19,627 research outputs found
Homogenization approach to water transport in plant tissues with periodic microstructures
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
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
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
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
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Two-phase flow and oxygen transport in the perforated gas diffusion layer of proton exchange membrane fuel cell
Liquid water transport in perforated gas diffusion layers (GDLs)is numerically investigated using a three-dimensional (3D)two-phase volume of fluid (VOF)model and a stochastic reconstruction model of GDL microstructures. Different perforation depths and diameters are investigated, in comparison with the GDL without perforation. It is found that perforation can considerably reduce the liquid water level inside a GDL. The perforation diameter (D = 100 μm)and the depth (H = 100 μm)show pronounced effect. In addition, two different perforation locations, i.e. the GDL center and the liquid water break-through point, are investigated. Results show that the latter perforation location works more efficiently. Moreover, the perforation perimeter wettability is studied, and it is found that a hydrophilic region around the perforation further reduces the water saturation. Finally, the oxygen transport in the partially-saturated GDL is studied using an oxygen diffusion model. Results indicate that perforation reduces the oxygen diffusion resistance in GDLs and improves the oxygen concentration at the GDL bottom up to 101% (D = 100 μm and H = 100 μm)
Homogenization of the Poisson-Nernst-Planck Equations for Ion Transport in Charged Porous Media
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
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
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