Peristaltic manipulation of a bio-particle contained in a closed cavity filled with a Bingham fluid: A numerical study

Poursharifi, Zahra; Sadeghy, Kayvan

doi:10.1016/j.jnnfm.2018.01.001

Cited by 4 publications

(6 citation statements)

References 32 publications

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“…This mechanism is known as peristalsis. Computationally, the forward problem of simulating the particle transport for a given peristaltic wave shape has been considered in a number of works; a few recent ones that consider various physical scenarios include [24,6,1,19,23]. However, the inverse problem of finding the optimal wave shapes (e.g., that minimize the pump's power loss) received little attention, primarily owing to the computational challenges associated with its solutionevery shape iteration requires time-dependent solution of a rigid (or deformable) particle motion through constrained geometries in Stokes flow.…”

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confidence: 99%

“…The adjoint solution evolves backwards in time, from the final condition (23e). The particle motion in problem (23) is given, whereas it was unknown in problem (6).…”

mentioning

confidence: 99%

“…Shape derivative using adjoint solution. Now, combining the derivative problem (19) and the adjoint problem (23) with appropriate choices of test functions, we obtain an expression of J (Γ; θ) that no longer involves the derivative solution:…”

mentioning

confidence: 99%

“…in terms of the transformation velocity θ on Γ, of (u, p, f ) solving the forward problem (6), and of (û, p, f ) solving the adjoint problem (23).…”

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confidence: 99%

“…Proof. The test functions (v, q, g, k, ρ) are set to (û, p, f , ĥ, x) in the derivative problem (19) and to ( u, p, f , h, x) in the adjoint problem (23), and the combination (19a) + (19b) + (19c) + (19d) − (23a) + (23b) − (23c) − (23d) then evaluated (using û = ∂ f G on Γ, implied by (23b), along the way). This results in…”

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confidence: 99%

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Shape optimization of peristaltic pumps transporting rigid particles in Stokes flow

Bonnet¹,

Liu²,

Veerapaneni³

et al. 2021

Preprint

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This paper presents a computational approach for finding the optimal shapes of peristaltic pumps transporting rigid particles in Stokes flow. In particular, we consider shapes that minimize the rate of energy dissipation while pumping a prescribed volume of fluid, number of particles and/or distance traversed by the particles over a set time period. Our approach relies on a recently developed fast and accurate boundary integral solver for simulating multiphase flows through periodic geometries of arbitrary shapes. In order to fully capitalize on the dimensionality reduction feature of the boundary integral methods, shape sensitivities must ideally involve evaluating the physical variables on the particle or pump boundaries only. We show that this can indeed be accomplished owing to the linearity of Stokes flow. The forward problem solves for the particle motion in a slip-driven pipe flow while the adjoint problems in our construction solve quasi-static Dirichlet boundary value problems backwards in time, retracing the particle evolution. The shape sensitivies simply depend on the solution of one forward and one adjoint (for each shape functional) problems. We validate these analytic shape derivative formulas by comparing against finite-difference based gradients and present several examples showcasing optimal pump shapes under various constraints.

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confidence: 99%

“…The adjoint solution evolves backwards in time, from the final condition (23e). The particle motion in problem (23) is given, whereas it was unknown in problem (6).…”

mentioning

confidence: 99%

mentioning

confidence: 99%

“…in terms of the transformation velocity θ on Γ, of (u, p, f ) solving the forward problem (6), and of (û, p, f ) solving the adjoint problem (23).…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Shape optimization of peristaltic pumps transporting rigid particles in Stokes flow

Bonnet¹,

Liu²,

Veerapaneni³

et al. 2021

Preprint

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Sedimentation of an elliptic rigid particle in a yield-stress fluid: A Lattice-Boltzmann simulation

Sobhani

Bazargan²,

Sadeghy

2019

Physics of Fluids

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Sedimentation of a single, two-dimensional, rigid, elliptic particle in a biviscous fluid contained in a finite, closed-ended channel is studied in this work using the lattice-Boltzmann method. The main objective of the work is to numerically investigate the role played by a fluid’s yield stress on the trajectory, orientation, and terminal velocity of such a particle for different density and aspect ratios. Numerical results suggest that a new mode of settling might emerge for yield-stress fluids, which is nonexistent for Newtonian fluids. That is, a particle released from the rest state at the midplane with a prescribed, nonzero, inclination angle (with respect to the horizontal line) migrates toward the left side-wall (if the inclination angle is positive) soon after it is released but changes course after a short while and moves back toward the centerline where the voyage started. However, while for Newtonian fluids the particle eventually returns to the centerline and continues its free fall with a horizontal orientation, for yield-stress fluids, the particle might finally lodge at a specific distance away from the centerline and continue its fall assuming a nonhorizontal orientation. The offset position is predicted to be a function of the Bingham number and the density ratio but independent of the initial inclination angle.

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On the use of peristaltic waves for the transport of soft particles: A numerical study

2020

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Peristaltic transport of inelastic circular droplets immersed in an immiscible viscous fluid is numerically studied in a planar two-dimensional channel using the finite-volume method. Numerical results could be obtained for a wide range of droplet’s material properties at large deformations. Based on the results obtained in this work, for a particle that is initially placed at the centerline, an increase in the droplet’s viscosity is predicted to increase its transport velocity, but the effect can saturate at viscosity ratios as small as two. The transport velocity is shown to linearly increase with the droplet’s density, but the effect turns out to be quite weak. An increase in the interfacial tension is found to lower the transport velocity although the effect appears to approach an asymptote. Depending on their size and the Weber number, droplets are predicted to move faster or slower than rigid particles. The transport velocity of droplets is found to increase with an increase in the wave speed or, equivalently, the Reynolds number. Off-center droplets are predicted to migrate toward the wall or toward the centerline. Droplets that migrate toward the centerline remain a short distance away from it under steady conditions. Distribution of surface forces is used to explain some of these results with viscous normal stress predicted to play a key role in controlling the dynamics of droplets in peristaltic flow.

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Peristaltic manipulation of a bio-particle contained in a closed cavity filled with a Bingham fluid: A numerical study

Cited by 4 publications

References 32 publications

Shape optimization of peristaltic pumps transporting rigid particles in Stokes flow

Shape optimization of peristaltic pumps transporting rigid particles in Stokes flow

Sedimentation of an elliptic rigid particle in a yield-stress fluid: A Lattice-Boltzmann simulation

On the use of peristaltic waves for the transport of soft particles: A numerical study

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