Macroscopic Diffusion Model Research Articles

Capillary transport in paper porous materials at low saturation levels: normal, fast or superfast?

The problem of capillary transport in fibrous porous materials at low levels of liquid saturation has been addressed. It has been demonstrated that the process of liquid spreading in this type of porous material at low saturation can be described macroscopically by a similar super-fast, nonlinear diffusion model to that which had been previously identified in experiments and simulations in particulate porous media. The macroscopic diffusion model has been underpinned by simulations using a microscopic network model. The theoretical results have been qualitatively compared with available experimental observations within the witness card technique using persistent liquids. The long-term evolution of the wetting spots was found to be truly universal and fully in line with the mathematical model developed. The result has important repercussions for the witness card technique used in field measurements of the dissemination of various low-volatility agents in imposing severe restrictions on collection and measurement times.

Macroscopic and Мicroscopic Simulation of Processes of the Interaction of Water Vapor and Slit-like Pores

So-called slit-like pores are one of the types of pores often encountered in natural and artificial construction materials. The complexity of studying processes of the interaction between a gaseous substance, in particular, water vapor, and a slit-like pore is related to the complex relief of pore walls and the nonuniform distribution of the main thermodynamic characteristics of water vapor along the pore length. In this context, a combined approach to describing the processes of interaction between slit-like pores and water vapor is formulated in this paper. This approach is based on the joint use of macroscopic diffusion and molecular-dynamic models. If the complexity of the pore wall geometry is taken into account, equations of the macroscopic diffusion model can be solved numerically; to do this, a table of the spatial distribution of diffusion-coefficient values obtained using molecular dynamic simulation is applied. This approach makes it possible to obtain a more exact solution to the equations of the macroscopic diffusion model, and, accordingly, enhance the accuracy of simulation of the processes of interaction between a slit-like pore and water vapor.

Двумерное макроскопическое и микроскопическое моделирование процессов взаимодействия воды и пористых материалов

In various areas of science, technology, environment protection, construction, it is very important to study processes of porous materials interaction with different substances in different aggregation states. From the point of view of ecology and environmental protection it is particularly actual to investigate processes of porous materials interaction with water in liquid and gaseous phases. Since one mole of water contains $6,022140857\cdot 10^{23}$ molecules of $\mathtt{H_2O}$, macroscopic approaches considering the water vapor as continuum media in the framework of classical aerodynamics are mainly used to describe properties, for example properties of water vapor in the pore. In this paper we construct and use for simulation the macroscopic two-dimensional diffusion model describing the behavior of water vapor inside the isolated pore. Together with the macroscopic model it is proposed microscopic model of the behavior of water vapor inside the isolated pores. This microscopic model is built within the molecular dynamics approach. In the microscopic model a description of each water molecule motion is based on Newton classical mechanics considering interactions with other molecules and pore walls. Time evolution of water vapor - pore system is explored. Depending on the external to the pore conditions the system evolves to various states of equilibrium, characterized by different values of the macroscopic characteristics such as temperature, density, pressure. Comparisons of results of molecular dynamic simulations with the results of calculations based on the macroscopic diffusion model and experimental data allow to conclude that the combination of macroscopic and microscopic approach could produce more adequate and more accurate description of processes of water vapor interaction with porous materials.

Surface diffusion during shadow-mask-assisted molecular-beam epitaxy of III-V compounds

We present a comprehensive discussion of molecular-beam epitaxy of III-V compound semiconductors through shadow masks. Based on model calculations and growth experiments, we examine how the surface diffusion and the incorporation of group-III adatoms depend on the growth configuration, group-III and group-V fluxes, and the crystal orientation. According to a macroscopic diffusion model, gradients of the group-V flux drive the unidirectional migration of group-III adatoms. Although this effect is generally observed in the experiments, the different growth profiles obtained for [11¯0]- and [110]-oriented samples reflect the different roles of A-type and B-type steps in the incorporation of group-III adatoms. We also demonstrate that during the heteroepitaxial growth of InAs, the dissociation of the GaAs substrate is locally enhanced by the incidence of the In beam. This effect can be exploited for shadow-mask-assisted etching on selected areas. In addition, we show how the positions and sizes of III-V nanostructures can be controlled with high precision on a planar substrate by the usage of shadow masks with multiple nanoscale apertures.

