Bouncing or sticky droplets: impalement transitions on superhydrophobic micropatterned surfaces

When a liquid drops impinges a hydrophobic rough surface it can either bounce off the surface (fakir droplets) or be impaled and strongly stuck on it (Wenzel droplets). The analysis of drop impact and quasi static ''loading'' experiments on model microfabricated surfaces allows to clearly identify the forces hindering the impalement transitions. A simple semi-quantitative model is proposed to account for the observed relation between the surface topography and the robustness of fakir non-wetting states. Motivated by potential applications in microfluidics and in the fabrication of self cleaning surfaces, we finally propose some guidelines to design robust superhydrophobic surfaces.Comment: 7 pages, 5 figure

Collapse Dynamics of a Homopolymer: Theory and Simulation

We present a scaling theory describing the collapse of a homopolymer chain in poor solvent. At time t after the beginning of the collapse, the original Gaussian chain of length N is streamlined to form N/g segments of length R(t), each containing g ~ t monomers. These segments are statistical quantities representing cylinders of length R ~ t^{1/2} and diameter d ~ t^{1/4}, but structured out of stretched arrays of spherical globules. This prescription incorporates the capillary instability. We compare the time-dependent structure factor derived for our theory with that obtained from ultra-large-scale molecular dynamics simulation with explicit solvent. This is the first time such a detailed comparison of theoretical and simulation predictions of collapsing chain structure has been attempted. The favorable agreement between the theoretical and computed structure factors supports the picture of the coarse-graining process during polymer collapse.Comment: 4 pages, 3 figure

Glassy behavior of a homopolymer from molecular dynamics simulations

We study at- and out-of-equilibrium dynamics of a single homopolymer chain at low temperature using molecular dynamics simulations. The main quantities of interest are the average root mean square displacement of the monomers below the theta point, and the structure factor, as a function of time. The observation of these quantities show a close resemblance to those measured in structural glasses and suggest that the polymer chain in its low temperature phase is in a glassy phase, with its dynamics dominated by traps. In equilibrium, at low temperature, we observe the trapping of the monomers and a slowing down of the overall motion of the polymer as well as non-exponential relaxation of the structure factor. In out-of-equilibrium, at low temperatures, we compute the two-time quantities and observe breaking of ergodicity in a range of waiting times, with the onset of aging.Comment: 11 pages, 4 figure

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on {\em E. coli} have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with {\em E. coli}. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion

Early Stages of Homopolymer Collapse

Interest in the protein folding problem has motivated a wide range of theoretical and experimental studies of the kinetics of the collapse of flexible homopolymers. In this Paper a phenomenological model is proposed for the kinetics of the early stages of homopolymer collapse following a quench from temperatures above to below the theta temperature. In the first stage, nascent droplets of the dense phase are formed, with little effect on the configurations of the bridges that join them. The droplets then grow by accreting monomers from the bridges, thus causing the bridges to stretch. During these two stages the overall dimensions of the chain decrease only weakly. Further growth of the droplets is accomplished by the shortening of the bridges, which causes the shrinking of the overall dimensions of the chain. The characteristic times of the three stages respectively scale as the zeroth, 1/5 and 6/5 power of the the degree of polymerization of the chain.Comment: 11 pages, 3 figure

Modeling E. coli Tumbles by Rotational Diffusion. Implications for Chemotaxis

The bacterium Escherichia coli in suspension in a liquid medium swims by a succession of runs and tumbles, effectively describing a random walk. The tumbles randomize incompletely, i.e. with a directional persistence, the orientation taken by the bacterium. Here, we model these tumbles by an active rotational diffusion process characterized by a diffusion coefficient and a diffusion time. In homogeneous media, this description accounts well for the experimental reorientations. In shallow gradients of nutrients, tumbles are still described by a unique rotational diffusion coefficient. Together with an increase in the run length, these tumbles significantly contribute to the net chemotactic drift via a modulation of their duration as a function of the direction of the preceding run. Finally, we discuss the limits of this model in propagating concentration waves characterized by steep gradients. In that case, the effective rotational diffusion coefficient itself varies with the direction of the preceding run. We propose that this effect is related to the number of flagella involved in the reorientation process

Morphing in nature and beyond: a review of natural and synthetic shape-changing materials and mechanisms

Shape-changing materials open an entirely new solution space for a wide range of disciplines: from architecture that responds to the environment and medical devices that unpack inside the body, to passive sensors and novel robotic actuators. While synthetic shape-changing materials are still in their infancy, studies of biological morphing materials have revealed key paradigms and features which underlie efficient natural shape-change. Here, we review some of these insights and how they have been, or may be, translated to artificial solutions. We focus on soft matter due to its prevalence in nature, compatibility with users and potential for novel design. Initially, we review examples of natural shape-changing materials—skeletal muscle, tendons and plant tissues—and compare with synthetic examples with similar methods of operation. Stimuli to motion are outlined in general principle, with examples of their use and potential in manufactured systems. Anisotropy is identified as a crucial element in directing shape-change to fulfil designed tasks, and some manufacturing routes to its achievement are highlighted. We conclude with potential directions for future work, including the simultaneous development of materials and manufacturing techniques and the hierarchical combination of effects at multiple length scales.</p

“Čerenkov” dewetting at soft interfaces

A non-wetting liquid is pressed between a rubber cap and a solid plate. When the plate slides at a velocity U larger than a critical value U_{\ab{c}}, the contact is lubricated. However, if the sliding surface carries a nucleating centre (a local depression), a “dry wake” can be induced, with a well-defined wake angle $\alpha_{0}$, as in Čerenkov radiation. We interpret this by a competition between a dewetting velocity V_{\ab{d}} and an invasion velocity U. The Mach relation \sin \alpha_{0}=V_{\ab{d}}/U is obeyed. These effects are relevant to the hydroplaning of cars on wet roads

Vibrated sessile drops: Transition between pinned and mobile contact line oscillations

We study the effects of vertical vibrations on non-wetting large water sessile drops flattened by gravity. The solid substrate is characterized by a finite contact angle hysteresis (10-15 degrees). By varying the frequency and the amplitude of the vertical displacement, we observe two types of oscillations. At low amplitude, the contact line remains pinned and the drop presents eigen modes at different resonance frequencies. At higher amplitude, the contact line moves: it remains circular but its radius oscillates at the excitation frequency. The transition between these two regimes arises when the variations of contact angle exceed the contact angle hysteresis. We interpret different features of these oscillations, such as the decrease of the resonance frequencies at larger vibration amplitudes. The hysteresis acts as “solid” friction on the contour oscillations, and gives rise to a stick-slip regime at intermediate amplitude

Vibrations of sessile drops

This study focuses on the effects of vertical vibrations on sessile drops deposited on hydrophobic substrates. At low amplitudes the contact line remains pinned because of contact angle hysteresis and only drop surface modes are observed. Above a first threshold the contact line starts to move and exhibits a stick-slip behavior that presents some analogies with the solid friction on a mechanical oscillator. At larger amplitudes, non-axisymmetric contour modes show up (modes m=2, 3...). They can be interpreted as a coupling between surface modes and contact line motion. These subharmonic modes are well described within the framework of parametric oscillators. We also discuss here why vibrations can help to measure equilibrium contact angle