Deformation and breakup of a non-Newtonian slender drop in an extensional flow |
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| Affiliation: | 1. Section Transport Phenomena, Department of Chemical Engineering, Faculty of Applied Sciences, Delft University of Technology, Delft, Van der Maasweg 9, 2629HZ, Netherlands;2. J. M. Burgerscentre for Fluid Mechanics;3. Laboratory for Aero and Hydrodynamics, Delft University of Technology;1. Helmut Schmidt University, Institute of Mechanics, Hamburg D-22039, Germany;2. IAV GmbH, Entwicklungszentrum, Berlin D-10587, Germany;1. Otto H. York Department of Chemical and Materials Engineering, New Jersey Institute of Technology, Newark, New Jersey 07102, USA;2. Colgate Global Technology Center, Colgate-Palmolive Company, Piscataway, New Jersey 08854, USA |
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| Abstract: | The deformation and breakup of a non-Newtonian slender drop in a Newtonian liquid in a simple extensional and creeping flow has been theoretically studied. The power-law was chosen for the fluid inside the drop, and the deformation of the drop is described by a single ordinary differential equation, which was numerically solved. Asymptotic analytical expressions for the local radius were derived near the center and close to the end of the drop. The results for the shape of the drop and the breakup criterion are presented as a function of the capillary number, the viscosity ratio and type of non-Newtonian fluid inside the drop. An approximate analytical solution is also suggested which is in good agreement with the numerical results. |
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