Publications

2007
Benny Davidovitch, Michael J. Aziz, and Michael P. Brenner. 2007. “On the stabilization of ion sputtered surfaces.” Physical Review B, 76, 20.Abstract
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.
Shang-You Tee, P. J. Mucha, M.P. Brenner, and D. A. Weitz. 2007. “Velocity fluctuations of initially stratified sedimenting spheres.” Physics of Fluids, 19, 11, Pp. 113304.Abstract
The study of velocity fluctuations in the sedimentation of spheres is complicated by the time evolution of the underlying particle distribution, both at the microscale and in the bulk. We perform a series of experiments and simulations to isolate the effect of an initial, stable stratification in the particle concentration. The directly observed dependence of velocity fluctuations on stratification agrees with a previously obtained scaling theory. (c) 2007 American Institute of Physics.
2006
Michael Schnall-Levin, Eric Lauga, and Michael P. Brenner. 2006. “Self-Assembly of Spherical Particles on an Evaporating Sessile Droplet.” Langmuir, 22, 10, Pp. 4547–4551.Abstract
Particles adsorbed on the Surface of a droplet form three-dimensional packings when the droplet evaporates. We study the final packings when the liquid droplet is attached to a solid Substrate. In contrast to a droplet evaporating away from a substrate, here the final packings are highly dependent on both the number of particles and the contact angle between the droplet and the surface. Simple geometrical constraints quantitatively determine the parameter regions that particular packings can form.
Itai Cohen, Benny Davidovitch, Andrew B. Schofield, Michael P. Brenner, and DavidA. Weitz. 2006. “Slip, Yield, and Bands in Colloidal Crystals under Oscillatory Shear.” Physical Review Letters, 97, 21.Abstract
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.
2005
Jian Li, M.P. Brenner, T. Christen, M.S. Kotilainen, J.H. Lang, and A.H. Slocum. 2005. “Deep-reactive ion-etched compliant starting zone electrostatic zipping actuators.” Journal of Microelectromechanical Systems, 14, 6, Pp. 1283–1297.Abstract
This paper presents the modeling, design, fabrication and testing of monolithic electrostatic curved-electrode zipping actuators fabricated by deep reactive ion etching (DRIE). In contrast to traditional curved-electrode zipping actuators, the design of the actuators presented here utilizes a compliant starting, cantilever to significantly reduce the initial pull-in voltage by closing the gap (kerf) generated by DRIE. Thus, the actuators achieve high actuation force at a relatively low voltage. For example, two actuators each with dimensions of 4.5 mm (*) 100 mu m (*) 300 mu m are used to drive a bistable MEMS relay. Together, the two actuators provide up to 10 mN of force over their 80 mu m stroke at 140 V. Measurements of the force-displacement relation of these aciuators confirm theoretical expectations based both on numerical and analytical methods. Finite element analysis is employed to predict the behavior of the complete bistable relay system.
H. H. Chen. 2005. “Shocks in Ion Sputtering Sharpen Steep Surface Features.” Science, 310, 5746, Pp. 294–297.Abstract
We report a regime of ion beam sputtering that occurs for sufficiently steep slopes. High slopes propagate over large distances without dissipating the steepest features. Both the propagation velocity and the dynamically selected slope are universal, independent of the details of the initial shape of the surface. The resulting behavior can be understood as the propagation of a shock front that self-selects a stable slope, as has been previously observed in thin-film fluid flows. Experiments confirm predictions of the theory. An important implication of the propagative behavior at high surface slopes is that a pattern can be fabricated at a large length scale and, through uniform ion irradiation, reduced to a smaller length scale while preserving or even sharpening, the sharpest features.
2004
Eric Lauga and Michael P. Brenner. 2004. “Dynamic mechanisms for apparent slip on hydrophobic surfaces.” Physical Review E, 70, 2.Abstract
Recent experiments [Y. Zhu and S. Granick, Phys. Rev. Lett. 87, 096105 (2001)] have measured a large, shear-dependent fluid slip at partially wetting fluid-solid surfaces. We present a simple model for such a 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 recent atomic force microscopy, the model predicts a force decrease consistent with the experimental measurements of Zhu and Granick.
Baochi Nguyen, Arpita Upadhyaya, Alexander van Oudenaarden, and Michael P. Brenner. 2004. “Elastic Instability in Growing Yeast Colonies.” Biophysical Journal, 86, 5, Pp. 2740–2747.Abstract
The differential adhesion between cells is believed to be the major driving force behind the formation of tissues. The idea is that an aggregate of cells minimizes the overall adhesive energy between cell surfaces. We demonstrate in a model experimental system that there exist conditions where a slowly growing tissue does not minimize this adhesive energy. A mathematical model demonstrates that the instability of a spherical shape is caused by the competition between elastic and surface energies.
