Adhesion energy can regulate vesicle fusion and stabilize partially fused states

Release of neurotransmitters from nerve terminals occurs by fusion of synaptic vesicles with the plasma membrane, and this process is highly regulated. Although major molecular components that control docking and fusion of vesicles to the synaptic membrane have been identified, the detailed mechanics of this process is not yet understood. We have developed a mathematical model that predicts how adhesion forces imposed by docking and fusion molecular machinery would affect the fusion process. We have computed the membrane stress that is produced by adhesion-driven vesicle bending and find that it is compressive. Further, our computations of the membrane curvature predict that strong adhesion can create a metastable state with a partially opened pore that would correspond to the ‘kiss and run’ release mode. Our model predicts that the larger the vesicle size, the more likely the metastable state with a transiently opened pore. These results contribute to understanding the mechanics of the fusion process, including possible clamping of the fusion by increasing molecular adhesion, and a balance between ‘kiss and run’ and full collapse fusion modes.     

How Compliance Compensates for Surface Roughness in Fibrillar Adhesion

Fibrillar interfaces play an important role in the ability of many small animals to adhere to surfaces. Surface roughness is generally deleterious to adhesion because it hinders the ability of mating surfaces to make contact, but fibrillar surfaces compensate for surface roughness by virtue of their enhanced compliance. We examine the relationship between roughness and compliance by analyzing the mechanics of detaching an array of fibrils from a substrate. The theory of Johnson, Kendall, and Roberts is used to describe the interfacial adhesion of each fibril, and roughness is modeled by making the fibril length a random variable subject to a probability distribution. We solve for the mean force response of a fibrillar array as a function of the displacement of the entire array. From these results we extract the mean fibrillar pull-off force and work to separate the fibrillar array and substrate. We show how the mean fibrillar pull-off force decreases with increasing roughness-height standard deviation: the relationship is linear for small height standard deviation, and the pull-off force trails off to zero for very rough surfaces. Conversely, the work of separation is shown to be unaffected by small roughness-height standard deviation, although it decreases toward zero for rougher surfaces. The effects of roughness may be offset by increasing fibrillar compliance; for small roughness-height standard deviation, we show that the reduction in pull-off force is inversely proportional to the normalized compliance. We also show that the work of separation increases linearly with the compliance when the compliance is large compared with the roughness-height standard deviation.     

Isotropic Constitutive Model for Sintering Particle Packings

This paper presents an isotropic model for the effective viscosities of sintering particle packings. The relationship between the macroscopic stress and deformation rate is based on the behavior of individual interparticle contacts, represented by contact viscosities, and the statistics of the packing. The contact viscosities depend on the contact area, which is the primary variable used to describe the state of the packing. A direct consequence of this choice of state variable is that the effective viscosities are identically zero for an undeformed and unsintered packing. Specific results are presented for the case of Newtonian viscous materials. The model is compared with existing models for porous Newtonian viscous materials. Experiments conducted with spherical glass powder packings show good agreement with the model. Finite-element simulations using the model have been used to study forging of a pellet.     

Simulation of the Viscous Sintering of Two Particles

The viscous sintering of two initially spherical particles is modeled as creeping flow in response to surface tension. The governing equations are solved using the finite-element method. The condensed results of this simulation, the center-to-center approach velocity, and the rate of change of contact area were presented earlier. Some details of the flow field during sintering and the evolution of the neck geometry in the early stages of sintering are presented here. Important numerical issues are detailed.     

Natural Frequencies of Stable Griffith Cracks

A quasi-statically growing stable crack, if perturbed from its equilibrium position, will accelerate back towards it. Within quasi-static, ideal, Griffith fracture theory, vibrations of the crack and the structure have characteristic natural frequencies. We explore this feature of Griffith fracture theory in two simple geometries: a crack between a bar and a substrate, and a crack in a double-cantilever beam (DCB) specimen. For small perturbations about the stable quasi-static configuration, the dynamic equations of motion reduce to simple eigenvalue problems, leading to exact expressions for natural frequencies and mode shapes. An interesting feature of the mode shapes is that they correspond to force-free or moment-free conditions at the crack tip. Using an extended form of Hamilton's principle, we have developed a variable-length finite element technique to calculate natural frequencies and mode shapes of deformations perturbed from the stable equilibrium state. Its accuracy is demonstrated by application to the two problems analyzed previously. The possibility of crack tip oscillations in real brittle materials with irreversibility in crack tip decohesion is discussed in light of Rice's generalization of the Griffith theory.     

Radial mixing and residence times in the liquid phase in gas-liquid annular flow in vertical tubes

Theory for calculating the mean velocities of the drops and of the film in gas-liquid cocurrent annular flow by use of tracer pulse techniques has been developed. It is shown that the interaction between the film and the drops affects the mean residence times in each, and is much greater in its effect than is axial dispersion in the film or in the core. The theory also describes a relatively simple means of determining the mean amounts of droplet entrainment and liquid interchange between droplets and film from measurements made with continuous tracer injection. Knowledge of the entrainment and the mean velocities of film and drops is essential in determining the extent of interaction between the liquid film and the entrained liquid flow.     

Controlled two-dimensional pattern of spontaneously aligned carbon nanotubes

We report a simple solution process to form controlled patterns of aligned single-walled carbon nanotubes on solid substrates. The essential step of the process is to deposit a dilute solution of DNA-wrapped carbon nanotubes (DNA-CNTs) on a SiO(2) surface covered with a thin hydrophobic layer. This leads to deposition of fully aligned CNTs. The alignment pattern can be controlled by metal electrodes in the deposition region and can be quantitatively modeled by the behavior of a quasi-two-dimensional DNA-CNT nematic phase near the solution/SiO(2) interface. These results point to the possibility of rational design and economical fabrication of CNT alignment patterns on solid substrates.