Michael P. Brenner

Experimental characterization of electrospinning: the electrically forced jet and instabilities

In the electrospinning process, polymer fibers with submicron-scale diameters are formed by subjecting a fluid jet to a high electric field. We report an experimental investigation of the electrically forced jet and its instabilities. The results are interpreted within the framework of a recently developed theory for electrified fluid jets. We find that the process can be described by a small set of operating parameters and summarized through the use of operating diagrams of electric field versus flow rate. In addition, the jet current is related to the net charge density and found to depend on the fluid properties, the applied electric field and the equipment configuration. The net charge density appears to be relatively insensitive to the flow rate, at least for high flow rates. The experiments reveal that a key process in the formation of submicron-scale solid fibers is a convective instability, the rapidly whipping jet. The dependence of this instability on electric field and flow rate, and the exponential nature of its growth rate are in accord with the theory.

Electrospinning and electrically forced jets. I. Stability theory

Electrospinning is a process in which solid fibers are produced from a polymeric fluid stream (solution or melt) delivered through a millimeter-scale nozzle. The solid fibers are notable for their very small diameters (<1 μm). Recent experiments demonstrate that an essential mechanism of electrospinning is a rapidly whipping fluid jet. This series of papers analyzes the mechanics of this whipping jet by studying the instability of an electrically forced fluid jet with increasing field strength. An asymptotic approximation of the equations of electrohydrodynamics is developed so that quantitative comparisons with experiments can be carried out. The approximation governs both long wavelength axisymmetric distortions of the jet, as well as long wavelength oscillations of the centerline of the jet. Three different instabilities are identified: the classical (axisymmetric) Rayleigh instability, and electric field induced axisymmetric and whipping instabilities. At increasing field strengths, the electrical instabilities are enhanced whereas the Rayleigh instability is suppressed. Which instability dominates depends strongly on the surface charge density and radius of the jet. The physical mechanisms for the instability are discussed in the various possible limits.

Electrospinning : A Whipping Fluid Jet Generates Submicron Polymer Fibers

Polymeric fibers with diameters in the range from 50 nm to 5 μm are produced by accelerating a fluid jet in an electric field, in a process known as “electrospinning.” Here we show that an essential element of the process is a fluid instability, the rapidly whipping jet. The phenomena responsible for the onset of whipping are revealed by a linear instability analysis that describes the jet behavior in terms of known fluid properties and operating conditions. The behavior of two competing instabilities, the Rayleigh mode and the axisymmetric conducting mode, is also described. The results are summarized using operating diagrams, delineating regimes of operation in electrospinning, which are in good agreement with experimental observations.

Electrospinning and electrically forced jets. II. Applications

Electrospinning is a process in which solid fibers are produced from a polymeric fluid stream (solution or melt) delivered through a millimeter-scale nozzle. This article uses the stability theory described in the previous article to develop a quantitative method for predicting when electrospinning occurs. First a method for calculating the shape and charge density of a steady jet as it thins from the nozzle is presented and is shown to capture quantitative features of the experiments. Then, this information is combined with the stability analysis to predict scaling laws for the jet behavior and to produce operating diagrams for when electrospinning occurs, both as a function of experimental parameters. Predictions for how the regime of electrospinning changes as a function of the fluid conductivity and viscosity are presented.

A Cascade of Structure in a Drop Falling from a Faucet

A drop falling from a faucet is a common example of a mass fissioning into two or more pieces. The shape of the liquid in this situation has been investigated by both experiment and computer simulation. As the viscosity of the liquid is varied, the shape of the drop changes dramatically. Near the point of breakup, viscous drops develop long necks that then spawn a series of smaller necks with ever thinner diameters. Simulations indicate that this repeated formation of necks can proceed ad infinitum whenever a small but finite amount of noise is present in the experiment. In this situation, the dynamical singularity occurring when a drop fissions is characterized by a rough interface.

