Takens-Bogdanov bifurcation on the hexagonal lattice for double-layer convection

Abstract In the Bénard problem for two-fluid layers, Takens-Bogdanov bifurcations can arise when the stability thresholds for both layers are close to each other. In this paper, we provide an analysis of bifurcating solutions near such a Takens-Bogdanov point, under the assumption that solutions are doubly periodic with respect to a hexagonal lattice. Our analysis focusses on periodic solutions, secondary bifurcations from steady to periodic solutions and heteroclinic solutions arising as limits of periodic solutions. We compute the coefficients of the amplitude equations for a number of physical situations. Numerical integration of the amplitude equations reveals quasiperiodic and chaotic regimes, in addition to parameter regions where steady or periodic solutions are observed

A new volume-of-fluid formulation for surfactants and simulations of drop deformation under shear at a low viscosity ratio

Renardy, Yuriko Y.; Renardy, Michael. (2001). A new volume-of-fluid formulation for surfactants and simulations of drop deformation under shear at a low viscosity ratio. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3633

Effect of inertia on drop breakup under shear

A spherical drop, placed in a second liquid of the same density and viscosity, is subjected to shear between parallel walls. The subsequent flow is investigated numerically with a volume-of-fluid continuous-surface-force algorithm. Inertially driven breakup is examined. The critical Reynolds numbers are examined for capillary numbers in the range where the drop does not break up in Stokes flow.Renardy, Yuriko Y.; Cristini, Vittorio. (2001). Effect of inertia on drop breakup under shear. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3622

Scalings for fragments produced from drop breakup in shear flow with inertia

When a drop is sheared in a matrix liquid, the largest daughter drops are produced by elongative end-pinching. The daughter drop size is found to scale with the critical drop size that would occur under the same flow conditions and fluid properties.Renardy, Yuriko Y.; Cristini, Vittorio. (2001). Scalings for fragments produced from drop breakup in shear flow with inertia. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3626