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A 2D boundary element method for simulating the deformation of axisymmetric compound non‐Newtonian drops
Author(s) -
Toose E.M.,
Geurts B.J.,
Kuerten J.G.M.
Publication year - 1999
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19990730)30:6<653::aid-fld852>3.0.co;2-h
Subject(s) - rotational symmetry , non newtonian fluid , newtonian fluid , finite element method , mechanics , deformation (meteorology) , boundary element method , classical mechanics , geometry , physics , mathematics , thermodynamics , meteorology
The boundary integral formulation of the solution to the Stokes equations is used to describe the deformation of small compound non‐Newtonian axisymmetric drops suspended in a Newtonian fluid that is subjected to an axisymmetric flow field. The non‐Newtonian stress is treated as a source term in the Stokes equations, which yields an extra integral over the domains containing non‐Newtonian material. By transforming the integral representation for the velocity to cylindrical co‐ordinates and performing the integration over the azimuthal direction analytically, the dimension of the problem can be reduced from three to two. A boundary element method for the remaining two‐dimensional problem aimed at the simulation of the deformation of such axisymmetric compound non‐Newtonian drops is developed. Apart from a numerical validation of the method, simulation results for a drop consisting of an Oldroyd‐B fluid and a viscoelastic material are presented. Moreover, the method is extended to compound drops that are composed of a viscous inner core encapsulated by a viscoelastic material. The simulation results for these drops are verified against theoretical results from literature. Moreover, it is shown that the method can be used to identify the dominant break‐up mechanism of compound drops in relation to the specific non‐Newtonian character of the membrane. Copyright © 1999 John Wiley & Sons, Ltd.