Moshe Favelukis

Dynamics of spherical bubble growth

A model for the dynamics of spherical bubble growth in a quiescent viscous liquid is presented. The gas inside the bubble is a van der Waals fluid, and the viscous liquid outside the bubble is a Flory–Hugins solvent–polymer solution. The growth of the bubble in the viscous liquid is assumed to be controlled by momentum, heat and mass transfer. Using the integral method, the transport equations were transformed into ordinary differential equations, which were numerically solved. An analytical criterion of when it is justified to make the usual isothermal assumption is also derived. The relevance of this work to the processes of polymer melt devolatilization and the production of foamed plastics is discussed.

Unsteady mass transfer in the continuous phase around axisymmetric drops of revolution

Abstract Unsteady mass transfer in the continuous phase around any axisymmetric drop of revolution at high Peclet numbers has been theoretically studied. General equations for the concentration profile, the molar flux, the concentration boundary layer thickness, and the time to reach steady state have been obtained using a similarity transformation and by the method of characteristics. Solutions for large number of problems can be immediately obtained, with the only requirements being the shape of the drop and the tangential velocity at the surface of the drop.

Deformation and breakup of a non-Newtonian slender drop in an extensional flow: inertial effects and stability

We consider the deformation and breakup of a non-Newtonian slender drop in a Newtonian liquid, subject to an axisymmetric extensional flow, and the influence of inertia in the continuous phase. The non-Newtonian fluid inside the drop is described by the simple power-law model and the unsteady deformation of the drop is represented by a single partial differential equation. The steady-state problem is governed by four parameters: the capillary number; the viscosity ratio; the external Reynolds number; and the exponent characterizing the power-law model for the non-Newtonian drop. For Newtonian drops, as inertia increases, drop breakup is facilitated. However, for shear thinning drops, the influence of increasing inertia results first in preventing and then in facilitating drop breakup. Multiple stationary solutions were also found and a stability analysis has been performed in order to distinguish between stable and unstable stationary states.

Deformation of a slender bubble in a non-Newtonian liquid in an extensional flow

Abstract The deformation of a slender bubble in a non-Newtonian liquid in a simple extensional and creeping flow has been theoretically studied. Assuming a constant pressure in the liquid, the deformation of the bubble is described by a single ordinary differential equation, which was solved numerically. Analytical expressions for the local radius were obtained near the center and close to the end of the bubble. The results for the shape of the bubble are presented as a function of the capillary number and type of liquid.

On the diffusion from a slender bubblein an extensional flow

Mass transfer between a slender bubble and a Newtonian liquid in a simple extensional and creeping flow has been theoretically studied. The analytical steady-state solution when the Peclet number is zero has been obtained using the works of Szegö and Payne, who studied the electrostatic capacity of a spindle surface in a bispherical coordinate system. The result shows, as expected, that the modified Sherwood number increases as the capillary number increases since the surface area of the bubble also increases.

DEFORMATION AND BREAKUP OF A NON-NEWTONIAN DROP IN MICROGRAVITY ENVIRONMENTS

The deformation and breakup of a non-Newtonian slender drop in a Newtonian liquid in a simple extensional and creeping flow has been theoretically studied. The power law was chosen for the fluid inside the drop, and the deformation of the drop is described by a single ordinary differential equation, which was numerically solved. Asymptotic analytical expressions for the local radius were derived near the center and close to the end of the drop. The results for the shape of the drop and the breakup criterion are presented as a function of the capillary number, the viscosity ratio and type of non-Newtonian fluid inside the drop. An approximated analytical solution is also suggested which is in good agreement with the numerical results.