Competition and interaction of polydisperse bubbles in polymer foams

The e®ects of interactions between bubbles of di®erent sizes during bubble growth in a polymeric foam are investigated. Two models are used: a two-dimensional sim-ulation in which both the e®ects of gas di®usion through the polymer and bubble interactions through °uid stresses are included, and a three-dimensional model in which bubbles are assumed to interact only through direct competition for gas, and di®usion of gas into the bubbles is instantaneous. In the two-dimensional model, two di®erent bubble sizes are used in a hexagonal array. For slow gas di®usion, the additional polymer stresses have little e®ect on the ¯nal bubble size distribution. For faster gas di®usion the growth occurs in two phases, just as was found in earlier work for isolated bubbles: an initial rapid viscous phase and a later phase controlled by the rate of polymer relaxation. In this later phase, polymers in the windows between neighbouring bubbles become highly stretched and these regions of high stress determine the dynamics of the growth. In the three-dimensional model we consider the e®ects of rheology on a pair of di®erent-sized spherical bubbles, interacting only through competition for available gas. Viscoelastic e®ects result in a wider distribution of bubble volumes than would be found for a Newtonian °uid. Key words: Polymeric °uid; bubble growth; foam; bubble interactions; size distribution ¤ To whom correspondence should be addressed

A Stochastic Finite Element Model for the Dynamics of Globular Macromolecules

We describe a novel coarse grained simulation method for modelling the dynamics of globular macromolecules, such as proteins. The macromolecule is treated as a viscoelastic continuum that is subject to thermal fluctuations. The model includes a non-linear treatment of elasticity and viscosity with thermal noise that is solved using finite element analysis. We have validated the method by demonstrating that the model provides average kinetic and potential energies that are in agreement with the classical equipartition theorem. In addition, we have performed Fourier analysis on the simulation trajectories obtained for a series of linear beams to confirm that the correct average energies are present in the first two Fourier bending modes. We have then used the new modelling method to simulate the thermal fluctuations of a representative protein over 500ns timescales. Using reasonable parameters for the material properties, we have demonstrated that the overall deformation of the biomolecule is consistent with the results obtained for proteins in general from atomistic molecular dynamics simulations

Jetting behavior in drop-on-demand printing: Laboratory experiments and numerical simulations

The formation and evolution of micron-sized droplets of a Newtonian liquid generated on demand in an industrial inkjet printhead are studied experimentally and simulated numerically. The shapes and positions of droplets during droplet formation are observed using a high-speed camera and compared with their numerically obtained analogs. Both the experiments and the simulations use practical length scales for inkjet printing. The results show how fluid properties, specifically viscosity and surface tension, affect the drop formation, ligament length, and breakoff time. We identify the parameter space of fluid properties for producing single drops at a prescribed speed and show this is not simply a restriction on the Ohnesorge number, but that there is an additional restriction on the Reynolds number that is distinct from the Reynolds number limit associated with the prevention of splashing. This phase diagram provides more precise guidance on the space of fluid parameters for jetting single droplets in drop-on-demand inkjet printers

PolySTRAND Model of Flow-Induced Nucleation in Polymers

We develop a thermodynamic continuum-level model, polySTRAND, for flow-induced nucleation in polymers suitable for use in computational process modeling. The model’s molecular origins ensure that it accounts properly for flow and nucleation dynamics of polydisperse systems and can be extended to include effects of exhaustion of highly deformed chains and nucleus roughness. It captures variations with the key processing parameters, flow rate, temperature, and molecular weight distribution. Under strong flow, long chains are over-represented within the nucleus, leading to superexponential nucleation rate growth with shear rate as seen in experiments

Molecular physics of a polymer engineering instability: Experiments and computation

Entangled polymer melts exhibit a variety of flow instabilities that limit production rates in industrial applications. We present both experimental and computational findings, using flow of monodisperse linear polystyrenes in a contraction-expansion geometry, which illustrate the formation and development of one such flow instability. This viscoelastic disturbance is observed at the slit outlet and subsequently produces large-scale fluid motions upstream. A numerical linear stability study using the molecular structure based Rolie-Poly model confirms the instability and identifies important parameters within the model, which gives physical insight into the underlying mechanism. Chain stretch was found to play a critical role in the instability mechanism, which partially explains the effectiveness of introducing a low-molecular weight tail into a polymer blend to increase its processability

Capillary breakup of suspensions near pinch-off

We present new findings on how the presence of particles alters the pinch-off dynamics of a liquid bridge. For moderate concentrations, suspensions initially behave as a viscous liquid with dynamics determined by the bulk viscosity of the suspension. Close to breakup, however, the filament loses its homogeneous shape and localised accelerated breakup is observed. This paper focuses on quantifying these final thinning dynamics for different sized particles with radii between 3 μm and 20 μm in a Newtonian matrix with volume fractions ranging from 0.02 to 0.40. The dynamics of these capillary breakup experiments are very well described by a one-dimensional model that correlates changes in thinning dynamics with the particle distribution in the filament. For all samples, the accelerated dynamics are initiated by increasing particle-density fluctuations that generate locally diluted zones. The onset of these concentration fluctuations is described by a transition radius, which scales with the particle radius and volume fraction. The thinning rate continues to increase and reaches a maximum when the interstitial fluid is thinning between two particle clusters. Contrary to previous experimental studies, we observe that the final thinning dynamics are dominated by a deceleration, where the interstitial fluid appears not to be disturbed by the presence of the particles. By rescaling the experimental filament profiles, it is shown that the pinching dynamics return to the self-similar scaling of a viscous Newtonian liquid bridge in the final moments preceding breakup

Exploring the dynamics of flagellar dynein within the axoneme with Fluctuating Finite Element Analysis

Flagellar dyneins are the molecular motors responsible for producing the propagating bending motions of cilia and flagella. They are located within a densely packed and highly organised super-macromolecular cytoskeletal structure known as the axoneme. Using the mesoscale simulation technique Fluctuating Finite Element Analysis (FFEA), which represents proteins as viscoelastic continuum objects subject to explicit thermal noise, we have quantified the constraints on the range of molecular conformations that can be explored by dynein-c within the crowded architecture of the axoneme. We subsequently assess the influence of crowding on the 3D exploration of microtubule-binding sites, and specifically on the axial step length. Our calculations combine experimental information on the shape, flexibility and environment of dynein-c from three distinct sources; negative stain electron microscopy, cryo-electron microscopy (cryo-EM) and cryo-electron tomography (cryo-ET). Our FFEA simulations show that the super-macromolecular organisation of multiple protein complexes into higher-order structures can have a significant influence on the effective flexibility of the individual molecular components, and may, therefore, play an important role in the physical mechanisms underlying their biological function