated analytically. One of the spheres is conducting and assumed to be actively in motion under the action of an external oscillator field, and as the result, the other nonconducting sphere moves due to the induced flow oscillation of the surrounding fluid. The fluid flow past the spheres is described by the Stokes equation and the governing equation in the vector form for the two-sphere system is solved asymptotically using the two-timing method. For illustrations, applying a simple oscillatory external field, a systematic description of the average velocity of each sphere is formulated. The trajectory of the sphere was found to be inversely proportional to the frequency of the external field. The results demonstrated that no collisions occur between the spheres as the system moves in a circular motion with a fixed separation distance.

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Dumbbell micro-robot driven by flow oscillations

Cited by 8 publications

References 31 publications

Propulsion of a Two-Sphere Swimmer

Propulsion of a Two-Sphere Swimmer

Distinguished Limits and Drifts: between Nonuniqueness and Universality

On the Motion of Two Microspheres in a Stokes Flow Driven by an External Oscillator Field

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