About

Benny Davidovitch is a professor in the Department of Physics at the University of Massachusetts Amherst. His research interests focus on Condensed Matter Theory Physics. He is involved in award-winning teaching, research opportunities, and interdisciplinary programs within a diverse and inclusive community of excellence. His main office is located in the Department of Physics at 1126 Lederle Graduate Research Tower (LGRT), University of Massachusetts, Amherst, MA. His contact information includes a phone number (413-545-0381) and email, and he is associated with the Davidovitch group at HAS 405B.

Research topics

• Materials science
• Composite material
• Geology
• Mechanics
• Physics
• Computer Science
• Crystallography
• Optoelectronics
• Classical mechanics
• Geometry
• Mathematics
• Chemical physics
• Condensed matter physics
• Nanotechnology
• Optics
• Quantum mechanics
• Climatology
• Chemistry

Selected publications

• Retraction Dynamics of a Highly Viscous Liquid Sheet

  ArXiv.org · 2025-07-07

  preprintOpen access

  We study the one-dimensional capillary-driven retraction of a finite, planar liquid sheet in the asymptotic regime where both the Ohnesorge number $\mathrm{Oh}$ and the initial length-to-thickness ratio $l_0/h_0$ are large. In this regime, the fluid domain decomposes into two regions: a thin-film region governed by one-dimensional mass and momentum equations, and a small tip region near the free edge described by a self-similar Stokes flow. Asymptotic matching between these regions yields an effective boundary condition for the thin-film region, representing a balance between viscous and capillary forces at the free edge. Surface tension drives the thin-film flow only through this boundary condition, while the local momentum balance is dominated by viscous and inertial stresses. We show that the thin-film flow possesses a conserved quantity, reducing the equation of thickness to heat equation with time-dependent boundary conditions. The reduced problem depends on a single dimensionless parameter $\mathcal{L} = l_0 / (4 h_0 \mathrm{Oh})$. Numerical solutions of the reduced model agree well with previous studies and reveal that the sheet undergoes distinct retraction regimes depending on $\mathcal{L}$ and a dimensionless time after rupture $T$. We derive asymptotic approximations for the thickness profile, velocity profile, and retraction speed during the early and late stages of retraction. At early times, the retraction speed grows as $T^{1/2}$, while at late times it decays as $1/T^2$. An intermediate regime arises for very long sheets ($\mathcal{L} \gg 1$). During this phase, the retraction speed approaches the Taylor-Culick value. When $T \approx \mathcal{L}$, the speed undergoes fast deceleration from the Taylor-Culick speed to late-time asymptotics.

  PublisherOA PDFDOI

• How viscous bubbles collapse: Topological and symmetry-breaking instabilities in curvature-driven hydrodynamics

  Proceedings of the National Academy of Sciences · 2024-08-02 · 1 citations

  articleOpen access1st authorCorresponding

  The duality between deformations of elastic bodies and noninertial flows in viscous liquids has been a guiding principle in decades of research. However, this duality is broken when a spheroidal or other doubly curved liquid film is suddenly forced out of mechanical equilibrium, as occurs, e.g., when the pressure inside a liquid bubble drops rapidly due to rupture or controlled evacuation. In such cases, the film may evolve through a noninertial yet geometrically nonlinear surface dynamics, which has remained largely unexplored. We reveal the driver of such dynamics as temporal variations in the curvature of the evolving surface. Focusing on the prototypical example of a floating bubble that undergoes rapid depressurization, we show that the bubble surface evolves via a topological instability and a subsequent front propagation, whereby a small planar zone that includes a singular flow structure, analogous to a disclination in elastic systems, nucleates spontaneously and expands in the spherically shaped film. This flow pattern brings about hoop compression and triggers another, symmetry-breaking instability to the formation of radial wrinkles that invade the flattening film. Our analysis reveals the dynamics as a nonequilibrium branch of "jellium" physics, whereby a rate-of-change of surface curvature in a viscous film is akin to charge in an electrostatic medium that comprises polarizable and conducting domains. We explain key features underlying recent experiments and highlight a qualitative inconsistency between the prediction of linear stability analysis and the observed "wavelength" of surface wrinkles.

  PublisherOA PDFDOI

• Peeling from a liquid

  arXiv (Cornell University) · 2023-03-08

  preprintOpen accessSenior author

  We establish the existence of a cusp in the curvature of a solid sheet at its contact with a liquid subphase. We study two configurations in floating sheets where the solid-vapor-liquid contact line is a straight line and a circle, respectively. In the former case, a rectangular sheet is lifted at its edge, whereas in the latter a gas bubble is injected beneath a floating sheet. We show that in both geometries the derivative of the sheet's curvature is discontinuous. We demonstrate that the boundary condition at the contact is identical in these two geometries, even though the shape of the contact line and the stress distribution in the sheet are sharply different.

