Fluid dynamics of drips, filaments and strings

Patrick Thomas McGough, Purdue University

Abstract

Drop formation and breakup are fascinating free surface flows that are very relevant in many industrial fields, from traditional inkjet printing, through many novel applications that involve the controlled deposition of various reagents, to larger scale operations like bottle filling. The primary goal of this thesis is the rigorous computational investigation of the dynamics of drop formation and breakup, focusing on: (1) the contraction behavior of Newtonian satellite drops that can form during drop formation, (2) the dripping of a Herschel-Bulkley yield stress fluid, and (3) the final stages of bottle filling when jetting flow from a nozzle is turned off. These cases are studied by either a 1D analysis based on the slender-jet approximation or a 3D but axisymmetric, or 2D analysis that utilizes the Galerkin/finite element method (G/FEM) along with an elliptic mesh routine to accurately track and solve the deforming domains prevalent in these free surface flow problems. For (1), the contraction behavior of satellites is studied as Newtonian asymmetric filament contraction using a 2D analysis. The contraction dynamics are studied, identifying three modes of contraction including end-pinching, complex capillary wave influenced breakup, and contraction to a sphere without breakup. The breakup dynamics are studied as a function of the level of asymmetry, the initial axial length, and the Ohnesorge number of the filaments, where the Ohnesorge number represents the viscous forces relative to the surface tension forces of the fluid. The filaments are categorized based on their breakup behavior in a series of phase plots. For (2), the steady dripping of Herschel-Bulkley yield stress fluids is studied using a 2D analysis, including an algorithm that adaptively steps in the yield stress and power law parameters at each moment in time to allow solution of the stiff, highly non-linear system. The dripping dynamics, breakup lengths, and breakup volumes are studied as a function of the yield stress and power law parameters of the model. The effects of changing fluid parameters, nozzle sizes, and input flow rates on the forming drops were studied in the context of the Herschel-Bulkley model. For (3), the final stage of bottle filling, which occurs after the flow in the nozzle is shutoff, is modeled using a 1D slender-jet model for Newtonian fluids. This simplified model, which ejects into air instead of a bottle to avoid complicated bottle filling flow, focuses on the contraction of the jet below the nozzle once the flow is shutoff, and the time it takes for the fluid pendant from the nozzle to detach. This detachment time is translated into a measure of whether or not the flow shutoff event would be expected to present problems in automated bottle filling operations. Problematic bottle filling operations are termed "stringers", and phase plots of "stringers" and "non-stringers" as a function of the physical properties of the fluids, the ejection flowrate, and the nozzle size are generated. A fixed contact line boundary condition is employed for the majority of this study, but a moving contact line boundary condition is required to generate 1D results that are physically acceptable for very high flowrates. Limited 2D results indicate good agreement at low flow rates, with poorer agreement at high flowrates.

Degree

Ph.D.

Advisors

Basaran, Purdue University.

Subject Area

Chemical engineering

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