Numerical Simulation Of Mass Transport Research Articles

Generation of Multiple Concentration Gradients Using a Two-Dimensional Pyramid Array.

Concentration heterogeneity of diffusible reactants is a prevalent phenomenon in biochemical processes, requiring the generation of concentration gradients for the relevant experiments. In this study, we present a high-density pyramid array microfluidic network for the effective and precise generation of multiple concentration gradients. The complex gradient distribution in the 2D array can be adaptively adjusted by modulating the reactant velocities and concentrations at the inlets. In addition, the unique design of each reaction chamber and mixing block in the array ensures uniform concentrations within each chamber during dynamic changes, enabling large-scale reactions with low reactant volumes. Through detailed numerical simulation of mass transport within the complex microchannel networks, the proposed method allows researchers to determine the desired number of reaction chambers within a given concentration range based on experimental requirements and to quickly obtain the operating conditions with the help of machine learning-based prediction. The effectiveness in generating a multiple concentration gradient environment was further demonstrated by concentration-dependent calcium carbonate crystallization experiments. This device provides a highly efficient mixing and adaptable concentration platform that is well suited for high-throughput and multiplexed reactions.

A Numerical Simulation of Mass Transport in Deep Convection over the Tibet Plateau

By using the WRF-Chem model to simulate a deep convection process that occurred in the eastern part of the Tibetan Plateau, the vertical transport process and main mechanisms of water and ozone in the upper troposphere-lower stratosphere were studied. The air in the lower layer of the troposphere, which is rich in water vapor and low ozone concentration, is transported near the top of the troposphere. The enhancement of convective motion causes the height of the troposphere to rise and the temperature to decrease. Therefore, water vapor is prone to condensation and dehydration, and ice crystals are formed near the top of the troposphere, resulting in a low value zone of water vapor at 100 hPa. By analyzing the distribution of ozone, it is found that there is a high concentration of ozone transported on both sides of the deep convection area. The stronger the convection, the stronger the downward transport. It further explains that this deep convection process not only causes the upward transport of tropospheric air in the deep convection area, but also causes the transport of stratospheric air to the troposphere on both sides of the deep convection area.

A Semi-Continuum Model for Numerical Simulations of Mass Transport in 3-D Fractured Rock Masses

Natural discontinuities are the major concern when considering mass transport in engineered barrier systems and their host rocks. Numerical simulations of highly fractured geological formations are limited because of the contradiction between results accuracy and computational costs. To alleviate such a contradiction, this study proposes an improved fracture continuum method to simulate the radioactive spreading in a complex 3-D fracture system. With Boolean operations and the unified pipe-network method, discontinuities are mapped on structured subdomains and standardized to equivalent paths. Moreover, adaptive mesh refinement is utilized to ease the complexity further. We verify the accuracy of this method in two metric cases, and results show that perfect agreement is achieved with analytical solutions. This method demonstrates its applicability to the simulation of a nuclear leak in a repository for high-level radioactive waste. Effects of the maximum refinement level are discussed. For a room-scale problem, flow rates and mass fluxes on boundary surface converge to stable values when the maximum refinement level is larger than 4. An extensive case with complex fracture networks is modeled and compared with the conventional finite-difference method. The proposed method is capable of conducting robust results with significantly lower computational complexity and negligible errors by avoiding ill-conditioned mesh elements.

PORE SIZE DISTRIBUTION IN SIMULATION OF MASS TRANSPORT IN POROUS MEDIA: A CASE STUDY IN RESERVOIR ANALYSIS

The modeling and numerical simulation of mass transport in porous media is discussed in this work by using the so-called pore size distribution for computing transport properties. The pore-size distribution is a property of the pore structure of a porous medium. This can be used to estimate the different transport properties, amongst other, the permeability. By starting with a formula for the absolute permeability, the simulation of water and oil transport in reservoirs is considered by solving mass conservation equations with the help of the control volume method. The influence of the pore size distribution on the transport behavior is discussed to demonstrate the adequacy of the use of pore size distribution in studying the behavior of reservoirs.

Hydrogel films and coatings by swelling-induced gelation

Hydrogel films used as membranes or coatings are essential components of devices interfaced with biological systems. Their design is greatly challenged by the need to find mild synthesis and processing conditions that preserve their biocompatibility and the integrity of encapsulated compounds. Here, we report an approach to produce hydrogel films spontaneously in aqueous polymer solutions. This method uses the solvent depletion created at the surface of swelling polymer substrates to induce the gelation of a thin layer of polymer solution. Using a biocompatible polymer that self-assembles at high concentration [poly(vinyl alcohol)], hydrogel films were produced within minutes to hours with thicknesses ranging from tens to hundreds of micrometers. A simple model and numerical simulations of mass transport during swelling capture the experiments and predict how film growth depends on the solution composition, substrate geometry, and swelling properties. The versatility of the approach was verified with a variety of swelling substrates and hydrogel-forming solutions. We also demonstrate the potential of this technique by incorporating other solutes such as inorganic particles to fabricate ceramic-hydrogel coatings for bone anchoring and cells to fabricate cell-laden membranes for cell culture or tissue engineering.

