Fluid mechanics of coupled interfacial systems

Santhosh K Ramalingam, Purdue University

Abstract

The formation and control of capillary systems such as drop, bubble and liquid bridges are central to many industrial applications. When a single continuous phase of liquid is bound between two disconnected interfaces, the physics of interaction between these two interfaces, coupled by the liquid bulk, is more complex when compared to simple capillary systems, giving rise to some interesting applications such as droplet manipulator and variable focus lens. In this thesis, the study is focused on one such coupled interfacial system called the double droplet system, which is a pendant drop and a sessile drop connected through a liquid filled hole in a plate. In the application as a droplet manipulator, the sessile drop is grown at the expense of the pendant drop so that it coalesces with a second pendant drop encapsulating an immiscible pendant droplet. Breakup of the resulting liquid bridge provides the energy to detach the encapsulated droplet from its solid support and transfer it into the capillary switch for easy handling. In this work, rigorous numerical algorithms based on Galerkin finite element method (G/FEM) are developed to analyze the dynamics. Success of this technique can be partly attributed to development of elliptic mesh that deforms significantly, aiding in study of singularities such as coalescence and bridge break-up. The dynamics of this process, which are affected by many parameters including but limited to volume, height of bridge, thickness of plate, and external pressure, are studied by two methods (i) exact 2-D analysis and (ii) 1-D analysis based on slender jet approximation. The parameter space is reduced by identifying the feasible regions using computationally inexpensive equilibrium analysis of the intermediate coupled bridge-droplet system. By combining a robust arc length formulation and continuation technique, families of equilibrium curves are efficiently tracked. Results show that the coupled bridge-droplet system shows both stable to unstable transition similar to a liquid bridge and multi stable states similar to capillary switch, with much more complexity. While the small size and highly spherical droplet shapes enable the capillary switch to act as a miniature liquid lens, oscillating it at its natural frequency doubles its utility as a variable focus lens, capable of scanning different focal lengths within one cycle. The frequency response of the capillary switch to both free and forced oscillations are studied numerically using G/FEM for a Newtonian liquid. Complex interactions between the two interfaces produce twice as many oscillatory modes of that of a pendant or a sessile drop. In addition, a lower mode not exhibited by pendant (sessile) drops or free drops is also discovered. The effect of parameters, such as volume, plate thickness, and liquid viscosity, on the shift in modal frequencies are investigated and verified with existing experimental results in literature. Appropriate Green's functions developed to verify the results analytically, indicate excellent agreement in the limit of vanishing plate thickness for inviscid liquids.

Degree

Ph.D.

Advisors

Basaran, Purdue University.

Subject Area

Chemical engineering|Mechanical engineering

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