arXiv subjects

Michael P. Brenner

Publications and source records attributed to Michael P. Brenner.

89 records · Page 5Linked to original sources

arXiv2010

Breakup of diminutive Rayleigh jets

Discharging a liquid from a nozzle at sufficient large velocity leads to a continuous jet that due to capillary forces breaks up into droplets. Here we investigate the formation of microdroplets from the breakup of micron-sized jets with ultra high-speed imaging. The diminutive size of the jet implies a fast breakup time scale $τ_\mathrm{c} = \sqrt{ρr^3 / γ}$ of the order of 100\,ns{}, and requires imaging at 14 million frames per second. We directly compare these experiments with a numerical lubrication approximation model that incorporates inertia, surface tension, and viscosity [Eggers and Dupont, J. Fluid Mech. 262, 205 (1994); Shi, Brenner, and Nagel, Science 265, 219 (1994)]. The lubrication model allows to efficiently explore the parameter space to investigate the effect of jet velocity and liquid viscosity on the formation of satellite droplets. In the phase diagram we identify regions where the formation of satellite droplets is suppressed. We compare the shape of the droplet at pinch-off between the lubrication approximation model and a boundary integral (BI) calculation, showing deviations at the final moment of the pinch-off. Inspite of this discrepancy, the results on pinch-off times and droplet and satellite droplet velocity obtained from the lubrication approximation agree with the high-speed imaging results.

physics.flu-dyn↗

arXiv2008

Dynamic equilibrium Mechanism for Surface Nanobubble Stabilization

Recent experiments have convincingly demonstrated the existence of surface nanobubbles on submerged hydrophobic surfaces. However, classical theory dictates that small gaseous bubbles quickly dissolve because their large Laplace pressure causes a diffusive outflux of gas. Here we suggest that the bubbles are stabilized by a continuous influx of gas near the contact line, due to the gas attraction towards hydrophobic walls (Dammer & Lohse, PRL96, 206101 (2006); Zhang {\it et al.}, PRL98, 136101 (2007); Mezger {\it et al.}, J.\ Chem. Phys. 128, 244705 (2008)). This influx balances the outflux and allows for a meta-stable equilibrium, which however vanishes in thermodynamic equilibrium. Our theory predicts the equilibrium radius of the surface nanobubbles, as well as the threshold for surface nanobubble formation as a function of hydrophobicity and gas concentration.

physics.flu-dyn↗

arXiv2007

On the stabilization of ion sputtered surfaces

The classical theory of ion beam sputtering predicts the instability of a flat surface to uniform ion irradiation at any incidence angle. We relax the assumption of the classical theory that the average surface erosion rate is determined by a Gaussian response function representing the effect of the collision cascade and consider the surface dynamics for other physically-motivated response functions. We show that although instability of flat surfaces at any beam angle results from all Gaussian and a wide class of non-Gaussian erosive response functions, there exist classes of modifications to the response that can have a dramatic effect. In contrast to the classical theory, these types of response render the flat surface linearly stable, while imperceptibly modifying the predicted sputter yield vs. incidence angle. We discuss the possibility that such corrections underlie recent reports of a ``window of stability'' of ion-bombarded surfaces at a range of beam angles for certain ion and surface types, and describe some characteristic aspects of pattern evolution near the transition from unstable to stable dynamics. We point out that careful analysis of the transition regime may provide valuable tests for the consistency of any theory of pattern formation on ion sputtered surfaces.

cond-mat.mtrl-sci↗

arXiv2005

Microfluidics: The no-slip boundary condition

The no-slip boundary condition at a solid-liquid interface is at the center of our understanding of fluid mechanics. However, this condition is an assumption that cannot be derived from first principles and could, in theory, be violated. We present a review of recent experimental, numerical and theoretical investigations on the subject. The physical picture that emerges is that of a complex behavior at a liquid/solid interface, involving an interplay of many physico-chemical parameters, including wetting, shear rate, pressure, surface charge, surface roughness, impurities and dissolved gas.

