Flow Past a Liquid Drop with a Large Non-uniform Radial Velocity

In this analysis, the translation of a liquid drop experiencing a strong non-uniform radial velocity has been investigated. The situation arises when a moving liquid drop experiences condensation, evaporation or material decomposition at the surface. By simultaneously treating the flow fields inside and outside the drop, we have obtained physical results relevant to the problem. The magnitude of the radial velocity is allowed to be very large, but the drop motion is restricted to slow translation. The solution to the problem has been developed by considering a uniform radial flow with the translatory motion introduced as a perturbation. The role played by the inertial terms due to the strong radial field has been clearly delineated. The study has revealed several interesting features. An inward normal velocity on a slowly moving drop increases the drag. An increasing outward normal velocity decreases the drag up to a minimum beyond which it increases. The total drag force not only consists of contributions from the viscous and the form drags but also from the momentum transport at the interface. Since the liquid drop admits a non-zero tangential velocity, the tangential momentum convected by the radial velocity forms a part of this drag force. The circulation inside the drop decreases (increases) with an outward (inward) normal velocity. A sufficiently large non-uniform outward velocity causes the circulation to reverse. In the limit of the internal viscosity becoming infinite, our analysis collapses to the simple case of a translating rigid sphere experiencing a large non-uniform radial velocity. By letting the radial velocity become vanishingly small the Stokes-flow solution is recovered. An important contribution of the present study is the identification of a new singularity in the flow description. It accounts for both the inertial and the viscous forces and displays Stokeslet-like characteristics at infinity. Disciplines Engineering | Mechanical Engineering Comments Suggested Citation: Sadhal, Satwindar S. and Portonovo S. Ayyaswamy. (1983). Flow past a liquid drop with a large non-uniform radial velocity.. Journal of Fluid Mechanics. Vol. 133, p. 65-81. Copyright 1983 Cambridge University Press. This journal article is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/187 J . Fluid Meek (1983), vol. 133, p p . 65-81 Printed in Great Britain 65 Flow past a liquid drop with a large non-uniform radial velocity By S. S. SADHAL Department of Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453 AND P. s. AYYASWAMY Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104 (Received 1 October 1982 and in revised form 1 February 1983) In this analysis, the translation of a liquid drop experiencing a strong non-uniform radial velocity has been investigated. The situation arises when a moving liquid drop experiences condensation, evaporation or material decomposition at the surface. By simultaneously treating the flow fields inside and outside the drop, we have obtained physical results relevant to the problem. The magnitude of the radial velocity is allowed to be very large, but the drop motion is restricted to slow translation. The solution to the problem has been developed by considering a uniform radial flow with the translatory motion introduced as a perturbation. The role played by the inertial terms due to the strong radial field has been clearly delineated. The study has revealed several interesting features. An inward normal velocity on a slowly moving drop increases the drag. An increasing outward normal velocity decreases the drag up to a minimum beyond which it increases. The total drag force not only consists of contributions from the viscous and the form drags but also from the momentum transport at the interface. Since the liquid drop admits a non-zero tangential velocity, the tangential momentum convected by the radial velocity forms a part of this drag force. The circulation inside the drop decreases (increases) with an outward (inward) normal velocity. A sufficiently large non-uniform outward velocity causes the circulation to reverse. In the limit of the internal viscosity becoming infinite, our analysis collapses to the simple case of a translating rigid sphere experiencing a large non-uniform radial velocity. By letting the radial velocity become vanishingly small the Stokes-flow solution is recovered. An important contribution of the present study is the identification of a new singularity in the flow description. It accounts for both the inertial and the viscous forces and displays Stokeslet-like characteristics at infinity.