Modeling,Mathematical and Numerical Analysis of Electrorheological Fluids

Many electrorheological fluids are suspensions consisting of solid particles and a carrier oil. If such a suspension is exposed to a strong electric field the effective viscosity increases dramatically. In this paper we first derive a model which captures this behaviour. For the resulting system of equations we then prove local in time existence of strong solutions for large data. For these solutions we finally derive error estimates for a fully implicit time-discretization.     

Steady Nonintegrable High-Dimensional Fluids

We consider the existence of steady incompressible fluids (solutions to the Euler equations) on Riemannian manifolds of dimensions three and higher. We demonstrate that, as in the case of the ABC fields in dimension three, there exist chaotic Beltrami fields – nonsingular eigenfields of the curl operator – in higher dimensions. We give an explicit set of analytic examples on a non-Euclidean five-torus T ⁵. We also detail a plug construction for inserting chaotic vortices into a Beltrami field. These constructions employ contact-topological techniques.     

极性分子型电流变液

电流变液在电场作用下软硬连续可调的奇特性质具有广泛和重要的应用价值。传统电流变液是基于颗粒极化产生的相互作用,根据介电理论预测,其剪切屈服强度的上限约为10kPa。电流变液被发明50年来,阻碍其应用的主要原因是剪切强度低。近年来发明的"极性分子型电流变液"是一类新型电流变液,其屈服强度比传统电流变液大一个数量级以上,且与电场强度呈线性关系,这一点和传统电流变液中的平方关系也明显不同。文章作者提出了极性分子在颗粒间强局域电场中的取向并与极化电荷作用的模型,成功地解释了观察到的实验现象。根据这一原理,有可能制备出屈服强度高达MPa的电流变液。     

Magnetohydrodynamic properties of incompressible Meissner fluids

We consider a superconducting material that exists in the liquid state, more precisely, in which the Meissner-Ochsenfeld effect persists in the liquid state. First, we investigate how the shape of such a hypothetical Meissner liquid will adapt to accomodate for an applied external field. In particular, we analyse the case of a droplet of Meissner fluid, and compute the elongation of the droplet and its quadrupole frequency as a function of the applied field. Next, the influence of an applied field on the flow of the liquid is studied for the case of a surface wave. We derive the dispersion relation for surface waves on an incompressible Meissner fluid. We discuss some candidate realizations of the Meissner fluids and for the case of a superconducting colloid discuss which regime of wave lengths would be most affected by the Meissner effect.     

Application of inertia-induced excitation theory for nonlinear acoustic modes in colloidal plasma equilibrium flow

Application of inertia-induced acoustic excitation theory offers a new resonant excitation source channel of acoustic turbulence in the transonic domain of plasma flow. In bi-ion plasmas like colloidal plasma, two well-defined transonic points exist corresponding to the parent ion and the dust grain-associated acoustic modes. As usual, the modified ion acoustic mode (also known as dust ion-acoustic (DIA) wave) dynamics associated with parent ion inertia is excitable for both nanoscale-and micronscale-sized dust grains. It is found that the so-called (ion) acoustic mode (also known as dust-acoustic (DA) wave) associated with nanoscale dust grain inertia is indeed resonantly excitable through the active role of weak but finite parent ion inertia. It is interestingly conjectured that the same excitation physics, as in the case of normal plasma sound mode, operates through the active inertial role of plasma thermal species. Details of the nonlinear acoustic mode analyses of current interest in transonic domains of such impure plasmas in hydrodynamic flow are presented.      

Living fluids

One of the major emerging fields of research of the beginning of this century concerns living fluids. By “living fluids”, we mean two major categories of complex fluids: (i) fluids which are essential to life, like blood, and (ii) active fluids made of particles that are able to propel themselves in the suspending fluid by converting a form of their energy into mechanical motion. Studies on active fluids have known a considerable interest since the last decade. Blood might be viewed as an old topic, but the progresses in experimental techniques, analytical concepts and numerics, have contributed nowadays to a dramatic renewal of the interest in this field, with a great potential towards understanding physical and mechanical factors in cardiovascular diseases. These fields have considerably strengthened interdisciplinary research. The series of reviews of this dossier focus on the tremendous recent progress achieved in research on living fluids both from the experimental and theoretical points of views. These reviews present also the major open issues, making of this dossier a unique guide for future research in these fields. This project grew up thanks to the international summer school that we organized on the topic “living fluids” at the IES (Institut dʼétudes scientifiques) of Cargèse (Corsica) in 2012.     

Compressed‐gas‐induced crystallization in tert‐butyl poly(ether ether ketone)

tert‐Butyl‐substituted poly(ether ether ketone) (tBuPEEK), which does not undergo crystallization with thermal annealing, crystallizes readily when treated with compressed CO₂. The dissolved CO₂ causes a reduction in the glass‐transition temperature of the polymer–gas system and enhances the chain mobility of the macromolecules, thereby bringing about crystallization. In the presence of CO₂, crystallization is increasingly favored with increasing CO₂ pressure and treatment temperature. The melting point of tBuPEEK crystals increases linearly with the CO₂ pressure applied in the treatment, indicating an increase in the order and/or size of the crystals. The extent of crystallinity increases when small amounts of methanol or dichloromethane are used as a cosolute with CO₂. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1505–1512, 2001     

A simple proof of the linear instability of rotating liquid drops

We give a simplified proof of the linear instability of equilibrium figures of rotating liquid based on energy estimates.      

Tuning intermicellar potential of Triton X-100-anthranilic acid mixed micelles

Structural parameters of micelles formed by Triton X-100 in the presence of solubilized anthranilic acid at different pH values was investigated using light scattering and small angle neutron scattering. Analysis of the SANS data indicate that micelles are oblate ellipsoidal in nature with little variation in the dimensions, in the investigated pH range (from 0.5 to 6.0). The interaction potential of the micelles shows a minimum closer to the isoelectric point of anthranilic acid. A similar variation is observed in the cloud point of the micelles with pH. The observed variation in the interaction potential with pH of the micellar solution can be explained in terms of the reversal of charge on anthranilic acid due to shift in the acid-base equilibrium. The variation in interaction potential and cloud point with pH is modelled using Coulombic repulsion of charged molecules at the micelle interface.