Eric Lauga and Michael P. Brenner. 2004. “Evaporation-Driven Assembly of Colloidal Particles.” Physical Review Letters, 93, 23.Abstract
Colloidal particles absorbed at the interface of a liquid droplet arrange into unique packings during slow evaporation [V. N. Manoharan , Science 301, 483 (2003)]. 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.
PETER J. MUCHA, Shang-You Tee, DavidA. Weitz, BORIS I. SHRAIMAN, and Michael P. Brenner. 2004. “A model for velocity fluctuations in sedimentation.” Journal of Fluid Mechanics, 501, Pp. 71–104.Abstract
We present a model for velocity fluctuations of dilute sedimenting spheres at low Reynolds number. The central idea is that a vertical stratification causes the fluctuations to decrease below those of an independent uniform distribution of particles, such a stratification naturally occurring from the broadening of the sedimentation front. We use numerical simulations, scaling arguments, structure factor calculations, and experiments to show that there is a critical stratification above which the characteristics of the density and velocity fluctuations change significantly. For thin cells, the broadening of the sediment front (and the resulting stratification) is small, so the velocity fluctuations are predicted by independent-Poisson-distribution estimates. In very thick cells, the stratification is significant, leading to persistent decay of the velocity fluctuations for the duration of the experiment. Estimated stratifications quantitatively agree with the simulations, and indicate the likelihood that previous experimental measurements were also affected by stratification. The Velocity fluctuations in sedimentation are therefore not universal but instead depend on both the cell shape and developing stratification.
H. Henry Chen and Michael P. Brenner. 2004. “The Optimal Faucet.” Physical Review Letters, 92, 16.Abstract
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.
2003
Sergey V. Fridrikh, Jian H. Yu, Michael P. Brenner, and Gregory C. Rutledge. 2003. “Controlling the Fiber Diameter during Electrospinning.” Physical Review Letters, 90, 14.Abstract
We present a simple analytical model for the forces that determine jet diameter during electrospinning as a function of surface tension, flow rate, and electric current in the jet. The model predicts the existence of a terminal jet diameter, beyond which further thinning of the jet due to growth of the whipping instability does not occur. Experimental data for various electrospun fibers attest to the accuracy of the model.
Martine Ben Amar, Michael P. Brenner, and James R. Rice. 2003. “Cristallisation par onde acoustique : le cas de l\textquotesinglehélium.” Comptes Rendus Mécanique, 331, 9, Pp. 601–607.Abstract
We establish a theoretical model to explain the nucleation of a crystal of helium by an acoustic over-pressure. We explain the interfacial laws for this ultra-fast cristallization, close to the sound speed. Assuming spherical symmetry and taking into account the experimental data, we recover the dynamics of the growth and melting during an over-pressure impulse. (C) 2003 Academie des sciences. Publie par Editions scientifiques et medicales Elsevier SAS. Tous droits, reserves.
P. J. Mucha and M.P. Brenner. 2003. “Diffusivities and front propagation in sedimentation.” Physics of Fluids, 15, 5, Pp. 1305–1313.Abstract
Continuum models for particles sedimenting in a fluid often assume that the diffusivity is a local function of the particulate volume fraction. Since the hydrodynamically induced diffusivity is a result of the velocity fluctuations of particles, the recent identification [e.g., Tee , Phys. Rev. Lett. 89, 054501 (2002)] of particle density stratification as a controlling parameter for the velocity fluctuations also extends to the diffusivities. In particular, the stratification control strongly affects the diffusivity in the vicinity of the falling sediment front between particle-laden fluid below and clarified fluid above. The resulting scaling for stratification-controlled diffusivities in creeping flow sedimentation is presented and compares favorably with measurements from dilute-limit particle simulations. Steadily falling concentration profiles for dilute sedimentation with these diffusivities are then presented, and an extension of the model to higher volume fractions is discussed. (C) 2003 American Institute of Physics.
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M.P. Brenner, C. Gay, and D. A. Weitz. 2003. “Like-charged particles at liquid interfaces.” Nature, 424, 6952, Pp. 1014–1014.
