A boundary integral method for twodimensional (non)Newtonian drops in slow viscous flow
Toose, E.M. and Geurts, B.J. and Kuerten, J.G.M. (1995) A boundary integral method for twodimensional (non)Newtonian drops in slow viscous flow. Journal of nonNewtonian fluid mechanics, 60 (23). pp. 129154. ISSN 03770257

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Abstract:  A boundary integral method for the simulation of the timedependent deformation of Newtonian or nonNewtonian drops suspended in a Newtonian fluid is developed. The boundary integral formulation for Stokes flow is used and the nonNewtonian stress is treated as a source term which yields an extra integral over the domain of the drop. The implementation of the boundary conditions is facilitated by rewriting the domain integral by means of the Gauss divergence theorem. To apply the divergence theorem smoothness assumptions are made concerning the nonNewtonian stress tensor. The correctness of these assumptions in actual simulations is checked with a numerical validation procedure. The method appears mathematically correct and the numerical algorithm is second order accurate. Besides this validation we present simulation results for a Newtonian drop and a drop consisting of an OldroydB fluid. The results for Newtonian and nonNewtonian drops in two dimensions indicate that the steady state deformation is quite independent of the dropfluid. The deformation process, however, appears to be strongly dependent on the dropfluid. For the nonNewtonian drop a mechanical model is developed to describe the timedependent deformation of the cylinder for small capillary numbers. 
Item Type:  Article 
Copyright:  © 1995 Elsevier Science 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
Research Group:  
Link to this item:  http://purl.utwente.nl/publications/30268 
Official URL:  http://dx.doi.org/10.1016/03770257(95)013863 
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