Linear stability and transient growth in driven contact lines

Fluid flowing down an inclined plane commonly exhibits a fingering instability in which the contact line corrugates. We show that below a critical inclination angle the base state before the instability is linearly stable. Several recent experiments explore inclination angles below this critical angle, yet all clearly show the fingering instability. We explain this paradox by showing that regardless of the long time linear stability of the front, microscopic scale perturbations at the contact line grow on a transient time scale to a size comparable with the macroscopic structure of the front. This amplification is sufficient to excite nonlinearities and thus initiate finger formation. The amplification is a result of the well-known singular dependence of the macroscopic profiles on the microscopic length scale near the contact line. Implications for other types of forced contact lines are discussed.

The free-energy landscape of clusters of attractive hard spheres.

Packing Puzzle The packing of a large number of spheres is a well-studied problem with maximal packing based on the arrangement of nearest neighbors. With much smaller numbers of particles, it is the free energy that governs which packing arrangements dominate. Meng et al. (p. 560; see the Perspective by Crocker) looked at the assembly of colloidal clusters where the number of particles was limited from 2 to 10. For five particles or fewer, only one packing arrangement was found. For six or more particles, while a number of similar energy structures could form, the probability of formation was biased toward those structures with the greater number of nearest-neighbor connections. Entropic effects favor the formation of small clusters of colloidal particles that have lower symmetry. The study of clusters has provided a tangible link between local geometry and bulk condensed matter, but experiments have not yet systematically explored the thermodynamics of the smallest clusters. Here we present experimental measurements of the structures and free energies of colloidal clusters in which the particles act as hard spheres with short-range attractions. We found that highly symmetric clusters are strongly suppressed by rotational entropy, whereas the most stable clusters have anharmonic vibrational modes or extra bonds. Many of these clusters are subsets of close-packed lattices. As the number of particles increases from 6 to 10, we observe the emergence of a complex free-energy landscape with a small number of ground states and many local minima.

Physical mechanisms for chemotactic pattern formation by bacteria.

This paper formulates a theory for chemotactic pattern formation by the bacteria Escherichia coli in the presence of excreted attractant. In a chemotactically neutral background, through chemoattractant signaling, the bacteria organize into swarm rings and aggregates. The analysis invokes only those physical processes that are both justifiable by known biochemistry and necessary and sufficient for swarm ring migration and aggregate formation. Swarm rings migrate in the absence of an external chemoattractant gradient. The ring motion is caused by the depletion of a substrate that is necessary to produce attractant. Several scaling laws are proposed and are demonstrated to be consistent with experimental data. Aggregate formation corresponds to finite time singularities in which the bacterial density diverges at a point. Instabilities of swarm rings leading to aggregate formation occur via a mechanism similar to aggregate formation itself: when the mass density of the swarm ring exceeds a threshold, the ring collapses cylindrically and then destabilizes into aggregates. This sequence of events is demonstrated both in the theoretical model and in the experiments.

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 and Lohse, Phys. Rev. Lett. 96, 206101 (2006); 10.1103/PhysRevLett.96.206101Zhang, Phys. Rev. Lett.10.1103/PhysRevLett.98.136101 98, 136101 (2007); 10.1103/PhysRevLett.98.136101Mezger, J. Chem. Phys. 128, 244705 (2008)10.1063/1.2931574]. This influx balances the outflux and allows for a metastable 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.

Physical Ageing of the Contact Line on Colloidal Particles at Liquid Interfaces

Youngs law predicts that a colloidal sphere in equilibrium with a liquid interface will straddle the two fluids, its height above the interface defined by an equilibrium contact angle. This has been used to explain why colloids often bind to liquid interfaces, and has been exploited in emulsification, water purification, mineral recovery, encapsulation and the making of nanostructured materials. However, little is known about the dynamics of binding. Here we show that the adsorption of polystyrene microspheres to a water/oil interface is characterized by a sudden breach and an unexpectedly slow relaxation. The relaxation appears logarithmic in time, indicating that complete equilibration may take months. Surprisingly, viscous dissipation appears to play little role. Instead, the observed dynamics, which bear strong resemblance to ageing in glassy systems, agree well with a model describing activated hopping of the contact line over nanoscale surface heterogeneities. These results may provide clues to longstanding questions on colloidal interactions at an interface.