Lipid aggregate formation at an oscillating bubble surface: A simulation study

We perform a molecular dynamics simulation study of the behavior of a lipid coating layer on an oscillating bubble surface. Micrometer sized bubbles, stabilized with a lipid monolayer coating, are used in acoustic imaging as a contrast agent. The coating layer is expected to be strongly influenced by the oscillation of the bubble in the high frequency sound field, with a period of a microsecond. The typical time scale of molecular motion, however, is of the order of femtoseconds. One of the challenges is to bridge this nine decade gap in time scales. To this end we have developed a model that is highly coarse grained, but still features the essential mechanisms determining lipid dynamics, with time scales of picoseconds. This approach allows us to severely restrict the computing times, although we make use of very modest computing equipment. We show in our simulation that the amphiphilic monolayer folds upon contraction of the bubble, and forms micellar aggregates at the air-water interface. Some micellar structures survive consecutive re-expansion and indeed remain persistent over several cycles. These structures may add to the anisotropic behavior of the bubbles under oscillating conditions. We also investigated temperature and frequency dependenc

Dynamics of chains grafted on solid wall during polymer melt extrusion

The objective of the present work is the mathematical modeling of the dynamics of polymer molecules grafted on a solid boundary during polymer melt extrusion. This topic is closely related to the long-standing problem of polymer flow instabilities encountered in industry when extruding melts. In order to describe the behavior of the tethered chains, we introduce the bond vector probability distribution function (BVPDF) which appears to be a simple, yet effective mathematical 'tool'. The bond vector, i.e. the tangent vector to a polymer chain depending on the position along the chain and on time, describes the local geometry via its direction and the local stretching of the chain via its length. The BVPDF contains all information about the geometry of the ensemble of chains. Via averaging over the BVPDF we can calculate all interesting macrsocopic quantities, e.g. the thickness of and stress in the layer of tethered molecules. The time dependence of the BVPDF yields the time evolution of the system. We derive the equation of motion for the BVPDF taking into account all important mechanisms, such as reptation and (convective) constraint release. Besides that, we show that all macroscopic quantities of practical interest can be expressed via second order moments of this distribution function. \u

Aerated bunker discharge of fine dilating powders

The discharge rate of coarse powders (mean particle size 500 ¿m) from bunkers without aeration can be described by both empirical relations and theoretical models. In the case of small particles the discharge rate is largely overestimated. As the powder dilates during flow a negative pressure gradient develops near the hopper outlet, inducing an air flow into the hopper. This extra drag force decreases the discharge rate for fine particles. Aeration of the hopper through a porous cone section will create an opposite pressure gradient, and thereby increase the discharge rate. The aim of this investigation was to incorporate the dilation in an ad hoc way into the model of Altiner in order to improve its predictive power. To test the modified model we carried out experiments with a fluid catalytic cracking powder to study its discharge as a function of aeration. As the improved model needs a dilation parameter as input, the local bulk density was measured during flow at the outlet and at the bin/hopper junction using gamma-ray absorption. At the bin/hopper junction the bulk density was found to be independent of the discharge rate and equal to the bulk density at minimum fluidisation. At the outlet the bulk density goes through a maximum when the amount of aeration gas is increased. Without aeration gas a large dilation, i.e. a 15¿35% lower bulk density, was observed. With these data the model predictions improved from 600% overestimation error to 25¿90% underestimation for pure gravity discharge, and from 100% to 0¿20% error for aerated discharge. However, the bulk density at the outlet cannot be predicted from the powder compressibility, as it seems to depend on dilation at fluidisation

A rigorous model for constraint release in the bulk and the near-wall region

In the present work an attempt is made to build a rigorous theoretical model for the constraint release mechanism found to play an important role in the dynamics of polymer melts. Our goal is a formalism free of adjustable parameters and ''ad-hoc'' assumptions which are inherent to existing theories for constraint release. Our model is capable to describe both thermal and convective constraint release. These processes have the same effect on chains and accordingly can be unified in a single framework. Since polymer chains in the bulk and in the near-wall layer may experience different types of constraint release, the latter case is studied separately. This topic is closely related to the long-standing problem of polymer melt flow instabilities encountered during extrusion. Nowadays it is believed that constraint release plays a crucial role in the dynamics of tethered chains preventing them from being squeezed against the wall. The resulting non-monotonous slip-law is the most probable reason of the so-called spurt instability. \u

A universal constitutive model for the interfacial layer between a polymer melt and a solid wall

In a preceeding report we derived the evolution equation for the bond vector probability distribution function (BVPDF) of tethered molecules. It describes the behavior of polymer molecules attached to a solid wall interacting with an adjacent flowing melt of bulk polymer molecules and includes all the major relaxation mechanisms such as constraint release, retraction and convection. The derived equation is quite universal and valid for all flow regimes. In the present paper the developed formalism is further analyzed. We begin our analysis with the simple case of slow flows. Then, as expected, a remarkable reduction of the theory is possible. Later on the more general case is considered. \u

Flow-induced correlation effects within a linear chain in a polymer melt

A framework for a consistent description of the flow-induced correlation effects within a linear polymer chain in a melt is proposed. The formalism shows how correlations between chain segments in the flow can be incorporated into a hierarchy of distribution functions for tangent vectors. The present model allows one to take into account all the major relaxation mechanisms. Special cases of the derived set of equations are shown to yield existing models and shed some light on the connection between them. Consequences of several assumptions widely used in the literature are analyzed within the developed framework