Unsteady stokes equations: Some complete general solutions

Venkatlaxmi, A.; Padmavathi, B.S.; Amaranath, T.

doi:10.1007/bf02829854

Cited by 8 publications

(2 citation statements)

References 5 publications

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“…We solve the corresponding unsteady Stokes equation with appropriate boundary conditions, using the double curl representation (Venkatalaxmi, Padmavathi & Amarnath 2004 a ). Note that the former method has been proved to provide a complete general solution to the unsteady Stokes equation (Venkatalaxmi, Padmavathi & Amarnath 2004 b ). We calculate the flow field, migration velocity and rotation rate of an unsteady chiral swimmer in a closed form.…”

Section: Introductionmentioning

confidence: 99%

Unsteady chiral swimmer and its response to a chemical gradient

Maity

Burada

2022

J. Fluid Mech.

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Unsteadiness occurs in the motion of swimmers while they start from rest or escape from a predator, or attack prey. In this paper, we study the behaviour of an unsteady chiral swimmer, with a prescribed surface slip velocity, in the low-Reynolds-number regime, and its response to an external chemical gradient. In the first part, by solving the unsteady Stokes equation, we calculate the migration velocity ( $\boldsymbol {U}$ ), rotation rate ( $\boldsymbol {\varOmega }$ ) and flow field of the unsteady swimmer in a closed form. We compare these results with some previously known results in appropriate limits. In the second part, we investigate the response of the unsteady chiral swimmer to an external chemical gradient, which can influence the swimmer's surface slip velocity. Consequently, the swimmer either steers towards the source of the chemical gradient or moves away from it, depending on the strengths of $\boldsymbol {U}$ and $\boldsymbol {\varOmega }$ , and the corresponding angle ( $\chi$ ) between them. Interestingly, the swimmer swims in a closed orbit in the vicinity of the chemical target, depending on the strengths of $\boldsymbol {\varOmega }$ and $\chi$ . We present a complete state diagram representing the successful, unsuccessful and orbital states for various strengths of $\boldsymbol {\varOmega }$ and $\chi$ . This study is useful to understand the unsteady propulsion of ciliated microorganisms and their response to external gradients.

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Section: Introductionmentioning

confidence: 99%

Unsteady chiral swimmer and its response to a chemical gradient

Maity

Burada

2022

J. Fluid Mech.

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“…We solve the corresponding unsteady Stokes equation, with appropriate boundary conditions, using the double curl representation [29]. Note that the former method has been proved to provide a complete, general solution of the unsteady Stokes equation [30]. For the first time, we provide the flow field, migration velocity, and rotation rate in a closed form for an unsteady chiral squirmer.…”

Section: Introductionmentioning

confidence: 99%

Unsteady chiral swimmer in presence of an external chemical gradient

Maity,

Burada

2021

Preprint

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Unsteadiness occurs in the low Reynolds number swimmers' motion while they start from rest or escape from a predator or attack prey. In this paper, we study an unsteady chiral swimmer's behavior, with a prescribed surface slip velocity, in the low Reynold number regime and its response to an external chemical gradient. Using the general solution of unsteady Stokes equation and appropriate boundary conditions, i.e., slip velocity at the body surface and the ambient velocity field at the far-field, we calculate the migration velocity, rotation rate, and the flow field of the swimmer in a closed-form. We compare the velocity with some previously known results in appropriate limits.The continuous unsteady motion of the swimmer affects its tactic movement. A relevant example of this situation is chemotaxis, where the presence of chemical stimulus alters the swimmer's surface slip velocity. As a result, the swimmer either steers towards the chemical target or moves away from it, depending on the system parameters. Here, the rotation rate controls the success of the chemotaxis. In addition to the successful and unsuccessful cases, we observe a unique orbiting state where the swimmer keeps revolving around the chemical target in diffusive orbits.

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A study of an arbitrary unsteady Stokes flow in and around a liquid sphere

Choudhuri

Padmavati

2014

Applied Mathematics and Computation

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Unsteady stokes equations: Some complete general solutions

Cited by 8 publications

References 5 publications

Unsteady chiral swimmer and its response to a chemical gradient

Unsteady chiral swimmer and its response to a chemical gradient

Unsteady chiral swimmer in presence of an external chemical gradient

A study of an arbitrary unsteady Stokes flow in and around a liquid sphere

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