Deformation of a non-Newtonian ellipsoidal drop in a non-Newtonian matrix: extension of Maffettone–Minale model

• Published in: Journal of non-Newtonian fluid mechanics 2004-11, Vol.123 (2), p.151-160
• Main Author: Minale, Mario
• Format: Article
• Language: English
• Subjects: Blend; Drop; Drops and bubbles; Dynamics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Non-Newtonian; Non-newtonian fluid flows; Nonhomogeneous flows; Physics
• ISSN: 0377-0257; 1873-2631
• DOI: 10.1016/j.jnnfm.2004.07.017

A phenomenological model for the dynamics of a buoyancy free non-Newtonian drop immersed in a non-Newtonian fluid subjected to a flow field with an arbitrary uniform velocity gradient is presented. The model is based on the assumption that the drop deforms while remaining ellipsoidal and the volume is preserved. The analytical limits of Taylor for both small deformations and high viscosity ratios are exactly recovered. Also, the affine deformation limit is recovered under the appropriate conditions. In addition, the second-order theory for non-Newtonian systems [F. Greco, J. Non-Newtonian Fluid Mech. 107 (2002) 111–131] is also recovered to within a minor term. As a consequence, the major and minor drop semiaxes, together with the drop angle, properly degenerate into the analytical limits, while the third semiaxis differs only slightly from the exact theory. Model predictions are compared with experimental data for both Newtonian and non-Newtonian systems, throughout a significant range of parameters values.