N. Mittal, E. O. Budrene, M.P. Brenner, and A. van Oudenaarden. 2003. “Motility of Escherichia coli cells in clusters formed by chemotactic aggregation.” Proceedings of the National Academy of Sciences, 100, 23, Pp. 13259–13263.Abstract
Cells of Escherichia coli under conditions of certain cellular stresses excrete attractants. Cells of chemotactic strains respond to these excreted signaling molecules by moving up their local concentration gradients and forming different types of stable multicellular structures. Multicellular clusters are the simplest among these structures. Fluorescence microscopy was used to characterize the macroscopic properties of the clusters and to track individual E. coli cells in the clusters in real time. A quantitative analysis reveals that the equilibrium cluster size is only Weakly dependent on the total number of cells in the cluster. The tumble frequency of an individual cell strongly depends on the position of the cell within the cluster and its direction of movement. In the central region of the cluster, tumbles are strongly suppressed whereas near the edge of the cluster, the tumble frequency is restored for exiting cells, thereby preventing them from leaving the cluster, resulting in the maintenance of sharp cluster boundaries. A simulation based on a model of the sensory memory of E coli reproduces the experimental data and indicates that the tumble rate and consequently the morphology of the cluster are determined by the sensory memory of cells.
M.P. Brenner, J.H. Lang, J. Li, J. Qiu, and A.H. Slocum. 2003. “Optimal design of a bistable switch.” Proceedings of the National Academy of Sciences, 100, 17, Pp. 9663–9667.Abstract
Determining optimally designed structures is important for diverse fields of science and engineering. Here we describe a procedure for calculating the optimal design of a switch and apply the method to a bistable microelectromechanical system relay switch. The approach focuses on characterizing the unstable transition state connecting the two stable equilibria to control the force displacements. Small modifications in component shape lead to a substantial improvement in device operation. Fabrication of the optimized devices confirms the predictions.
Michael P. Brenner and Srinivas Paruchuri. 2003. “Thermal bending of liquid sheets and jets.” Physics of Fluids, 15, 11, Pp. 3568–3571.Abstract
We present an analytical model for the bending of liquid jets and sheets from temperature gradients, as recently observed by Chwalek [Phys. Fluids 14, L37 (2002)]. The bending arises from a local couple caused by Marangoni forces. The dependence of the bending angle on experimental parameters is presented, in qualitative agreement with reported experiments. The methodology gives a simple framework for understanding the mechanisms for jet and sheet bending. (C) 2003 American Institute of Physics.
2002
M. G. Nikolaides, A. R. Bausch, M. F. Hsu, A. D. Dinsmore, M.P. Brenner, C. Gay, and D. A. Weitz. 2002. “Electric-field-induced capillary attraction between like-charged particles at liquid interfaces.” Nature, 420, 6913, Pp. 299–301.Abstract
Nanometre- and micrometre-sized charged particles at aqueous interfaces are typically stabilized by a repulsive Coulomb interaction. If one of the phases forming the interface is a nonpolar substance ( such as air or oil) that cannot sustain a charge, the particles will exhibit long-ranged dipolar repulsion(1); if the interface area is confined, mutual repulsion between the particles can induce ordering(2) and even crystallization(3,4). However, particle ordering has also been observed in the absence of area confinement(5), suggesting that like-charged particles at interfaces can also experience attractive interactions(6). Interface deformations are known to cause capillary forces that attract neighbouring particles to each other, but a satisfying explanation for the origin of such distortions remains outstanding(7,8). Here we present quantitative measurements of attractive interactions between colloidal particles at an oil - water interface and show that the attraction can be explained by capillary forces that arise from a distortion of the interface shape that is due to electrostatic stresses caused by the particles' dipolar field. This explanation, which is consistent with all reports on interfacial particle ordering so far, also suggests that the attractive interactions might be controllable: by tuning the polarity of one of the interfacial fluids, it should be possible to adjust the electrostaticstresses of the system and hence the interparticle attractions.
Shang-You Tee, P.\hspace0.167emJ. Mucha, Luca Cipelletti, S. Manley, M.\hspace0.167emP. Brenner, P.\hspace0.167emN. Segre, and D.\hspace0.167emA. Weitz. 2002. “Nonuniversal Velocity Fluctuations of Sedimenting Particles.” Physical Review Letters, 89, 5.Abstract
Velocity fluctuations in sedimentation are studied to investigate the origin of a hypothesized universal scale [P. N. Segre, E. Herbolzheimer, and P. M. Chaikin, Phys. Rev. Lett. 79, 2574 (1997)]. Our experiments show that fluctuations decay continuously in time for sufficiently thick cells, never reaching steady state. Simulations and scaling arguments suggest that the decay arises from increasing vertical stratification of particle concentration due to spreading of the sediment front. The results suggest that the velocity fluctuations in sedimentation depend sensitively on cell geometry.

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