Evolution and stationarity of liquid toroidal drop in compressional Stokes flow

• Published in: Journal of fluid mechanics Vol. 835; pp. 1 - 23
• Main Authors: Ee, B. K., Lavrenteva, O. M., Smagin, I., Nir, A.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.01.2018
• Subjects: Collapse; Computational fluid dynamics; Deformation; Deformation mechanisms; Dimensions; Dynamics; Fluid flow; Initial conditions; JFM Papers; Physical properties; Ratios; Simulation; Stokes flow; Stokes law (fluid mechanics); Studies; Toruses; Viscosity; Viscosity ratio; Viscous flow; low-Reynolds-number flows; drops and bubbles; boundary integral methods
• DOI: 10.1017/jfm.2017.752
• ISSN: 0022-1120

Dynamics of fluid tori in slow viscous flow is studied. Such tori are of interest as future carriers of biological and medicinal substances and are also viewed as potential building blocks towards more complex particles. In this study the immiscible ambient fluid is subject to a compressional flow (i.e., bi-extensional flow), and it comprises a generalization of our earlier report on the particular case with viscosity ratio $\unicode[STIX]{x1D706}=1$ (see Zabarankin et al., J. Fluid Mech., vol. 785, 2015, pp. 372–400), where $\unicode[STIX]{x1D706}$ is the ratio between the torus viscosity and that of the ambient fluid. It is found that, for all viscosity ratios, the torus either collapses towards the axis of symmetry or expands indefinitely, depending on the initial conditions and the capillary number, Ca. During these dynamic patterns the cross-sections exhibit various forms of deformation. The collapse and expansion dynamic modes are separated by a limited deformation into a deformed stationary state which appears to exist in a finite interval of the capillary number, $0<Ca<Ca_{cr}(\unicode[STIX]{x1D706})$ , and is unstable to axisymmetric disturbances, which eventually cause the torus either to collapse or to expand indefinitely. The characteristic dimensions and shapes of these unstable stationary tori and their dependence on the physical parameters Ca and $\unicode[STIX]{x1D706}$ are reported.