DOI: 10.1063/1.868745. Collision rates of spherical drops or particles in a shear flow at arbitrary Péclet numbers

Collision rates of spherical drops or particles in a shear flow at arbitrary Péclet numbers

10.1063/1.868745

Crossref journal-article

AIP Publishing

Physics of Fluids (317)

Abstract

Collision rates of two nondeformable, freely suspended drops (or particles) subject to Brownian motion in a simple shear at low Reynolds number are calculated from the solution of the full Fokker–Plank equation for the pair distribution function. Unlike previous studies on shear-induced collisions, the solution is presented for arbitrary Péclet number (Pe), thus covering a broad range of drop sizes. An efficient numerical technique includes a mixed Galerkin/finite-difference approximation and the ideas of analytical continuation, to represent the solution of the discrete problem as a convergent series for all real Pe. The mobility functions are provided from exact two-drop hydrodynamics and near-contact asymptotics. Extensive calculations are presented for the collision efficiency as a function of the size ratio, drop-to-medium viscosity ratio (μ̂), and Pe≤O(102), for the case of no interdroplet forces. For μ̂≳0, the correction to the collision efficiency for Pe≫1 is O(Pe−1/2). For bubbles (μ̂=0), there is also an O(Pe−2/3) correction of opposite sign, resulting in a local minimum for the collision efficiency. The asymptotic analysis for the opposite limit of Pe≪1 is in excellent agreement with the numerical calculations. For intermediate Pe, the exact numerical solution is compared with different ‘‘additive approximations.’’ The simple two-term additivity approximation is generally unsuccessful, whereas a modified, three-term approximation provides reasonable results except at small size ratios and large viscosity ratios. The effect of the van der Waals attractions on the collision efficiency for typical emulsion drops of 1–10 micron size with μ̂=O(1) is relatively small, of the order 10% in the Brownian regime. As a limiting case of drops, the collision efficiency for equal-sized solid spheres with van der Waals attractions is calculated for Pe≤200; this limit shows a stronger dependence on the Hamaker constant and the retardation parameter. The solution for solid spheres is in excellent agreement with reported experimental data on flocculation dynamics for suspensions with moderate Péclet numbers.

Bibliography

Zinchenko, A. Z., & Davis, R. H. (1995). Collision rates of spherical drops or particles in a shear flow at arbitrary PÃ©clet numbers. Physics of Fluids, 7(10), 2310â2327.

Authors 2

Alexander Z. Zinchenko (first)
Robert H. Davis (additional)

References 39 Referenced 31

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Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 8:39 a.m.)
Deposited	1 year, 6 months ago (Feb. 7, 2024, 9:21 a.m.)
Indexed	3 weeks, 3 days ago (Aug. 6, 2025, 8:01 a.m.)
Issued	29 years, 10 months ago (Oct. 1, 1995)
Published	29 years, 10 months ago (Oct. 1, 1995)
Published Print	29 years, 10 months ago (Oct. 1, 1995)

Funders 0

None

BibTeX

@article{Zinchenko_1995, title={Collision rates of spherical drops or particles in a shear flow at arbitrary Péclet numbers}, volume={7}, ISSN={1089-7666}, url={http://dx.doi.org/10.1063/1.868745}, DOI={10.1063/1.868745}, number={10}, journal={Physics of Fluids}, publisher={AIP Publishing}, author={Zinchenko, Alexander Z. and Davis, Robert H.}, year={1995}, month=oct, pages={2310–2327} }

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