The effect of a concentration-dependent viscosity on\ud particle transport in a channel flow with porous walls

We analyse the transport of a dilute suspension of particles through a channel with porous walls accounting for the concentration dependence of the viscosity. Two cases of leakage flow of fluid through the porous channel walls are studied: (i) constant flux, and (ii) dependent on the pressure drop across the wall. The effect of mixing the suspension first compared with point injection is examined by considering inlet concentration distributions of different widths. We find that a pessimal distribution width exists that maximizes the required hydrodynamic pressure for a constant fluid influx. We also show that the presence of an osmotic pressure may lead to fluid being sucked into the channel. We consider how the application of an external hydrodynamic pressure affects this observation and discuss the significance of our results for water filtration

Interfacial deflection and jetting of a paramagnetic particle-laden fluid: theory and experiment

We describe the results of experiments and mathematical analysis of the deformation of a free surface by an aggregate of magnetic particles. The system we study is differentiated from ferrofluid systems because it contains regions rich with magnetic material as well as regions of negligible magnetic content. In our experiments, the magnetic force from a spherical permanent magnet collects magnetic particles to a liquid–air interface, and deforms the free surface to form a hump. The hump is composed of magnetic and non-magnetic regions due to the particle collection. When the magnet distance falls below a threshold value, we observe the transition of the hump to a jet. The mathematical model we develop, which consists of a numerical solution and an asymptotic approximation, captures the shape of the liquid–air interface during the deformation stage and a scaling prediction for the critical magnet distance for the hump to become a jet

Nematode movement along a chemical gradient in a structurally heterogeneous environment : 2. Theory

L'influence de l'hétérogénéité sur la diffusion chimique et le déplacement des nématodes est étudiée par le biais d'un modèle théorique. Ce modèle prend en compte trois facteurs influant sur le déplacement des nématodes : la structure du sol, la stratégie de recherche de nourriture et la chémotaxie. Utilisant un modèle continu, nous avons mis au point un système discret permettant de simuler les traces des nématodes dans chacune des quatre situations définies par Anderson et al. (1997). Nous avons montré que l'hétérogénéité structurale provoque aussi bien des taux variables de concentrations du composé attractif dans des aires réduites que la reconnaissance de ce composé. L'hétérogénéité structurale du sol limite également la stratégie de recherche de nourriture du nématode lequel adopte alors une stratégie permettant d'éviter les pièges structuraux. Il est démontré que des augmentations localisées de la densité structurale accroissent significativement la reconnaissance du composé attractif. (Résumé d'auteur

Nematode movement along a chemical gradient in a structurally heterogeneous environment : 1 . Experiment

L'interaction entre l'hétérogénéité structurale et les gradients chimiques, ainsi que leur influence sur le déplacement des nématodes, ont été étudiées. Trois dispositifs expérimentaux ont été utilisés qui comprennent un nématode (#Caenorhabditis elegans) placé sur une couche homogène de milieu nutritif gélosé dans une boîte de Petri avec ou sans présence d'une source bactérienne de nourriture (#Escherichia coli) utilisée comme attractif. L'hétérogénéité structurale est réalisée en ajoutant des grains de sable en une seule épaisseur dans chacun des traitements homologues. Toutes les traces ont été relevées à l'aide d'un dispositif de vidéo à séquences temporelles et les données digitalisées avant analyse. Les répartitions des angles de changement de direction et les dimensions fractales des traces sont calculées pour chaque traitement. Il se révèle un effet statistiquement significatif (P inférieur ou égal à 0,01) de tous les traitements sur le déplacement des nématodes. En présence d'un produit attractif, le déplacement du nématode est plus linéaire et dirigé vers la source bactérienne. L'hétérogénéité structurale provoque un déplacement plus linéaire que dans le cas d'un milieu homogène. La dimension fractale des traces du nématode est significativement (P inférieur ou égal à 0,01) plus élevée pour les traitements sans sable ni bactéries que pour les autres traitements. Ces résultats permettent, pour la première fois, de quantifier le degré auquel les nématodes utilisent un comportement de recherche de nourriture au hasard dans un milieu homogène et adoptent un déplacement mieux orienté en présence d'un produit attractif. Finalement, lorsqu'une hétérogénéité est présente, la stratégie de recherche de nourriture devient plutôt une stratégie d'évitement permettant au nématode d'échapper aux "pièges" structuraux, tels les pores en cul-de-sac, et de pouvoir ainsi continuer à réagir à l'attraction. (Résumé d'auteur

Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras

Darboux coordinates are constructed on rational coadjoint orbits of the positive frequency part \wt{\frak{g}}^+ of loop algebras. These are given by the values of the spectral parameters at the divisors corresponding to eigenvector line bundles over the associated spectral curves, defined within a given matrix representation. A Liouville generating function is obtained in completely separated form and shown, through the Liouville-Arnold integration method, to lead to the Abel map linearization of all Hamiltonian flows induced by the spectral invariants. Serre duality is used to define a natural symplectic structure on the space of line bundles of suitable degree over a permissible class of spectral curves, and this is shown to be equivalent to the Kostant-Kirillov symplectic structure on rational coadjoint orbits. The general construction is given for $\frak{g}=\frak{gl}(r)$ or $\frak{sl}(r)$, with reductions to orbits of subalgebras determined as invariant fixed point sets under involutive automorphisms. The case $\frak{g=sl}(2)$ is shown to reproduce the classical integration methods for finite dimensional systems defined on quadrics, as well as the quasi-periodic solutions of the cubically nonlinear Schr\"odinger equation. For $\frak{g=sl}(3)$, the method is applied to the computation of quasi-periodic solutions of the two component coupled nonlinear Schr\"odinger equation.Comment: 61 pg

Solution landscapes in nematic microfluidics

We study the static equilibria of a simplified Leslie–Ericksen model for a unidirectional uniaxial nematic flow in a prototype microfluidic channel, as a function of the pressure gradient G and inverse anchoring strength, B. We numerically find multiple static equilibria for admissible pairs (G,B) and classify them according to their winding numbers and stability. The case G=0 is analytically tractable and we numerically study how the solution landscape is transformed as G increases. We study the one-dimensional dynamical model, the sensitivity of the dynamic solutions to initial conditions and the rate of change of G and B. We provide a physically interesting example of how the time delay between the applications of G and B can determine the selection of the final steady state

Beyond the String Genus

In an earlier work we used a path integral analysis to propose a higher genus generalization of the elliptic genus. We found a cobordism invariant parametrized by Teichmuller space. Here we simplify the formula and study the behavior of our invariant under the action of the mapping class group of the Riemann surface. We find that our invariant is a modular function with multiplier just as in genus one.Comment: 40 pages, 1 figur

Optimising dead-end cake filtration using poroelasticity theory

Understanding the operation of filters used to remove particulates from fluids is important in many practical industries. Typically the particles are larger than the pores in the filter so a cake layer of particles forms on the filter surface. Here we extend existing models for filter blocking to account for deformation of the filter material and the cake layer due to the applied pressure that drives the fluid. These deformations change the permeability of the filter and the cake and hence the flow. We develop a new theory of compressible-cake filtration based on a simple poroelastic model in which we assume that the permeability depends linearly on local deformation. This assumption allows us to derive an explicit filtration law. The model predicts the possible shutdown of the filter when the imposed pressure difference is sufficiently large to reduce the permeability at some point to zero. The theory is applied to industrially relevant operating conditions, namely constant flux, maximising flux and constant pressure drop. Under these conditions, further analytical results are obtained, which yield predictions for optimal filter design with respect to given properties of the filter materials and the particles

The role of tortuosity in filtration efficiency: a general network model for filtration

Filters are composed of a complex network of interconnected pores each with tortuous paths. We present a general network model to describe a filter structure comprising a random network of interconnected pores, relaxing traditional assumptions made with simplified theoretical models. We use the model to examine the dependence of the filter performance on both its underlying pore structure (expressed through the pore interconnectivity and porosity gradient) and the feed composition (expressed through the size of the contaminants). We find that a simple scaling allows the performance curves over a wide range of the filter material properties to be mapped onto a single master curve. We also study the link between the tortuosity of a filter and its resulting performance, leading to further self-similarity observations. When we vary the properties of the feed, however, the performance curves are distinct from one another and do not collapse onto a single master curve. Our network model allows us to probe the behaviour of a complex and realistic filter configuration within a framework that is easy to implement and study, enabling accelerated testing and reducing experimental costs in filtration challenges