The effect of the dispersed to continuous-phase viscosity ratio on film drainage between interacting drops

Bazhlekov, Ivan B.; Chesters, A.K.; Vosse, F.N. van de

doi:10.1016/s0301-9322(99)00032-4

Cited by 91 publications

(79 citation statements)

References 5 publications

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“…The viscosity ratio is ϭ1 and the capillary number is relatively small, Caϭ0.025, in order to guarantee the validity of the asymptotic theory. In the asymptotic theory the evolution of the film is given by the solution of simplified axisymmetric film-drainage equations [29][30][31][32] in the gap between the drops. The drop interaction enters as a boundary condition for the film drainage model, 31 to take into account the external flow or force.…”

Section: Drop-to-drop Interactionmentioning

confidence: 99%

“…In the asymptotic theory the evolution of the film is given by the solution of simplified axisymmetric film-drainage equations [29][30][31][32] in the gap between the drops. The drop interaction enters as a boundary condition for the film drainage model, 31 to take into account the external flow or force. In the present comparison the formula of Hadamar and Rybczinski 33 for the force between two spherical drops in simple shear flow is used:…”

Section: Drop-to-drop Interactionmentioning

confidence: 99%

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Nonsingular boundary integral method for deformable drops in viscous flows

2004

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A three-dimensional boundary integral method for deformable drops in viscous flows at low Reynolds numbers is presented. The method is based on a new nonsingular contour-integral representation of the single and double layers of the free-space Green's function. The contour integration overcomes the main difficulty with boundary-integral calculations: the singularities of the kernels. It also improves the accuracy of the calculations as well as the numerical stability. A new element of the presented method is also a higher-order interface approximation, which improves the accuracy of the interface-to-interface distance calculations and in this way makes simulations of polydispersed foam dynamics possible. Moreover, a multiple time-step integration scheme, which improves the numerical stability and thus the performance of the method, is introduced. To demonstrate the advantages of the method presented here, a number of challenging flow problems is considered: drop deformation and breakup at high viscosity ratios for zero and finite surface tension; drop-to-drop interaction in close approach, including film formation and its drainage; and formation of a foam drop and its deformation in simple shear flow, including all structural and dynamic elements of polydispersed foams.

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Section: Drop-to-drop Interactionmentioning

confidence: 99%

Section: Drop-to-drop Interactionmentioning

confidence: 99%

Nonsingular boundary integral method for deformable drops in viscous flows

2004

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“…Modelling the thinning of the liquid film is the object of a huge literature (see, e.g. Platikanov, 1964;Nakamura and Uchida, 1980;Lin and Slattery, 1982;Chen and Slattery, 1982;Doubliez, 1991;Bazhlekov et al, 2000). Two competitive scenarios hold:…”

Section: Dimple Formation Reboundmentioning

confidence: 99%

Numerical Simulation of the Buoyancy-Driven Bouncing of a 2-D Bubble at a Horizontal Wall

Canot

Davoust

Hammoumi

et al. 2003

Theoretical and Computational Fluid Dynamics

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Abstract. The rise of a buoyant bubble and its interaction with a target horizontal wall is simulated with a 2-D numerical code based on the Boundary Element Method (BEM). Developed from a viscous potential flow approximation, the BEM takes into account only the part of the energy dissipation related to the normal viscous stresses. Hence, a simple analytical model based on lubrication approximation is coupled to the BEM in order to compute the drainage of the interstitial liquid film filling the gap between the bubble and the near wall. In this way the bubble-wall interaction is fully computed: the approach stage, the bubble deformation stage and, depending on the values of the Reynolds number and the Weber number, the rebound and the bubble oscillations. From computation of both the bubble interface motion and the liquid velocity field, a physical analysis in terms of energy budget is proposed. Though, in the present study, the bubble under consideration is basically supposed to be a 2-D gaseous cylinder, a comparison between our numerical results and the experiments of Tsao and Koch (1997) enlightens interestingly the physics of bouncing.

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“…The flow in the film is mostly treated on the basis of the lubrication model, see e.g. Davis et al [2], Chesters [3], Klaseboer et al [4], Bazhlekov et al [5]. From this model, equations for calculating the film thickness as funcion of time were derived, but a determination of the film thickness at the rupture instant is not possible.…”

Section: Introductionmentioning

confidence: 99%

On The Rupture of a Liquid Film Formed on a Droplet Crossing a Horizontal Liquid-Liquid Interface

Mitrovic¹

2012

JEAS

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A gravity droplet crossing a liquid-liquid interface is covered on the forefront with a film of the leaving liquid phase. The film thickness is not homogeneous over the droplet surface, and it reduces as the droplet penetrates the interface, particularly in the stretched area where it then ruptures. An expression for the film thickness in the stretched region is deduced from a force balance. The film rupture is expected to occur at a droplet position when the normal stress in the stretched film reaches the tensile strength of the liquid. By using some experimental data from literature the expression delivers 26 nm for the film thickness at rupture, while Burrill and Woods [1] obtained experimentally values between 30 nm and 50 nm.

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The effect of the dispersed to continuous-phase viscosity ratio on film drainage between interacting drops

Cited by 91 publications

References 5 publications

Nonsingular boundary integral method for deformable drops in viscous flows

Nonsingular boundary integral method for deformable drops in viscous flows

Numerical Simulation of the Buoyancy-Driven Bouncing of a 2-D Bubble at a Horizontal Wall

On The Rupture of a Liquid Film Formed on a Droplet Crossing a Horizontal Liquid-Liquid Interface

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