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Flow past a liquid drop with a large non-uniform radial velocity

Published online by Cambridge University Press:  20 April 2006

S. S. Sadhal
Affiliation:
Department of Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453
P. S. Ayyaswamy
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104

Abstract

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.

Type
Research Article
Copyright
© 1983 Cambridge University Press

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References

Baker, D. R. 1970 Analogical determination of drag coefficient of a burning drop in a freefall. Engineer's thesis, Department of Mechanical Engineering, University of Southern California.
Chung, J. N., Ayyaswamy, P. S. & Sadhal, S. S. 1983a Laminar condensation on a moving drop. Part 1. Singular perturbation technique. Unpublished manuscript.
Chung, J. N., Ayyaswamy, P. S. & Sadhal, S. S. 1983b Laminar condensation on a moving drop. Part 2. Numerical solutions. Unpublished manuscript.
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops and Particles. Academic.
Fendell, F. E., Sprankle, M. L. & Dodson, D. S. 1966 Thin flame theory for a fuel drop in slow viscous flow J. Fluid Mech. 26, 267280.Google Scholar
Gal-Or, B. & Yaron, I. 1973 Diffusion drag upon slowly evaporating drops Phys. Fluids 16, 18261829.Google Scholar
Hadamard, J. 1911 Mouvement permanent lent d'une sphère liquide et visqueuse dans un liquide visqueux C.R. Acad. Sci. Paris 152, 17351738.Google Scholar
Harper, J. F. 1972 The motion of drops and bubbles through liquids Adv. Appl. Mech. 12, 59129.Google Scholar
Johnson, R. E. & Wu, T. Y. 1979 Hydrodynamics of low-Reynolds-number flow. Part 5. Motion of a slender torus J. Fluid Mech. 95, 263277.Google Scholar
Law, C. K. 1982 Recent advances in droplet evaporation and combustion Prog. Energy Combust. Sci. 8, 171201.Google Scholar
Rybczynski, W. 1911 On the translatory motion of a fluid sphere in a viscous medium (in German) Bull. Int. Acad. Pol. Sci. Lett. Cl. Sci. Math. Nat. A, 4046.Google Scholar
Schneider, W. 1981 Drag on droplets moving through their own vapour. Part I – Continuum flow PhysicoChem. Hydrodyn. 2, 135141.Google Scholar
Saito, S. 1913 Sci. Rep. Tohoku Imp. Univ., Sendai, Japan 2, 179.
Taylor, T. D. & Acrivos, A. 1964 On the deformation and drag of a falling viscous drop at low Reynolds number J. Fluid Mech. 18, 466476.Google Scholar
Wu, T. Y. & Yates, G. 1977 Finite amplitude unsteady slender body flow theory. In Unsteady Hydrodynamics of Marine Vehicles (ed. R. E. E. Bishop, A. G. Parkinson & W. G. Price), pp. 517528.
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