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

I.B. Bajlekov, A.K. Chesters, F.N. Vosse, van de

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Abstract

The deformation and drainage of the film between colliding drops is studied numerically at small capillary numbers, small Reynolds numbers and a range of dispersed to continuous-phase viscosity ratios, ¿, covering the transition from partially-mobile to immobile interfaces. Two types of collision are considered: constant approach velocity and constant interaction force. The problem is solved numerically by means of a finite difference method for the equations in the continuous phase and a boundary integral method or finite-element method in the drops. The velocity profile in the gap between the drops is the sum of a uniform and a parabolic contribution, governed respectively by viscous forces within the dispersed and the continuous phases. Solutions to date concern the limiting cases of partially-mobile or immobile interfaces, in which either the parabolic or plug contribution is negligible. A transformation of variables then results in a universal set of governing equations. In the intermediate regime a transformed viscosity ratio, ¿*, enters these equations. In the constant-force case, the transformed drainage rate increases monotonically with ¿* and the final (rate-determining) stage of drainage is well described by a power-law dependence of the minimum film thickness on time, enabling compact analytical approximations to be developed for the drainage time. These expressions reduce to those in the partially-mobile and immobile limits for ¿*-values outside the range 10
Original languageEnglish
Pages (from-to)445-466
JournalInternational Journal of Multiphase Flow
Volume26
Issue number3
DOIs
Publication statusPublished - 2000

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drainage
Drainage
Viscosity
viscosity
boundary integral method
plugs
Finite difference method
Film thickness
Reynolds number
finite element method
coverings
film thickness
velocity distribution
Finite element method
collisions
approximation
interactions

Cite this

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title = "The effect of the dispersed to continuous-phase viscosity ratio on film drainage between interacting drops",
abstract = "The deformation and drainage of the film between colliding drops is studied numerically at small capillary numbers, small Reynolds numbers and a range of dispersed to continuous-phase viscosity ratios, ¿, covering the transition from partially-mobile to immobile interfaces. Two types of collision are considered: constant approach velocity and constant interaction force. The problem is solved numerically by means of a finite difference method for the equations in the continuous phase and a boundary integral method or finite-element method in the drops. The velocity profile in the gap between the drops is the sum of a uniform and a parabolic contribution, governed respectively by viscous forces within the dispersed and the continuous phases. Solutions to date concern the limiting cases of partially-mobile or immobile interfaces, in which either the parabolic or plug contribution is negligible. A transformation of variables then results in a universal set of governing equations. In the intermediate regime a transformed viscosity ratio, ¿*, enters these equations. In the constant-force case, the transformed drainage rate increases monotonically with ¿* and the final (rate-determining) stage of drainage is well described by a power-law dependence of the minimum film thickness on time, enabling compact analytical approximations to be developed for the drainage time. These expressions reduce to those in the partially-mobile and immobile limits for ¿*-values outside the range 10",
author = "I.B. Bajlekov and A.K. Chesters and {Vosse, van de}, F.N.",
year = "2000",
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language = "English",
volume = "26",
pages = "445--466",
journal = "International Journal of Multiphase Flow",
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The effect of the dispersed to continuous-phase viscosity ratio on film drainage between interacting drops. / Bajlekov, I.B.; Chesters, A.K.; Vosse, van de, F.N.

In: International Journal of Multiphase Flow, Vol. 26, No. 3, 2000, p. 445-466.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Bajlekov, I.B.

AU - Chesters, A.K.

AU - Vosse, van de, F.N.

PY - 2000

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N2 - The deformation and drainage of the film between colliding drops is studied numerically at small capillary numbers, small Reynolds numbers and a range of dispersed to continuous-phase viscosity ratios, ¿, covering the transition from partially-mobile to immobile interfaces. Two types of collision are considered: constant approach velocity and constant interaction force. The problem is solved numerically by means of a finite difference method for the equations in the continuous phase and a boundary integral method or finite-element method in the drops. The velocity profile in the gap between the drops is the sum of a uniform and a parabolic contribution, governed respectively by viscous forces within the dispersed and the continuous phases. Solutions to date concern the limiting cases of partially-mobile or immobile interfaces, in which either the parabolic or plug contribution is negligible. A transformation of variables then results in a universal set of governing equations. In the intermediate regime a transformed viscosity ratio, ¿*, enters these equations. In the constant-force case, the transformed drainage rate increases monotonically with ¿* and the final (rate-determining) stage of drainage is well described by a power-law dependence of the minimum film thickness on time, enabling compact analytical approximations to be developed for the drainage time. These expressions reduce to those in the partially-mobile and immobile limits for ¿*-values outside the range 10

AB - The deformation and drainage of the film between colliding drops is studied numerically at small capillary numbers, small Reynolds numbers and a range of dispersed to continuous-phase viscosity ratios, ¿, covering the transition from partially-mobile to immobile interfaces. Two types of collision are considered: constant approach velocity and constant interaction force. The problem is solved numerically by means of a finite difference method for the equations in the continuous phase and a boundary integral method or finite-element method in the drops. The velocity profile in the gap between the drops is the sum of a uniform and a parabolic contribution, governed respectively by viscous forces within the dispersed and the continuous phases. Solutions to date concern the limiting cases of partially-mobile or immobile interfaces, in which either the parabolic or plug contribution is negligible. A transformation of variables then results in a universal set of governing equations. In the intermediate regime a transformed viscosity ratio, ¿*, enters these equations. In the constant-force case, the transformed drainage rate increases monotonically with ¿* and the final (rate-determining) stage of drainage is well described by a power-law dependence of the minimum film thickness on time, enabling compact analytical approximations to be developed for the drainage time. These expressions reduce to those in the partially-mobile and immobile limits for ¿*-values outside the range 10

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