Low reynolds number motion of a droplet between two parallel plates

Shapira, Moshe; Haber, S.

doi:10.1016/0301-9322(88)90024-9

Cited by 54 publications

(38 citation statements)

References 27 publications

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“…Theoretical work to include the effect of two parallel walls on the motion of, and the drag force acting upon, nearly spherical drops has been conducted by Shapria and Haber. 19,20 Studies for two-dimensional ͑2D͒ channel flows have been conducted to examine the migration of deformable drops, 21 the behavior of concentrated blends, 22 and the influence of surfactants and inertia. 23 In this study, we use a three-dimensional boundaryintegral method 24,25 to study the evolution of the shape of a single drop placed between two parallel plates.…”

Section: Introductionmentioning

confidence: 99%

Boundary-integral method for drop deformation between parallel plates

Janssen

Anderson

2007

Physics of Fluids

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A new boundary-integral method is proposed to study the deformation of drops between two parallel walls. The free-space Green's functions are extended to obey the no-slip condition at the walls. The current formulation is limited to drops with viscosity equal to the matrix fluid, but can be extended to study the effect of nonunit viscosity ratio systems. With this method, the influence of the capillary number and the degree of confinement on drop deformation is investigated. Results for small capillary are compared with small-deformation theory and large capillary results with recent experiments. In both cases, an excellent match is observed. Drops undergoing shear flow deform stronger and align themselves more in the flow direction as the distance between the walls becomes smaller relative to the drop size. Furthermore, the shapes of the drops start to divert significantly from the normal ellipsoidal shapes found, as they show more pointed tips closer to the walls. The transient deformation behavior for more confined systems shows that the drops stretch out to a maximum value, and they slowly retract again to a steady situation. For larger capillary numbers even damped, oscillatory behavior is observed. Investigating the critical capillary number reveals that a minimum is found at a mediocre degree of confinement, after which the critical capillary number increases again to values even larger than the unconfined system. The breakup mode also makes a significant change as it goes from binary to ternary breakup, where the breakup occurs as the drop is retracting.

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Section: Introductionmentioning

confidence: 99%

Boundary-integral method for drop deformation between parallel plates

Janssen

Anderson

2007

Physics of Fluids

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“…Keh and Hsu [22] employed the boundary collocation technique to examine the photophoretic motion of an aerosol sphere perpendicular to an infinite plane wall. The parallel motion of a spherical droplet in a quiescent immiscible fluid at an arbitrary position between two parallel plane walls was studied by Shapira and Haber [23] using the method of reflections and by Keh and Chen [24] using a boundary collocation technique. The slip boundary condition has been studied by many authors in the literature.…”

Section: Introductionmentioning

confidence: 99%

Slip at the surface of a sphere translating perpendicular to a plane wall in micropolar fluid

Sherif

Faltas

Saad

2007

Z. angew. Math. Phys.

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The Stokes axisymmetrical flow caused by a sphere translating in a micropolar fluid perpendicular to a plane wall at an arbitrary position from the wall is presented using a combined analytical-numerical method. A linear slip, Basset type, boundary condition on the surface of the sphere has been used. To solve the Stokes equations for the fluid velocity field and the microrotation vector, a general solution is constructed from fundamental solutions in both cylindrical, and spherical coordinate systems. Boundary conditions are satisfied first at the plane wall by the Fourier transforms and then on the sphere surface by the collocation method. The drag acting on the sphere is evaluated with good convergence. Numerical results for the hydrodynamic drag force and wall effect with respect to the micropolarity, slip parameters and the separation distance parameter between the sphere and the wall are presented both in tabular and graphical forms. Comparisons are made between the classical fluid and micropolar fluid. (2000). 76A05, 76D99. Mathematics Subject Classification

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“…Hiller and Kowalewski [82] first experimentally observed a dilute suspension of liquid drop in plane poiseuille flow. Shapira and Haber [83] used method of reflection to obtain analytical drop shape under the influence of drag force and pressure field. Couillette and Pozrikidis [84] studied pressure driven motion of a deformable drop through a cylindrical tube.…”

Section: Drop Deformation In Pressure Driven Flowmentioning

confidence: 99%

Incorporation of diffuse interface in smoothed particle hydrodynamics: Implementation of the scheme and case studies

Das

2011

Numerical Methods in Fluids

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SUMMARYAn algorithm is proposed to incorporate diffuse interface (DI) modelling in the Lagrangian smoothed particle hydrodynamics (SPH) for the simulation of interface and its evolution. The model assumes a smooth variation of properties across the interface of two immiscible fluids. The conventional CahnHilliard equation has been adopted to take care of the property variation across the DI. However, it has been recast to be compatible with the particle-based formulation. The momentum equation has also been modified to account for the surface energy. Three different case studies namely evolution of gas bubbles at submerged orifice, drop deformation in shear flow and deformation of droplets in parabolic flow have been selected for the application of DI-based SPH (DI-SPH) method of solution. For the sake of comparison the predictions have been made for all the cases by DI-SPH as well as by the basic SPH without incorporating DI. Results of these two simulations have been compared with those already reported in the literature. In all the cases DI-SPH shows a definite improvement in the prediction of the complex interface and their dynamics. The present work demonstrates the strength of the technique in the simulation of diverse multiphase flow problems with evolving interfaces.

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Low reynolds number motion of a droplet between two parallel plates

Cited by 54 publications

References 27 publications

Boundary-integral method for drop deformation between parallel plates

Boundary-integral method for drop deformation between parallel plates

Slip at the surface of a sphere translating perpendicular to a plane wall in micropolar fluid

Incorporation of diffuse interface in smoothed particle hydrodynamics: Implementation of the scheme and case studies

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