Boundary integral equation approach for stokes slip flow in rotating mixers

Nieto, César; Giraldo, Mauricio; Power, H.

doi:10.3934/dcdsb.2011.15.1019

Cited by 9 publications

(7 citation statements)

References 2 publications

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“…1is supplemented by the initial conditions u(x 1 , x 2 , 0) = u 0 (x 1 , x 2 ) and by velocity and surface force boundary conditions. The Navier slip boundary condition states that the relative tangential fluid velocity, u f t , with respect to the tangential wall velocity, U w t , is proportional to the tangential projection of the local shear rate [3], [13,14,15],…”

Section: Governing Equationsmentioning

confidence: 99%

“…Then, the boundary conditions are inserted into Eq. (15). When the boundary conditions are no-slip the corresponding columns ofH and G are interchanged so that the known values are transposed to the right-hand side and the unknown values are collected on the left-hand side of the equation.…”

Section: Boundary Element Formulationmentioning

confidence: 99%

“…The analytical solution of the linear and nonlinear slip problem in dimensional form is given respectively as [15]…”

Section: Flow In a Horizontal Channelmentioning

confidence: 99%

“…Frangi et al [12] employed a combined velocity-surface traction integral equation to study fluid damping in micro-electro-mechanical systems (MEMS), which also contains Cauchy and Hadamard singularities. Nieto et al [15] developed a BEM formulation to study linear slip flow in rotating mixers, based on the use of the normal and tangential projections of the velocity integral equation, resulting in a weakly-singular mixed system of integral equations for the normal and tangential components of the surface traction. Later, their formulation was extended to incorporate the nonlinear slip condition [16].…”

Section: Introductionmentioning

confidence: 99%

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DRBEM formulation for transient Stokes flow with slip boundary condition

Gümgüm

Wrobel

2017

Engineering Analysis with Boundary Elements

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In this study, the effect of linear and nonlinear slip boundary conditions on the flow of a slow viscous fluid is investigated numerically. The boundary integral representation of the transient Stokes equations is given in primitive variables form. The fundamental solution to the steady Stokes equations is employed in the boundary element method (BEM) formulation. The time derivative is taken to the boundary with the dual reciprocity method and approximated by the finite difference method (FDM) until a steady-state is achieved. It is assumed that the fluid is capable of slip, with the slip velocity expressed as a function of shear rate at the wall. In the numerical tests, the fluid is initially assumed to be stationary; at each time step, the velocity boundary conditions along the walls are updated as the shear forces vary with time.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Boundary Element Formulationmentioning

confidence: 99%

“…The analytical solution of the linear and nonlinear slip problem in dimensional form is given respectively as [15]…”

Section: Flow In a Horizontal Channelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

DRBEM formulation for transient Stokes flow with slip boundary condition

Gümgüm

Wrobel

2017

Engineering Analysis with Boundary Elements

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“…Another practical engineering application of the current technique is for fluid flow in micro and nano-fluidic rotating devices. Nieto et al [38] developed a BEM formulation for Stokes flow with linear slip to study the flow in micro-devices such as concentric and eccentric rotating Couette mixers, and a single rotor mixer, again considering rigid walls.…”

Section: Introductionmentioning

confidence: 99%

A coupled BEM/FEM formulation for drop interaction in Stokes flows with flexible and slip confining boundaries

Soares

Wrobel

2017

Engineering Analysis with Boundary Elements

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In this work, fluid-fluid-solid coupled models are analysed, considering the interaction of boundary and finite element techniques. In this context, the paper focuses on the study of deforming drops through bulk fluids bounded by flexible walls. Here, the fluid subdomains are assumed to be viscous and incompressible, and they are modelled by the BEM. The solid subdomains are assumed to be elastic, and they are modelled by the FEM. Both discontinuity of tractions on the fluid-fluid common boundaries and discontinuity of velocities on the fluidsolid interfaces are considered. For the discontinuity of velocities, a formulation based on nonlinear slip boundary conditions is adopted, which is treated employing a relaxed iterative approach. A Lagrangian representation is considered and remeshing is applied on the fluidfluid interfaces, reducing the appearance of numerical problems. Numerical results are presented to illustrate the performance and potentialities of the proposed techniques.

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Boundary elements solution of stokes flow between curved surfaces with nonlinear slip boundary condition

Nieto

Power

Giraldo

2012

Numerical Methods Partial

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This work presents a boundary integral equation formulation for Stokes nonlinear slip flows based on the normal and tangential projection of the Green's integral representational formulae for the velocity field. By imposing the surface tangential velocity discontinuity (slip velocity) in terms of the nonlinear slip flow boundary condition, a system of nonlinear boundary integral equations for the unknown normal and tangential components of the surface traction is obtained. The Boundary Element Method is used to solve the resulting system of integral equations using a direct Picard iteration scheme to deal with the resulting nonlinear terms. The formulation is used to study flows between curved rotating geometries: i.e., concentric and eccentric Couette flows and single rotor mixers, under nonlinear slip boundary conditions. The numerical results obtained for the concentric Couette flow is validated again a semianalytical solution of the problem, showing excellent agreements. The other two cases, eccentric Couette and single rotor mixers, are considered to study the effect of different nonlinear slip conditions in these flow configurations. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013

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Boundary integral equation approach for stokes slip flow in rotating mixers

Cited by 9 publications

References 2 publications

DRBEM formulation for transient Stokes flow with slip boundary condition

DRBEM formulation for transient Stokes flow with slip boundary condition

A coupled BEM/FEM formulation for drop interaction in Stokes flows with flexible and slip confining boundaries

Boundary elements solution of stokes flow between curved surfaces with nonlinear slip boundary condition

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