cond-mat.soft↗

arXiv2004

The Optimal Faucet

The production of small fluid droplets relies on an instability of solutions to the Young-Laplace equation. We ask whether smaller droplets can be produced by changing the shape of the nozzle. At a given critical pressure, the circular nozzle actually produces the largest droplet. The droplet volume can be decreased by up to 18% using a triangular nozzle with stretched corners.

physics.flu-dyn↗

arXiv2004

Evaporation-driven assembly of colloidal particles

Colloidal particles absorbed at the interface of a liquid droplet arrange into unique packings during slow evaporation (Manoharan et al. Science 301 pp 483-487). We present a numerical and theoretical analysis of the packing selection problem. The selection of a unique packing arises almost entirely from geometrical constraints during the drying.

cond-mat.soft↗

arXiv2004

Shear-dependent apparent slip on hydrophobic surfaces: The Mattress Model

Recent experiments (Zhu & Granick (2001) Phys. Rev. Lett. 87 096105) have measured a large shear dependent fluid slip at partially wetting fluid-solid surfaces. We present a simple model for such slip, motivated by the recent observations of nanobubbles on hydrophobic surfaces. The model considers the dynamic response of bubbles to change in hydrodynamic pressure due to the oscillation of a solid surface. Both the compression and diffusion of gas in the bubbles decrease the force on the oscillating surface by a ``leaking mattress'' effect, thereby creating an apparent shear-dependent slip. With bubbles similar to those observed by atomic force microscopy to date, the model is found to lead to force decreases consistent with the experimental measurements of Zhu & Granick.

cond-mat.soft↗

arXiv2000

Hydrodynamic Coupling of Two Brownian Spheres to a Planar Surface

We describe direct imaging measurements of the collective and relative diffusion of two colloidal spheres near a flat plate. The bounding surface modifies the spheres' dynamics, even at separations of tens of radii. This behavior is captured by a stokeslet analysis of fluid flow driven by the spheres' and wall's no-slip boundary conditions. In particular, this analysis reveals surprising asymmetry in the normal modes for pair diffusion near a flat surface.

cond-mat.soft↗

arXiv2000

Like-charge attraction through hydrodynamic interaction

We demonstrate that the attractive interaction measured between like-charged colloidal spheres near a wall can be accounted for by a nonequilibrium hydrodynamic effect. We present both analytical results and Brownian dynamics simulations which quantitatively capture the one-wall experiments of Larsen and Grier (Nature 385, p. 230, 1997).

cond-mat.soft↗

arXiv1999

Spinning jets

A fluid jet with a finite angular velocity is subject to centripetal forces in addition to surface tension forces. At fixed angular momentum, centripetal forces become large when the radius of the jet goes to zero. We study the possible importance of this observation for the pinching of a jet within a slender jet model. A linear stability analysis shows the model to break down at low viscosities. Numerical simulations indicate that angular momentum is expelled from the pinch region so fast that it becomes asymptotically irrelevant in the limit of the neck radius going to zero.

physics.flu-dyn↗

arXiv1999

Collapsing Bacterial Cylinders

Under special conditions bacteria excrete an attractant and aggregate. The high density regions initially collapse into cylindrical structures, which subsequently destabilize and break up into spherical aggregates. This paper presents a theoretical description of the process, from the structure of the collapsing cylinder to the spacing of the final aggregates. We show that cylindrical collapse involves a delicate balance in which bacterial attraction and diffusion nearly cancel, leading to corrections to the collapse laws expected from dimensional analysis. The instability of a collapsing cylinder is composed of two distinct stages: Initially, slow modulations to the cylinder develop, which correspond to a variation of the collapse time along the cylinder axis. Ultimately, one point on the cylinder pinches off. At this final stage of the instability, a front propagates from the pinch into the remainder of the cylinder. The spacing of the resulting spherical aggregates is determined by the front propagation.

