Nucleation and growth dynamics of ellipsoidal crystals in metastable liquids

When describing the growth of crystal ensembles from metastable solutions or melts, a significant deviation from a spherical shape is often observed. Experimental data show that the shape of growing crystals can often be considered ellipsoidal. The new theoretical models describing the transient nucleation of ellipsoidal particles and their growth with and without fluctuating rates at the intermediate stage of bulk phase transitions in metastable systems are considered. The nonlinear transport (diffusivity) of ellipsoidal crystals in the space of their volumes is taken into account in the Fokker–Planck equation allowing for fluctuating growth rates. The complete analytical solutions of integro-differential models of kinetic and balance equations are found and analysed. Our solutions show that the desupercooling dynamics is several times faster for ellipsoidal crystals as compared to spherical particles. In addition, the crystal-volume distribution function is lower and shifted to larger particle volumes when considering the growth of ellipsoidal crystals. What is more, this function is monotonically increasing to the maximum crystal size in the absence of fluctuations and is a bell-shaped curve when such fluctuations are taken into account. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

Measuring the surface diffusivity of argon in nanoporous carbon

Gas diffusion in porous media consists of surface hopping and non-surface ballistic/bulk diffusion. Unfortunately, only the overall diffusivity is usually measured, without being separated into various diffusion modes. Here we used the “gravitation method” for measuring transport diffusivity, and utilized a detailed trajectory analysis to calculate the surface diffusivity and non-surface diffusivity.

Investigation of Membrane Fouling along Membrane Surface during Cross-Flow Micro-Filtration of Semiconductor Wastewater

Simulation method was applied to study the fouling behavior during the Micro-filtration of Semi-conductor wastewater. In the numerical model, concentration dependent physical properties such as suspension viscosity, density and generalized particle transport diffusivity were considered. The mechanism of suspension transition from liquid phase to gel phase was adopted to characterize the formation of membrane fouling. Fouling resistance distribution along the membrane surface was obtained from the simulation. The results revealed the mass transfer character in the concentration boundary layer and its influence on the formation of membrane fouling. Agreement between the simulation and the experiment results demonstrated the applicability of this numerical method in evaluating membrane fouling during Micro-filtration.

Transport diffusivity of propane and propylene inside SWNTs from equilibrium molecular dynamics simulations

Direct determination of transport diffusivity of alkane–alkene in SWNTs is realized through equilibrium molecular dynamics simulations.

Continuum/Nano-Scale Simulation of Surface Diffusion Process in Flow

Fluid transport with diffusion through micro-/nano-channels is found in many natural phenomena and industrial processes, including fluid transport or diffusion through nano-materials, molecular/atomistic transfer across nuclear pores or in the MEMS devices among other applications. Those nano-pores can be treated as nano-channels in the thin layers of the membranes. The transport phenomena of fluid in such small confined channels, usually in the size of ten molecular diameters or less, differs significantly from its bulk behaviors and cannot be described with continuum theory. In this case, molecular dynamics (MD) simulation, rather than continuum methods, is better suited to study the phenomena. The surface diffusion, related to both the fluid and solid material properties and the flow rate, can be used as a parameter for estimating the adsorbing capacity of a porous nano-material. The transport of fluids through porous materials occurs mainly by diffusion. In this study, a molecular-continuum hybrid scheme is used for the study of the diffusion in a representative Couette flow problem. By varying the velocity of the moving-solid wall, we investigated the effect of the shearing condition on the mass flux going through the pores. The relationship of the physical mechanisms and the transport phenomena (e.g. Fick’s law) were then linked among the different length scales. Activated carbon with its high surface area has been emerging as a promising candidate for an adsorbent due to not only its stable thermodynamic and mechanical properties but also its homogenous and isotropic porous distribution and relatively even pore size. In this study, we focus on the characteristics of the permeation and the adsorption process between different gases and the carbon substrate under various shearing conditions. The investigation of the diffusion process of fluids through the pores of the nano-materials has become an interesting topic in recent decades. This investigation has been divided into two major areas: 1) the diffusivity estimation and 2) the transient diffusion rate. We apply a continuum/MD hybrid scheme to a model problem of various gases transport through a carbon substrate with several pores in a channel flow under different shear rates. Instead of inserting and deleting particles from the control volumes used in the DCV-GCMD method, we keep the number of particles in the simulation system constant. The interactions between fluid/fluid, fluid/solid and solid/solid are all assumed to be under Lennard-Jones potentials. In the modeled Couette flow, the two solid walls are constructed with nano-pores that allow fluids to go through the substrate to study the transient diffusion rate (flux). Before simulating the fluid transport through the nano-pores, we need to validate the natural diffusion properties of the bulk fluid. To do this, a system (as a cube) consisting of pure liquid argon molecules is used to perform the pure MD simulation. The radial distribution function (RDF) is used as the parameter to verify the natural diffusion of the liquid argon fluid in the bulk flow, which is a structural correlation. It describes the spherically averaged local organization around any given molecule. Figure 1 shows a good comparison of the radial distribution functions between the MD prediction and the experimental measurement of Eisenstein and Gingrich (1942). By comparing our calculation to Wu et al. (2008) under similar circumstances, we found that the average (from 8 pores) and corrected mass flux J · (RTh) is linearly proportional to the average pressure gradient along the pore. And the slope of this relationship is the transport diffusivity, which is 4.6 × 10−7m2/s under 273K and 4.9 × 10−7m2/s under 300K. This indicates that the current simulation follows the Fick’s law exactly. Similarly, for other gases, the same linear relationships can also be obtained. These calculations are listed in Table 1 that shows the transport diffusivity increases with temperature. The mass fluxes of three gases at various pore widths are calculated as shown in Fig. 2. Generally, with larger pores, the mass fluxes increase. However, among three gases, the increase of H2 is much faster than the other two gases because of hydrogen’s smaller molecular size. In another word, smaller molecules as H2 have faster diffusion rates during the adsorption process.