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Benny Davidovitch

Publications and source records attributed to Benny Davidovitch.

9 recordsLinked to original sources
PubMed2006

Slip, yield, and bands in colloidal crystals under oscillatory shear.

We study dense colloidal crystals under oscillatory shear using a confocal microscope. At large strains the crystals yield and the suspensions form shear bands. The pure harmonic response exhibited by the suspension rules out the applicability of nonlinear rheology models typically used to describe shear banding in other types of complex fluids. Instead, we show that a model based on the coexistence of linearly responding phases of the colloidal suspension accounts for the observed flows. These results highlight a new use of oscillatory measurements in distinguishing the contribution of linear and nonlinear local rheology to a globally nonlinear material response.

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PubMed2005

Spreading of viscous fluid drops on a solid substrate assisted by thermal fluctuations.

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 asymptotically 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 realizability of our results for thin molecular and complex fluid films, and predict that such phenomenon can in principal be observed in various flow geometries.

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PubMed2005

Average shape of transport-limited aggregates.

We study the relation between stochastic and continuous transport-limited growth models. We derive a nonlinear integro-differential equation for the average shape of stochastic aggregates, whose mean-field approximation is the corresponding continuous equation. Focusing on the advection-diffusion-limited aggregation (ADLA) model, we show that the average shape of the stochastic growth is similar, but not identical, to the corresponding continuous dynamics. Similar results should apply to DLA, thus explaining the known discrepancies between average DLA shapes and viscous fingers in a channel geometry.

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PubMed2005

Time-dependent strength of colloidal gels.

Colloidal silica gels are shown to stiffen with time, as demonstrated by both dynamic light scattering and bulk rheological measurements. Their elastic moduli increase as a power law with time, independent of particle volume fraction; however, static light scattering indicates that there are no large-scale structural changes. We propose that increases in local elasticity arising from bonding between neighboring colloidal particles can account for the strengthening of the network, while preserving network structure.

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PubMed2004

Ripening of porous media.

We address the surface-tension-driven dynamics of porous media in nearly saturated pore-space solutions. We linearize this dynamics in the reaction-limited regime near its fixed points--surfaces of constant mean curvature (CMC surfaces). We prove that the only stable interface for this dynamics is the plane and estimate the time scale for a CMC surface to become unstable. We also discuss the differences between dynamics in open and closed environments, pointing out the unlikelihood that CMC surfaces are ever realized in such environments on any time scale.

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PubMed2003

Dynamics of conformal maps for a class of non-Laplacian growth phenomena.

Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electromigration. Both continuous and stochastic dynamics are described by generalizing conformal-mapping techniques for viscous fingering and diffusion-limited aggregation, respectively. The theory is applied to simulations of advection-diffusion-limited aggregation in a background potential flow. A universal crossover in morphology is observed from diffusion-limited to advection-limited fractal patterns with an associated crossover in the growth rate, controlled by a time-dependent effective Péclet number. Remarkably, the fractal dimension is not affected by advection, in spite of dramatic increases in anisotropy and growth rate, due to the persistence of diffusion limitation at small scales.

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PubMed2002

Iterated conformal dynamics and Laplacian growth.

The method of iterated conformal maps for the study of diffusion limited aggregates (DLA) is generalized to the study of Laplacian growth patterns and related processes. We emphasize the fundamental difference between these processes: DLA is grown serially with constant size particles, while Laplacian patterns are grown by advancing each boundary point in parallel, proportional to the gradient of the Laplacian field. We introduce a two-parameter family of growth patterns that interpolates between DLA and a discrete version of Laplacian growth. The ultraviolet putative finite-time singularities are regularized here by a minimal tip size, equivalently for all the models in this family. With this we stress that the difference between DLA and Laplacian growth is not in the manner of ultraviolet regularization, but rather in their deeply different growth rules. The fractal dimensions of the asymptotic patterns depend continuously on the two parameters of the family, giving rise to a "phase diagram" in which DLA and discretized Laplacian growth are at the extreme ends. In particular, we show that the fractal dimension of Laplacian growth patterns is higher than the fractal dimension of DLA, with the possibility of dimension 2 for the former not excluded.

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