  PublisherOA PDFDOI

• Peeling from a liquid

  Soft Matter · 2023-01-01

  articleOpen accessSenior author

  We establish the existence of a cusp in the curvature of a solid sheet at its contact with a liquid subphase. We study two configurations in floating sheets where the solid-vapor-liquid contact line is a straight line and a circle, respectively. In the former case, a rectangular sheet is lifted at its one edge, whereas in the latter a gas bubble is injected beneath a floating sheet. We show that in both geometries the derivative of the sheet's curvature is discontinuous. We demonstrate that the boundary condition at the contact is identical in these two geometries, even though the shape of the contact line and the stress distribution in the sheet are very different.

  PublisherOA PDFDOI

• Delamination from an adhesive sphere: Curvature-induced dewetting versus buckling

  Proceedings of the National Academy of Sciences · 2023-03-17 · 23 citations

  articleOpen accessSenior author

  Everyday experience confirms the tendency of adhesive films to detach from spheroidal regions of rigid substrates—what is a petty frustration when placing a sticky band aid onto a knee is a more serious matter in the coating and painting industries. Irrespective of their resistance to bending, a key driver of such phenomena is Gauss’ Theorema Egregium , which implies that naturally flat sheets cannot conform to doubly curved surfaces without developing a strain whose magnitude grows sharply with the curved area. Previous attempts to characterize the onset of curvature-induced delamination, and the complex patterns it gives rise to, assumed a dewetting-like mechanism in which the propensity of two materials to form contact through interfacial energy is modified by an elastic energy penalty. We show that this approach may characterize moderately bendable sheets but fails qualitatively to describe the curvature-induced delamination of ultrathin films, whose mechanics is governed by their propensity to buckle and delaminate partially, under minute levels of compression. Combining mechanical and geometrical considerations, we introduce a minimal model for curvature-induced delamination accounting for the two buckling motifs that underlie partial delamination: shallow “rucks” and localized “folds”. We predict nontrivial scaling rules for the onset of curvature-induced delamination and various features of the emerging patterns, which compare well with experiments. Beyond gaining control on the use of ultrathin adhesives in cutting-edge technologies such as stretchable electronics, our analysis is a significant step toward quantifying the multiscale morphology that emerges upon imposing geometrical and mechanical constraints on highly bendable solid objects.

  PublisherDOI

• Effect of external tension on the wetting of an elastic sheet

  Physical review. E · 2023-03-01 · 5 citations

  articleOpen access

  Recent studies of elastocapillary phenomena have triggered interest in a basic variant of the classical Young-Laplace-Dupré (YLD) problem: the capillary interaction between a liquid drop and a thin solid sheet of low bending stiffness. Here we consider a two-dimensional model where the sheet is subjected to an external tensile load and the drop is characterized by a well-defined Young's contact angle θ_{Y}. Using a combination of numerical, variational, and asymptotic techniques, we discuss wetting as a function of the applied tension. We find that, for wettable surfaces with 0<θ_{Y}<π/2, complete wetting is possible below a critical applied tension due to the deformation of the sheet in contrast with rigid substrates requiring θ_{Y}=0. Conversely, for very large applied tensions, the sheet becomes flat and the classical YLD situation of partial wetting is recovered. At intermediate tensions, a vesicle forms in the sheet, which encloses most of the fluid, and we provide an accurate asymptotic description of this wetting state in the limit of small bending stiffness. We show that bending stiffness, however small, affects the entire shape of the vesicle. Rich bifurcation diagrams involving partial wetting and "vesicle" solution are found. For moderately small bending stiffnesses, partial wetting can coexist with both the vesicle solution and complete wetting. Finally, we identify a tension-dependent bendocapillary length, λ_{BC}, and find that the shape of the drop is determined by the ratio A/λ_{BC}^{2}, where A is the area of the drop.

  PublisherOA PDFDOI

• Delamination from an adhesive sphere: Curvature-induced dewetting versus buckling

  arXiv (Cornell University) · 2022-07-16

  preprintOpen accessSenior author

  Everyday experience confirms the tendency of adhesive films to detach from spheroidal regions of rigid substrates -- what is a petty frustration when placing a sticky bandage onto an elbow or knee is a more serious matter in the coating and painting industries. Irrespective of their resistance to bending, a key driver of such phenomena is Gauss' \textit{Theorema Egregium}, which implies that naturally flat sheets cannot conform to doubly-curved surfaces without developing a strain whose magnitude grows sharply with the curved area. Previous attempts to characterize the onset of curvature-induced delamination, and the complex patterns it gives rise to, assumed a dewetting-like mechanism in which the propensity of two materials to form contact through interfacial energy is modified by an elastic energy penalty. We show that this approach may characterize moderately bendable adhesive sheets, but fails qualitatively to describe the curvature-induced delamination of ultrathin films, whose mechanics is governed by their propensity to buckle under minute levels of compression. Combining mechanical and geometrical considerations, we introduce a minimal model for curvature-induced delamination that accounts for two elementary buckling motifs, shallow "rucks" and localized "folds". We predict nontrivial scaling rules for the onset of curvature-induced delamination and various features of the emerging patterns, which compare well with experimental observations. Beyond gaining control on the use of ultrathin adhesives in cutting edge technologies such as stretchable electronics, our analysis is a significant step towards quantifying the multiscale morphological complexity that emerges upon imposing geometrical and mechanical constraints on highly bendable solid objects.