Single-electron migration in nanostructured TiO 2

Electron migration in nanostructured anatase TiO 2 films is investigated with intensity-modulated photocurrent spectroscopy. Transport of electrons can be described with a macroscopic diffusion model. By fitting the data to this model it is possible to determine the absorption coefficient, the diffusion coefficient, and the lifetime of the electrons. Upon illumination, electrons accumulate in the nanostructured film. A fraction of these electrons is stored in deep surface states. Another fraction resides in the conduction band and is free to move. It is found that the average concentration of the excess conduction band electrons equals about one electron per nanoparticle, irrespective of the type of electrode, the film thickness, or the irradiation intensity. Equilibration of the quasi-Fermi level in combination with infinite fast extraction of electrons at the substrate explains this saturation effect.

The Nature of Electron Migration in Dye-Sensitized Nanostructured TiO2

The relationship between the morphology of nanostructured anatase TiO2 films and electron migration in these electrodes has been investigated. Toward this end, three different TiO2 powders have been studied, all of which have a unique microstructure. Photocurrent dynamics is used to elucidate electron transport in nanostructured TiO2 networks. In particular, intensity-modulated photocurrent spectroscopy proves to be a powerful characterization technique. In all cases the transport of electrons through a TiO2 network can be described with a macroscopic diffusion model. By fitting the data to this model it is possible to determine the absorption coefficient, the diffusion coefficient, and the lifetime of the electrons. Upon illumination, electrons accumulate in the nanostructured film. A fraction of these electrons are stored in deep surface traps. Another fraction of the electrons reside in the conduction band and are free to move. The average concentration of these excess mobile conduction band electrons amounts to one electron per nanoparticle, irrespective of the type of electrode, the film thickness, or the irradiation intensity. Equilibration of the quasi-Fermi level combined with infinite fast extraction of electrons at the substrate explains this saturation effect.

A Model of Near-Wall Conductivity and Its Application to Plasma Thrusters

We propose a macroscopic diffusion model to describe near-wall electron conduction in plasma thrusters. This model is obtained by a diffusion approximation technique from a collisionless electron-transport model in crossed electric and magnetic fields. It assumes that the transverse dimension of the thruster is small enough and that the scattering operator with the wall is randomizing. For isotropic scattering, analytic diffusion and conductivity coefficients are obtained, which are inversely proportional to the square of the magnetic field, as experimentally observed.

Rate theory models for ion transport through rigid: Pores. III. Continuum vs discrete models in single file diffusion

In studying the single file model in its discrete as well as in its continuum form the relationship between the phenomenological continuum theory of diffusion and the rate theory approach is analyzed. The single file model in its original form is discrete and represents the most general rate theory model for ion transport through rigid pores in biological membranes. In neglecting the interionic interactions which the single file model takes into account, the Nernst-Planck equation of macroscopic free diffusion can be derived from single file by means of the procedure n leads to infinity (where n is the number of binding sites within a pore) and the classical diffusion theory can thereby be integrated into the more general concept of single filing transport. Moreover, the single file model has been transformed in the limit n leads to infinity into the corresponding continuum form involving interionic interactions. The essential differences between the two derived continuum forms are: In the macroscopic diffusion model, the interionic interactions are regarded in the form of a "mean field". Thus we only get one equation of motion (Nernst-Planck equation) for the ionic concentration c(x, t) within the membrane. In the continuum version of the single file model, however, we obtain a hierarchy of Fokker-Planck equations for the probability density functions Pm(x1, . . . , xm, t) (where m is the number of ions within a pore). The interactions of the single file system are incorporated in detail into the Fokker-Planck equation as well as into the corresponding boundary conditions. As a consequence, the boundary conditions are highly complex in comparison with periodic conditions or Dirichlet conditions often used for the Nernst-Planck equation in electrophysiology. Two types of boundary conditions have been found which are principally different: The first one is to regulate the entry and exit of the ions at the pore mouth by a negative feedback mechanism, the second one describes the collisions of the ions within multiply occupied pores. In this context the question is discussed of whether the continuum version of single file has advantages over the discrete one.