19,627 research outputs found

    Homogenization approach to water transport in plant tissues with periodic microstructures

    Full text link
    Water flow in plant tissues takes place in two different physical domains separated by semipermeable membranes: cell insides and cell walls. The assembly of all cell insides and cell walls are termed symplast and apoplast, respectively. Water transport is pressure driven in both, where osmosis plays an essential role in membrane crossing. In this paper, a microscopic model of water flow and transport of an osmotically active solute in a plant tissue is considered. The model is posed on the scale of a single cell and the tissue is assumed to be composed of periodically distributed cells. The flow in the symplast can be regarded as a viscous Stokes flow, while Darcy's law applies in the porous apoplast. Transmission conditions at the interface (semipermeable membrane) are obtained by balancing the mass fluxes through the interface and by describing the protein mediated transport as a surface reaction. Applying homogenization techniques, macroscopic equations for water and solute transport in a plant tissue are derived. The macroscopic problem is given by a Darcy law with a force term proportional to the difference in concentrations of the osmotically active solute in the symplast and apoplast; i.e. the flow is also driven by the local concentration difference and its direction can be different than the one prescribed by the pressure gradient.Comment: 31 page

    Numerical simulation of the dynamics of molecular markers involved in cell polarisation

    Get PDF
    A cell is polarised when it has developed a main axis of organisation through the reorganisation of its cytosqueleton and its intracellular organelles. Polarisation can occur spontaneously or be triggered by external signals, like gradients of signaling molecules ... In this work, we study mathematical models for cell polarisation. These models are based on nonlinear convection-diffusion equations. The nonlinearity in the transport term expresses the positive loop between the level of protein concentration localised in a small area of the cell membrane and the number of new proteins that will be convected to the same area. We perform numerical simulations and we illustrate that these models are rich enough to describe the apparition of a polarisome.Comment: 15 page

    The role of the microvascular network structure on diffusion and consumption of anticancer drugs

    Get PDF
    We investigate the impact of microvascular geometry on the transport of drugs in solid tumors, focusing on the diffusion and consumption phenomena. We embrace recent advances in the asymptotic homogenization literature starting from a double Darcy—double advection-diffusion-reaction system of partial differential equations that is obtained exploiting the sharp length separation between the intercapillary distance and the average tumor size. The geometric information on the microvascular network is encoded into effective hydraulic conductivities and diffusivities, which are numerically computed by solving periodic cell problems on appropriate microscale representative cells. The coefficients are then injected into the macroscale equations, and these are solved for an isolated, vascularized spherical tumor. We consider the effect of vascular tortuosity on the transport of anticancer molecules, focusing on Vinblastine and Doxorubicin dynamics, which are considered as a tracer and as a highly interacting molecule, respectively. The computational model is able to quantify the treatment performance through the analysis of the interstitial drug concentration and the quantity of drug metabolized in the tumor. Our results show that both drug advection and diffusion are dramatically impaired by increasing geometrical complexity of the microvasculature, leading to nonoptimal absorption and delivery of therapeutic agents. However, this effect apparently has a minor role whenever the dynamics are mostly driven by metabolic reactions in the tumor interstitium, eg, for highly interacting molecules. In the latter case, anticancer therapies that aim at regularizing the microvasculature might not play a major role, and different strategies are to be developed

    Modeling Fixed Bed Membrane Reactors for Hydrogen Production through Steam Reforming Reactions: A Critical Analysis

    Get PDF
    Membrane reactors for hydrogen production have been extensively studied in the past years due to the interest in developing systems that are adequate for the decentralized production of high-purity hydrogen. Research in this field has been both experimental and theoretical. The aim of this work is two-fold. On the one hand, modeling work on membrane reactors that has been carried out in the past is presented and discussed, along with the constitutive equations used to describe the different phenomena characterizing the behavior of the system. On the other hand, an attempt is made to shed some light on the meaning and usefulness of models developed with different degrees of complexity. The motivation has been that, given the different ways and degrees in which transport models can be simplified, the process is not always straightforward and, in some cases, leads to conceptual inconsistencies that are not easily identifiable or identified

    Homogenization of the Poisson-Nernst-Planck Equations for Ion Transport in Charged Porous Media

    Get PDF
    Effective Poisson-Nernst-Planck (PNP) equations are derived for macroscopic ion transport in charged porous media under periodic fluid flow by an asymptotic multi-scale expansion with drift. The microscopic setting is a two-component periodic composite consisting of a dilute electrolyte continuum (described by standard PNP equations) and a continuous dielectric matrix, which is impermeable to the ions and carries a given surface charge. Four new features arise in the upscaled equations: (i) the effective ionic diffusivities and mobilities become tensors, related to the microstructure; (ii) the effective permittivity is also a tensor, depending on the electrolyte/matrix permittivity ratio and the ratio of the Debye screening length to the macroscopic length of the porous medium; (iii) the microscopic fluidic convection is replaced by a diffusion-dispersion correction in the effective diffusion tensor; and (iv) the surface charge per volume appears as a continuous "background charge density", as in classical membrane models. The coefficient tensors in the upscaled PNP equations can be calculated from periodic reference cell problems. For an insulating solid matrix, all gradients are corrected by the same tensor, and the Einstein relation holds at the macroscopic scale, which is not generally the case for a polarizable matrix, unless the permittivity and electric field are suitably defined. In the limit of thin double layers, Poisson's equation is replaced by macroscopic electroneutrality (balancing ionic and surface charges). The general form of the macroscopic PNP equations may also hold for concentrated solution theories, based on the local-density and mean-field approximations. These results have broad applicability to ion transport in porous electrodes, separators, membranes, ion-exchange resins, soils, porous rocks, and biological tissues

    Adhesion and detachment fluxes of micro-particles from a permeable wall under turbulent flow conditions

    Get PDF
    We report a numerical investigation of the deposition and re-entrainment of Brownian particles from a permeable plane wall. The tangential flow was turbulent. The suspension dynamics were obtained through direct numerical simulation of the Navier–Stokes equations coupled to the Lagrangian tracking of individual particles. Physical phenomena acting on the particles such as flow transport, adhesion, detachment and re-entrainment were considered. Brownian diffusion was accounted for in the trajectory computations by a stochastic model specifically adapted for use in the vicinity of the wall. Interactions between the particles and the wall such as adhesion forces and detachment were modeled. Validations of analytical solutions for simplified cases and comparisons with theoretical predictions are presented as well. Results are discussed focusing on the interplay between the distinct mechanisms occurring in the fouling of filtration devices. Particulate fluxes towards and away from the permeable wall are analyzed under different adhesion strengths
    corecore