Fluid dynamics and mass transfer of interacting drops -a mathematical modelling approach

Kleinstreuer, Clement; Ramachandran, S

doi:10.1016/0270-0255(87)90608-7

Cited by 1 publication

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“…The evaporative effect of ventilation due to a single drop freely falling in the atmosphere has frequently been considered (Dolezel, 1944;Ranz and Marshall, 1952;Duguid and Stampfer, 1971;Hughes and Stampfer, 1971;Carstens, 1979;Kleinstreuer and Ramachandran, 1987;Kukkonen et al, 1989;Chavarría et al, 2022;Sezen and Gungor, 2023) Most commonly, the drop is spherical, but deformation has been a topic of interest, as well (Petera and Weatherly, 2001). Interaction of two evaporating drops has been studied at low Reynolds number under the action of a prescribed blowing rate (Oguz and Prosperetti, 1989), at intermediate Reynolds numbers (Raju and Sirignano, 1990), and in combustion (Chiang and Sirignano, 1993;Yang et al, 2020) for tandem motion.…”

Section: Introductionmentioning

confidence: 99%

Gravitational Interactions of Two Small Evaporating Drops

Rother

2024

Preprint

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Relative trajectories are determined for a pair of water drops falling in air with radii between 2 μm and 30 μm. The droplets are small enough that diffusion dominates convection in evaporation, but significant drop inertia at low Reynolds number is considered. In addition to hydrodynamic and lubrication forces, attractive van der Waals forces and Maxwell slip are taken into account. Because the loss of mass is not uniform due to the presence of a second drop, and mass transfer and momentum transfer are effectively decoupled, the droplet position needs to be assessed. Three outcomes are compared. The isolated drop result for both droplets is employed as a base case, since the mass loss is constant over each drop surface. Alternatively, the bispherical coordinate solution for two evaporating drops is applied, with the drop positions 1) fixed by the hydrodynamics or 2) allowed to move based on the nonspherical mass loss. In all three cases, evaporation leads to weaker inertial effects and stronger hydrodynamic effects. The single sphere model has the largest drop gap, followed by the bispherical coordinate solutions with a fixed and movable center, respectively. Critical horizontal offsets for coalescence are also calculated with a finite vertical offset. With both attractive molecular forces and slip, all three approaches to evaporation lead to similar results, making the choice of method nearly inconsequential. Moderate agreement between previous experiments and an approximate, generalized form of the current theory is obtained for the evaporation rate of falling drops.

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Section: Introductionmentioning

confidence: 99%

Gravitational Interactions of Two Small Evaporating Drops

Rother

2024

Preprint

View full text Add to dashboard Cite

show abstract

Fluid dynamics and mass transfer of interacting drops -a mathematical modelling approach

Cited by 1 publication

References 26 publications

Gravitational Interactions of Two Small Evaporating Drops

Gravitational Interactions of Two Small Evaporating Drops

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