Analysis of core-annular dynamics in the presence of base flow for arbitrary fluid viscosities leads to an equation describing the temporal evolution of the fluid/fluid interface. The equation follows from the conservation of mass in the "small-slope" approximation. Its useful applications occur, for example, in chemical engineering and petroleum recovery. The nonlinear equation allows inexpensive numerical analysis. For sinusoidally constricted pores, a purely geometric criterion exists that enables or prohibits the core-fluid breakup in the necks of the constrictions. The geometrically favoring condition sets up capillary-pressure gradients that ensure a continuous outflow of the core fluid from the necks into the "crests" of the profile. Such behavior is indeed observed in the numerical solutions of the evolution equation. For relatively large slopes of the initial configuration, setting up larger pressure gradients, the interface shape remains "smooth," the evolution times are relatively fast, and the breakup is typically achieved by the growing film-fluid collar touching the axis of the channel at a single point. No satellite droplets are produced. Decreasing the slope lengthens the evolution times, allowing the formation and growth of "wavy" disturbances on the initial interface profile, which may touch the axis of the capillary in several places forming satellite drops. Thinner initial annuli also slow down the evolution process. Instability develops for the cases of the core both more and less viscous than the film. Finally, if the geometry prohibits the snap-off altogether, the initial interface configurations decay into steady-state solutions, and no breakup takes place. The solutions of the evolution equation validate well against two computational-fluid-dynamics codes.
I. A. Beresnev and W. Deng, "Theory of Breakup of Core Fluids Surrounded by a Wetting Annulus in Sinusoidally Constricted Capillary Channels," Physics of Fluids, vol. 22, no. 1, American Institute of Physics (AIP), Jan 2010.
The definitive version is available at https://doi.org/10.1063/1.3294887
Civil, Architectural and Environmental Engineering
Keywords and Phrases
Baseflows; Capillary channels; Conservation of mass; Evolution equations; Evolution process; Fluid viscosity; Growing films; Initial configuration; Interface configuration; Interface profiles; Interface shape; Numerical solution; Petroleum recovery; Satellite droplets; Satellite drops; Single point; Steady state solution; Temporal evolution; Differential equations; Groundwater flow; Nonlinear equations; Numerical analysis; Pressure gradient; Fluids
International Standard Serial Number (ISSN)
Article - Journal
© 2010 American Institute of Physics (AIP), All rights reserved.