physics.bio-ph↗

arXiv1999

The Two Fluid Drop Snap-off Problem: Experiments and Theory

We address the dynamics of a drop with viscosity $λη$ breaking up inside another fluid of viscosity $η$. For $λ=1$, a scaling theory predicts the time evolution of the drop shape near the point of snap-off which is in excellent agreement with experiment and previous simulations of Lister and Stone. We also investigate the $λ$ dependence of the shape and breaking rate.

physics.flu-dyn↗

arXiv1998

Electrostatic Edge Instability of Lipid Membranes

This paper considers the effect of electrostatics on the stability of a charged membrane. We show that at low ionic strength and high surface charge density, repulsion between charges on the membrane renders it unstable to the formation of holes. A free straight edge is unstable to modulations with wavelength longer than the Debye screening length. Hence at low ionic strength, membranes will disintegrate into vesicles. We use these results to interpret stable holes in red blood cell ghosts (Steck et. al., Science 168:255(1970)).

physics.bio-ph↗

arXiv1998

Analysis of Rayleigh-Plesset dynamics for sonoluminescing bubbles

Recent work on single bubble sonoluminescence (SBSL) has shown that many features of this phenomenon, especially the dependence of SBSL intensity and stability on experimental parameters, can be explained within a hydrodynamic approach. More specifically, many important properties can already be derived from an analysis of bubble wall dynamics. This dynamics is conveniently described by the Rayleigh-Plesset (RP) equation. In this work we derive analytical approximations for RP dynamics and subsequent analytical laws for parameter dependences. These results include (i) an expression for the onset threshold of SL, (ii) an analytical explanation of the transition from diffusively unstable to stable equilibria for the bubble ambient radius (unstable and stable sonoluminescence), and (iii) a detailed understanding of the resonance structure of the RP equation. It is found that the threshold for SL emission is shifted to larger bubble radii and larger driving pressures if surface tension is enlarged, whereas even a considerable change in liquid viscosity leaves this threshold virtually unaltered. As an enhanced viscosity stabilizes the bubbles against surface oscillations, we conclude that the ideal liquid for violently collapsing, surface stable SL bubbles should have small surface tension and large viscosity, although too large viscosity (>40 times the viscosity of water) will again preclude collapses.

chao-dyn↗

arXiv1997

Sonoluminescing air bubbles rectify argon

The dynamics of single bubble sonoluminescence (SBSL) strongly depends on the percentage of inert gas within the bubble. We propose a theory for this dependence, based on a combination of principles from sonochemistry and hydrodynamic stability. The nitrogen and oxygen dissociation and subsequent reaction to water soluble gases implies that strongly forced air bubbles eventually consist of pure argon. Thus it is the partial argon (or any other inert gas) pressure which is relevant for stability. The theory provides quantitative explanations for many aspects of SBSL.

chao-dyn↗

arXiv1995

Mechanisms for Stable Sonoluminescence

A gas bubble trapped in water by an oscillating acoustic field is expected to either shrink or grow on a diffusive timescale, depending on the forcing strength and the bubble size. At high ambient gas concentration this has long been observed in experiments. However, recent sonoluminescence experiments show that in certain circumstances when the ambient gas concentration is low the bubble can be stable for days. This paper presents mechanisms leading to stability which predict parameter dependences in agreement with the sonoluminescence experiments.

chao-dyn↗

arXiv1995

Bubble Shape Oscillations and the Onset of Sonoluminescence

An air bubble trapped in water by an oscillating acoustic field undergoes either radial or nonspherical pulsations depending on the strength of the forcing pressure. Two different instability mechanisms (the Rayleigh--Taylor instability and parametric instability) cause deviations from sphericity. Distinguishing these mechanisms allows explanation of many features of recent experiments on sonoluminescence, and suggests methods for finding sonoluminescence in different parameter regimes.

chao-dyn↗