(Invited) Numerical Simulations of Mass Transport Using Separation of Variables: an Old Method Rejuvenated with Symbolic Algebra Software

Separation of variables is a classic method of solving partial differential equations, such as the convective diffusion equations that are ubiquitous in electrochemistry. It leads to infinite series solutions, which are exact analytical solutions. However, various parameters involved in the series have to be numerically evaluated, and the series converge rather slowly, which has meant that this method has not been used for practical numerical calculations of concentration profiles for electrochemical problems. We show here that these difficulties can be overcome, and demonstrate the use of the symbolic algebra program Maple in a practical implementation of this for steady-state convective diffusion past electrodes in a 2-D channel [1]. The key to successful implementation has been the use of asymptotic formulas to reliably locate the eigenvalues, so that the numerical solver does not miss any. The method has the following advantages: 1. It is a mesh-free method, so a separate step of validating the mesh or grid is not necessary. 2. The global error can be estimated by evaluating the series to more terms. 3. Each segment (above an electrode or insulating section) is solved at once, so changing the length of an electrode does not change the difficulty of the calculation. 4. Workup of the concentrations to derived quantities such as currents or collection efficiencies can be done without any degradation of accuracy. The present implementation assumes diffusivities of reactant and product are equal, which allows the generation of both concentration profiles in a single calculation by using a recently developed transformation method [2]. It also neglects axial diffusion. Future work will seek to remove these limitations, and extend the results to 3-D and time-dependent systems.

Laboratory experiments on mass transport by large amplitude mode-2 internal solitary waves

The existence of internal solitary waves (ISWs) in the coastal ocean is well established. Numerous observations of large amplitude (both mode-1 and mode-2) solitary waves have facilitated the identification of their unique properties; in particular they contain regions of internal recirculation (trapped cores) that enable mass transport over large distances. However, the basic physics of mode-2 ISWs is as yet not well understood. The present experiments and the associated numerical simulations are focused on providing the first quantitative measure of the extent of mass transported by mode-2 ISWs and insight into the potential effects of mass transport on coastal mixing and the distribution of biochemical material. The ISWs were generated by the release of fluid from an initially mixed volume. It was found that the amplitude and amount of mass transported by the leading and second, following ISW, was proportional to the level of forcing and was attenuated at an approximately uniform rate as the ISW propagated downstream. At the highest level of ISW forcing, over 40% of the mixed fluid was transported within the leading ISW. Excellent agreement was found with the numerical simulations of Salloum, Knio, and Brandt [“Numerical simulation of mass transport in internal solitary waves,” Phys. Fluids 24, 016602 (2012)] that were designed to replicate the present experimental configuration. In addition, evidence of a new ISW regime was identified, termed very-large amplitude ISW, which exhibited strong internal recirculation, a smooth front face, and local mixing at the aft end. The present data extend to larger amplitudes than prior studies and exhibit a second order dependence of wave speed and wavelength on amplitude.

Numerical simulation of mass transport in a filter press type electrochemical reactor FM01-LC: Comparison of predicted and experimental mass transfer coefficient

This paper studies flow characteristics and their effect on local mass transfer rate to a flat plate electrode in a FM01-LC electrochemical reactor. 3D reactor simulations under limiting current and turbulent flow conditions were performed using potassium ferro-ferricyanide electrochemical system with sodium sulfate as supporting electrolyte. The model consists of mass-transport equations coupled to hydrodynamic solution obtained from Reynolds-averaged Navier–Stokes equations using standard k–ɛ turbulence model, where the average velocity field, the turbulence level given by the eddy kinetic energy and the turbulent viscosity of the hydrodynamic calculation were used to evaluate the convection, turbulent diffusion and the concentration wall function. The turbulent mass diffusivity was evaluated by Kays–Crawford equation using heat and mass transfer analogies, while wall functions, for mass transport, were adapted from Launder–Spalding equations. Simulation results describe main flow properties, concentration profiles throughout the entire volume of the reactor and local diffusion flux over the electrode. Overall mass transfer coefficients estimated by simulation, without fitting parameters, agree closely with experimental coefficients determined from limiting current measurements (1.85% average error) for Re between 187 and 1407.