  PublisherOA PDFDOI

• Effect of external tension on the wetting of an elastic sheet

  arXiv (Cornell University) · 2022-01-26

  preprintOpen access

  Recent studies of elasto-capillary phenomena have triggered interest in a basic variant of the classical Young-Laplace-Dupré (YLD) problem: The capillary interaction between a liquid drop and a thin solid sheet of low bending stiffness. Here, we consider a two-dimensional model where the sheet is subjected to an external tensile load and the drop is characterized by a well-defined Young's contact angle $θ_Y$. Using a combination of numerical, variational, and asymptotic techniques, we discuss wetting as a function of the applied tension. We find that, for wettable surfaces with $0&lt;θ_Y&lt;π/2$, complete wetting is possible below a critical applied tension thanks to the deformation of the sheet in contrast with rigid substrates requiring $θ_Y=0$. Conversely, for very large applied tensions, the sheet becomes flat and the classical YLD situation of partial wetting is recovered. At intermediate tensions, a vesicle forms in the sheet, which encloses most of the fluid and we provide an accurate asymptotic description of this wetting state in the limit of small bending stiffness. We show that bending stiffness, however small, affects the entire shape of the vesicle. Rich bifurcation diagrams involving partial wetting and ``vesicle'' solution are found. For moderately small bending stiffnesses, partial wetting can coexist both with the vesicle solution and complete wetting. Finally, we identify a tension-dependent bendo-capillary length, $λ_\text{BC}$, and find that the shape of the drop is determined by the ratio $A/λ_\text{BC}^2$, where $A$ is the area of the drop.

  PublisherOA PDFDOI

• How viscous bubbles collapse: topological and symmetry-breaking instabilities in curvature-driven hydrodynamics

  arXiv (Cornell University) · 2022-02-22

  preprintOpen access1st authorCorresponding

  The duality between deformations of elastic bodies and non-inertial flows in viscous liquids has been a guiding principle in decades of research. However, this duality is broken when a spheroidal or other doubly-curved liquid film is suddenly forced out of mechanical equilibrium, as occurs e.g. when the pressure inside a liquid bubble drops rapidly due to rupture or controlled evacuation. In such cases the film may evolve through a non-inertial yet geometrically-nonlinear surface dynamics, which has remained largely unexplored. We reveal the driver of such dynamics as temporal variations in the curvature of the evolving surface. Focusing on the prototypical example of a floating bubble that undergoes rapid depressurization, we show that the bubble surface evolves via a topological instability and a subsequent front propagation, whereby a small planar zone nucleates and expands in the spherically-shaped film, bringing about hoop compression and triggering another, symmetry-breaking instability and radial wrinkles that grow in amplitude and invade the flattening film. Our analysis reveals the dynamics as a non-equilibrium branch of "Jellium" physics, whereby a rate-of-change of surface curvature in a viscous film is akin to charge in an electrostatic medium that comprises polarizable and conducting domains. We explain key features underlying recent experiments and highlight a qualitative inconsistency between the prediction of linear stability analysis and the observed "wavelength" of surface wrinkles. Our analysis points to the existence of a nonlinear curvature-driven mechanism for pattern selection in viscous flows.

  PublisherOA PDFDOI

• Indentation of solid membranes on rigid substrates with van der Waals attraction

  Physical review. E · 2021-04-08 · 12 citations

  articleOpen access1st authorCorresponding

  We revisit the indentation of a thin solid sheet of size R_{sheet} suspended on a circular hole of radius R≪R_{sheet} in a smooth rigid substrate, addressing the effects of boundary conditions at the hole's edge. Introducing a basic theoretical model for the van der Waals (vdW) sheet-substrate attraction, we demonstrate the dramatic effect of replacing the clamping condition (Schwerin model) with a sliding condition, whereby the supported part of the sheet is allowed to slide towards the indenter and relax the induced hoop compression through angstrom-scale deflections from the thermodynamic equilibrium (determined by the vdW potential). We highlight the possibility that the indentation force F may not exhibit the commonly anticipated cubic dependence on the indentation depth (F∝δ^{3}), in which the proportionality constant is governed by the sheet's stretching modulus and the hole's radius R, but rather a pseduolinear response F∝δ, whereby the proportionality constant is governed by the bending modulus, the vdW attraction, and the sheet's size R_{sheet}≫R.

  PublisherOA PDFDOI

Frequent coauthors

• Vincent Démery

  ESPCI Paris

  22 shared

• Dominic Vella

  22 shared

• Narayanan Menon

  21 shared

• Robert D. Schroll

  12 shared

• Joseph D. Paulsen

  Syracuse University

  12 shared

• Thomas P. Russell

  Lawrence Berkeley National Laboratory

  11 shared

• Mokhtar Adda-Bedia

  11 shared

• Fabian Brau

  Université Libre de Bruxelles

  10 shared