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Full-Text Articles in Physics
The Average Shape Of Transport-Limited Aggregates, Benny Davidovitch, Jachyuk Choi, Martin Z. Bazant
The Average Shape Of Transport-Limited Aggregates, Benny Davidovitch, Jachyuk Choi, Martin Z. Bazant
Benny Davidovitch
We study the relation between stochastic and continuous transport-limited growth models, which generalize conformal-mapping formulations of diffusion-limited aggregation (DLA) and viscous fingering, respectively. We derive a nonlinear integro-differential equation for the asymptotic shape (average conformal map) of stochastic aggregates, whose mean-field approximation is the corresponding continuous equation, where the interface moves at its local expected velocity. Our equation accurately describes advection-diffusion-limited aggregation (ADLA), and, due to nonlinear averaging over fluctuations, the average ADLA cluster is similar, but not identical, to an exact solution of the mean-field dynamics. Similar results should apply to all models in our class, thus explaining the …
Spreading Of Thin Films Assisted By Thermal Fluctuations, Benny Davidovitch, Esteban Moro, Howard A. Stone
Spreading Of Thin Films Assisted By Thermal Fluctuations, Benny Davidovitch, Esteban Moro, Howard A. Stone
Benny Davidovitch
We study the spreading of viscous drops on a solid substrate, taking into account the effects of thermal fluctuations in the fluid momentum. A nonlinear stochastic lubrication equation is derived, and studied using numerical simulations and scaling analysis. We show that asymptoically spreading drops admit self-similar shapes, whose average radii can increase at rates much faster than these predicted by Tanner's law. We discuss the physical realizablility of our results for thin molecular and complex fluid films, and predict that such phenomenon can in principal be observed in various flow geometries.