Problems in Fluid Dynamics and Elasticity

点击翻译按钮获取中文摘要

Research is proposed on the following topics:1. Breakup of liquid jets: This research will mathematically analyze the capillary breakup of jets of Newtonian and viscoelastic liquids. The effect of polymer additives in suppressing breakup is well known and exploited both in nature (spider webs) and in technology (control of drops sizes in spraying of liquids). The research will concentrate on the asymptotics of breakup and compare various constitutive theories.2. Stability of viscoelastic flows: Elastic instabilities have been investigated extensively over the past ten years. Such instabilities often pose limits for polymer processing conditions. In the numerical investigation of instabilities in complex flows, continuous spectra which are poorly resolved pose a significant challenge. The research is aimed at using analytical techniques to determine the location of these continuous spectra.3. Shape control in elasticity: An elastic medium is controlled by actuators which can supply a stress of a given type. The research will investigate the question whether such controls can achieve a given shape of the medium.4. Numerical simulation of two-fluid flows: The research will continue work on simulation of flows of two liquids using a volume of fluid code. The following three problems will be investigated: a) Formation of ``staircase" structures on impacting drops due to capillary waves. b) Tipstreaming in drop breakup under shear when surfactants are present. c) Effect of normal stresses on breakup of viscoelastic drops under shear.The proposed research addresses fundamental issues which arise in the processing anduse of polymeric liquids, the control of deformations of elastic solids and theformation of emulsions by shear mixing. The proposed topics include a comparison ofthe qualitative behavior various models of polymeric fluids in jet breakup, thestability of polymeric flows, the question which shapes of an elastic medium canbe achieved by a given type of control, and the development of numerical methods fortwo-fluid flows.