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Collision statistics of finite-size monodisperse droplets in homogeneous isotropic turbulence

Published online by Cambridge University Press:  01 October 2025

Victor Boniou Open the ORCID record for Victor Boniou [Opens in a new window] ,
Stephane Jay ,
Guillaume Vinay  and
Jean-Lou Pierson Open the ORCID record for Jean-Lou Pierson [Opens in a new window]
Victor Boniou*
Affiliation:
IFP Energies Nouvelles, Institut Carnot IFPEN Transports Energie, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France
Stephane Jay
Affiliation:
IFP Energies Nouvelles, Institut Carnot IFPEN Transports Energie, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France
Guillaume Vinay
Affiliation:
IFP Energies Nouvelles, Institut Carnot IFPEN Transports Energie, Rond-point de l’échangeur de Solaize, BP 3, 69360 Solaize, France
Jean-Lou Pierson
Affiliation:
IFP Energies Nouvelles, Institut Carnot IFPEN Transports Energie, Rond-point de l’échangeur de Solaize, BP 3, 69360 Solaize, France
*
Corresponding author: Victor Boniou, victor.boniou@ifpen.fr
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Abstract

In this study we focus on the collision rate and contact time of finite-sized droplets in homogeneous, isotropic turbulence. Additionally, we concentrate on sub-Hinze–Kolmogorov droplet sizes to prevent fragmentation events. After reviewing previous studies, we theoretically establish the equivalence of spherical and cylindrical formulations of the collision rate. We also obtained a closed-form expression for the collision rate of inertial droplets under the assumption of inviscid interactions. We then perform droplet-resolved simulations using the Basilisk solver with a multi-field volume-of-fluid method to prevent numerical droplet coalescence, ensuring a constant number of droplets of the same size within the domain, thereby allowing for the accumulation of collision statistics. The collision statistics are studied from numerical simulations, varying parameters such as droplet volume fraction, droplet size relative to the dissipative scale, density ratio and viscosity ratio. Our results show that the contact time is finite, leading to non-binary droplet interactions at high volume fractions. Additionally, the contact duration is well predicted by the eddy turnover time. We also find that the radial distribution at contact is significantly smaller than that predicted by the hard-sphere model due to droplet deformation in close proximity. Furthermore, we show that for neutrally buoyant droplets, the mean relative velocity is similar to the mean relative velocity of the continuous phase, except when the droplets are close. Finally, we demonstrate that the collision rate obeys the appropriate theoretical law, although a numerical prefactor weakly varies as a function of the dimensionless parameters, which differs from the constant prefactor from theory.

JFM classification

Drops and Bubbles: Breakup/coalescence Multiphase and Particle-laden Flows: Multiphase flow Turbulent Flows: Homogeneous turbulence

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Journal of Fluid Mechanics , Volume 1020 , 10 October 2025 , A18
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© The Author(s), 2025. Published by Cambridge University Press

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