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Steady states, non-steady evolution, pinch-off and post-pinch-off of axisymmetric drops in Stokes flow

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Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/13161

Steady states, non-steady evolution, pinch-off and post-pinch-off of axisymmetric drops in Stokes flow

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dc.contributor.author Naderi, Shadi Askarian (9/15/1980)
dc.date.accessioned 2011-08-31T16:06:57Z
dc.date.available 2011-08-31T16:06:57Z
dc.date.issued 2011-08-31
dc.date.submitted July 2011
dc.identifier.uri http://hdl.handle.net/1928/13161
dc.description.abstract A good understanding of drop evolution and breakup is important in many applications. For instance, controlling the liquid droplet size is crucial in atomization processes such as fuel combustion and fertilizer application, as well as drop-on-demand technologies such as ink-jet printing and DNA arraying. In these applications, the length scales are very small relative to viscosity so that the Reynolds number is much less than unity. The aim of this work is to investigate the evolution and breakup of drops in Stokes flow. Drop evolution depends on different factors, such as the drop size, the viscosity, any applied force, or surface tension. In this dissertation, the behavior of axisymmetric viscous drops in a nonlinear strain field is investigated for various parameters. The three non-dimensional parameters that determine the flow in our case are: the capillary number Ca which measures the strength of the strain field and drop viscosity relative to surface tension, the ratio of inner to outer viscosities, and the relative nonlinearity c2 of the background flow. It is known that the drop approaches a steady state for sufficiently small values of Ca and that there exists a critical value of the capillary number, Cacr, above which no steady states exist. We examine the evolution of the drop as a function of these three parameters. Our main results are explained in three parts. (1) A full classification of the steady-state solutions in the parameter-space for Ca ≤ Cacr is presented. In particular, we describe the deformation, maximum curvature and the critical capillary number as functions of the key parameters. We find previously unobserved biconcave steady shapes. (2) The non-steady evolution for Ca > Cacr is studied and classified. With c2 = 0, the drop keeps elongating and becomes more pointed in time. With positive values of c2, the surface approaches a cusp as it increases in length. With negative values of c2, the surface collapses at two points on the axis in finite time. Thus the solution has a finite time pinch-off singularity. (3) Based on experimental observations, the drop surface is expected to break at the time of pinch-off and reconnect to form several smaller drops. We develop a numerical method to simulate the break-and-reconnection process. This enables us to compute the after pinch-off drop evolution. Our simulations indicate that this phenomenon has a linear self-similar behavior before and after pinch-off. Further pinch-offs is observed. Throughout this work the fifth-order boundary integral method presented by Nitsche et al. [1] is used. This method enables us to resolve the flow using fewer computational points compared to the commonly used second-order method. Furthermore, it is shown that the uniformly fifth-order method proposed in earlier work [1] makes a significant improvement in the results in certain cases. en_US
dc.description.sponsorship NATIONAL SCIENCE FOUNDATION en_US
dc.language.iso en_US en_US
dc.subject AXISYMMETRIC STOKES FLOW en_US
dc.subject DROPS en_US
dc.subject FLUID DYNAMICS en_US
dc.subject BOUNDARY INTEGRAL en_US
dc.subject PINCH-OFF en_US
dc.subject.lcsh Drops.
dc.subject.lcsh Stokes flow.
dc.subject.lcsh Axial flow.
dc.subject.lcsh Boundary element methods.
dc.title Steady states, non-steady evolution, pinch-off and post-pinch-off of axisymmetric drops in Stokes flow en_US
dc.type Dissertation en_US
dc.description.degree MATHEMATICS en_US
dc.description.level Doctoral en_US
dc.description.department University of New Mexico. Dept. of Mathematics and Statistics en_US
dc.description.advisor NITSCHE, MONIKA
dc.description.committee-member LAU, STEPHEN
dc.description.committee-member COUTSIAS, EVANGELOS
dc.description.committee-member PETER, VOROBIEFF


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