Numerical simulation of mass transport in internal solitary waves

A computational study of mass transport by large-amplitude, mode-2 internal solitary waves propagating on a pycnocline between two layers of different densities was conducted. The numerical model is based on the simulation of a vorticity-based formulation of the two-dimensional Navier-Stokes equations in the Boussinesq limit. Numerical experiments are conducted of the collapse of an initially mixed region, which leads to the generation of a train of internal solitary waves. The peak wave amplitude, a, is achieved by the leading wave, which encloses an intrusional bulge. The wave amplitude decays as it moves away from the collapsing mixing region. When the amplitude drops below a critical value, the wave is no longer able to transport mass and sharp-nosed intrusion is left behind. Mass transport by the leading wave, and by the trailing wave train and intrusion, is analyzed by tracking the motion of Lagrangian particles initially concentrated in the mixed region. Results indicate that for moderate wave amplitudes, a gradual decay in the wave amplitude occurs as the wave propagates, but the structure of the bulge is essentially maintained during this process. In contrast, for large-amplitude waves, the motion around the bulge is substantially more complex, exhibiting periodic shedding of vortex structures in the wake of the bulge and entrainment of external fluid into its core. It is shown that these motions have substantial impact on mass transport by the wave train, which is quantified through detailed analysis of the Lagrangian particle distributions.

Adaptive finite elements with large aspect ratio for mass transport in electroosmosis and pressure‐driven microflows

AbstractA space–time adaptive method is presented for the numerical simulation of mass transport in electroosmotic and pressure‐driven microflows in two space dimensions. The method uses finite elements with large aspect ratio, which allows the electroosmotic flow and the mass transport to be solved accurately despite the presence of strong boundary layers. The unknowns are the external electric potential, the electrical double layer potential, the velocity field and the sample concentration. Continuous piecewise linear stabilized finite elements with large aspect ratio and the Crank–Nicolson scheme are used for the space and time discretization of the concentration equation. Numerical results are presented showing the efficiency of this approach, first in a straight channel, then in crossing and multiple T‐form configuration channels. Copyright © 2009 John Wiley & Sons, Ltd.

Numerical Simulation of Mass Transport in a Microchannel Bioreactor With Cell Micropatterning

Micropatterning of two different cell types based on surface modification allows spatial control over two distinct cell subpopulations. This study considers a micropatterned coculture system, which has release and absorption parts alternately arranged at the base, and each part has a single cell type. A micropattern unit was defined and within each unit, there are one release part and one absorption part. The cells in the absorption parts consume species, which are secreted by the cells in the release parts. The species concentrations at the micropatterned cell base were computed from a three-dimensional numerical flow model incorporating mass transport. Different combined parameters were developed for the release and absorption parts to make the data collapse in each part. Combination of the collapse data in the release and absorption parts can be used to predict the concentration distribution through the whole channel. The correlated results were applied to predict the critical length ratio of the release and absorption parts for an actual micropatterned system (Bhatia et al., 1999, "Effect of Cell-Cell Interactions in Preservation of Cellular Phenotype: Co-Cultivation of Hepatocytes and Nonparenchymal Cell," FASEB J. 13, pp. 1883-1900) to avoid species insufficiency based on basic fibroblast growth factor (bFGF). The mass transfer effectiveness was found to be higher with more numbers of micropattern units. The optimal condition for micropatterned coculture bioreactors is achieved by having the product of the length ratio and the reaction ratio equal to 1. This condition was used to optimize the mass transfer in the micropatterned system (Bhatia et al., 1999, "Effect of Cell-Cell Interactions in Preservation of Cellular henotype: Co-Cultivation of Hepatocytes and Nonparenchymal Cell," FASEB J. 13, pp. 1883-1900) based on bFGF.

The role of under-rib convection in mass transport of methanol through the serpentine flow field and its neighboring porous layer in a DMFC

Numerical simulation of a direct methanol fuel cell (DMFC) operating under discharging conditions is challenged by the difficulties in modeling of complicated liquid–gas two-phase flows and coupled electrochemical kinetics. Under open-circuit conditions, the net electrochemical reactions in the DMFC anode cease, but, owing to the methanol concentration difference between the anode and cathode, the mass transport of methanol remains, creating a mass transport process of methanol in a single-phase liquid flow with no electrochemical reactions in the DMFC anode. Consequently, an accurate simulation of mass transport of methanol under such open-circuit conditions becomes possible. In this work, we performed a 3D numerical simulation of mass transport of methanol in the DMFC anode under open-circuit conditions and obtained the mass flux of methanol through the porous layer for different values of permeability. We also measured the mass flux of methanol permeation from the anode flow field to the cathode under open-circuit conditions. The comparison between the numerical and measured mass flux of methanol made it possible to in situ determine the permeability of the typical commercial porous layer. Using this in situ determined permeability, we then investigated numerically the effect of methanol feed rates on mass transport and found that the in-plane under-rib convection plays an important role, even at low methanol feed rate, to make the reactant evenly distributed over the entire catalyst layer.