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Surface roughness exists in most microfluidic devices due to the microfabrication technique or particle adhesion. The present study has developed a numerical model based on Finite Volume Method to simulate the fluid flow and mass transfer in a flat-plate microchannel bioreactor with an array of rough elements uniformly placed on the bottom wall. Both semicircle and triangle roughness are considered to include more shapes of roughness elements. A monolayer of cells is assumed to attach to the base of the channels and consumes species from culture medium. The results show that the roughness size ratio (α) and the roughness distribution ratio (β) have direct and significant effects on fluid flow and mass transfer. The dimensionless parameters Peclet number (Pe) and Damkohler number (Da) can also influence mass transfer greatly. Although the two types of roughness have similar effects, at the same condition, the triangle roughness has larger effect on shear stress by showing higher dimensionless values at the channel base; the semicircle roughness has larger effect on mass transfer by showing lower dimensionless minimum base concentration and higher dimensionless absorption rate (Δj%). However, it is important to ensure the lower maximum shear stress and the adequate minimum species concentration for cell growth in rough channels. Hence, if the maximum shear stress and minimum concentration in rough channels can satisfy the critical conditions for cell growth, rough channels would be better than smooth channels because of their lower shear stress at the flat-bed part and higher mass transfer efficiency. The results would provide guidance on the flow and perfusion requirements to avoid shear stress damage and solute depletion or toxicity during cell culture.

This paper presents an analytical solution for transient natural convection heat and mass transfer flow in a vertical channel with Soret and Dufour effects. Due to the presence of these two effects, energy and concentration equations are coupled. The dimensionless governing equations for momentum, energy and concentration are first decoupled using perturbation method and then solved using Laplace Transform Technique (LTT) under relevant initial and boundary conditions. The expressions for temperature, concentration, velocity, rate of heat transfer, rate of mass transfer and skin-friction are obtained. Numerical solutions are also obtained using pdepe in MATLAB so as to validate the accuracy of the proposed analytical method. The effects of Soret parameter, Dufour parameter, Grashof number, modified Grashof number, Prandtl number, Schmidt number and dimensionless time are presented graphically and discussed. It is observed that the temperature and velocity increase with increase in Dufour number, while concentration decreases with increase of Dufour number. The Dufour effect is more significant on the temperature and velocity in comparison to concentration. Moreover, it is observed that the concentration and velocity increase with increase in Soret number while the impact of Soret number is just contrast on temperature variation.

Convective heat and mass transport of radiative Williamson hybrid $(\mathrm{\text{SWCNT}}+\mathrm{\text{MWCNT}})$ nanofluid (NF) by a Riga surface with the novel features of Cattaneo–Christov double-diffusion has been investigated. Thermal contributions of internal heat mechanism and Arrhenius energy in Darcy–Forchheimer medium have also been incorporated in the modeling. Mathematical modeling has been completed by using suitable mathematical expressions for thermophysical features of hybrid nanofluid (HNF). Transport partial differential equations (PDEs) have been transformed into ordinary differential equations (ODEs) by means of similarity variables. Numerical approximation of the transformed system has been obtained by using shooting-based Runge–Kutta–Fehlberg approach. Results have been presented through various graphs and discussed physically in detail. Solution is validated for limited cases. Concentration of the hybrid mixture is reduced for progressive concentration-relaxation parameter. Temperature is alleviated for developing thermal-relaxation parameter. Nusselt number is observed to be higher for Williamson HNF than simple ordinary NF.

In this research work, we proposed a modern structured packing (SP) with perforated sheets with a specific surface area of 860${\mathrm{\text{m}}}^2$/${\mathrm{\text{m}}}^3$, which was determined using numerical techniques. This work aims to evaluate the major characteristics of PACK-860 for instance, height equivalent to a theoretical plate (HETP), dry pressure drop (DPD) and wet pressure drop (WPD). Additionally, the flow construction was defined for specific packing via computational simulation. To evaluate the value of HETP, DPD and WPD, the three-dimensional (3D) computational fluid dynamics (CFD) simulation with the Eulerian–Eulerian (EE) multi-phase method applied in this paper. According to the findings of this research, the performance of the mass transfer (MT), WPD and DPD was enhanced with the perforated-on sheets of packing. Based on the observation, numerical results are consistent well with the theoretical data which reveals the consistency of CFD tools for modeling methods to separation applications.

This study recommends a novel structured packing (SP) PACK-860X with a specific surface area of 860m²/m³, which is defined utilizing a numerical method. We attempt to investigate the main properties of PACK-860X for illustration, height equal to a theoretical plate (HETP), dry pressure drop (DPD) and wet pressure drop (WPD). In addition, the flow pattern is expressed for packing through computational simulation. To assess the amounts of HETP, WPD and DPD, the 3D CFD simulation with the Eulerian–Eulerian multi-phase technique is employed in this work. Based on the results of this work, WPD and DPD are improved. According to the data, numerical outcomes are in good agreement with the theoretical results, which shows the reliability of CFD methods for modeling the separation processes.

Hydrided Mg-3Ni-2MnO₂ composite powders were prepared by mechanical milling under hydrogen atmosphere. Heat and mass transfer, the effective thermal conductivity (ETC) of the hydrided Mg-3Ni-2MnO₂ powder reaction bed with various porosities were measured using a self-made apparatus. The effect of porosity on the bed is also analysized. The results show that the ETC of reaction bed is poor and it increases with decreasing porosity. Three porosities, 0.37, 0.53, 0.63 were selected in the present work. The bed with 0.53 porosity exhibits relatively fast reaction rates in both hydrogenation and dehydrogenation process. The hydrogenation process is a fast exothermic reaction resulting in a quick increase if the temperature of the bed during this process, and there is a temperature gradient: the temperature close to the bed wall is lower but higher at the center of bed. In dehydrogenation of the bed, the temperature of hydrided bed decreases due to the endothermic reaction, and the temperature at the center falls the lowest and keep at that temperature for a long time. The analyses reveal that increase of ETC don't always helps to improve the bed's hydriding and dehydriding rates. There should be an optimal porosity which helps to transfer both the heat and the mass.

This paper looks at the mass transfer effects on the unsteady two-dimensional and magnetohydrodynamic flow of an upper-convected Maxwell fluid bounded by a stretching surface. Homotopy analysis method is used for the development of series solution of the arising nonlinear problem. Plots of velocity and concentration fields are displayed and discussed. The values of surface mass transfer and gradient of mass transfer are also tabulated.

This study focuses on the numerical observation of the convective motion of chemically active magnetohydrodynamic (MHD) fluid through a vertically oriented permeable medium, incorporating variations in mass and heat transfer. The fluid type is assumed to be incompressible, chemically strongly ionized and viscous with some mass infusibility. The model associated with this problem is solved by a highly stable Implicit Finite Difference Method (IFDM). The method is used for small and large deflection of the physical parameters, which results in a noticeable fluid flow behavior. Numerical configuration is graphically depicted to scrutinize the fluid behavior. The momentum, energy, concentration diffusion, skin friction, Nusselt number and Sherwood number are investigated for numerous factors such as magnetic field, permeability and chemical reaction rate. The current study unveils significant findings, demonstrating that a heightened rate of chemical reaction in the presence of magnetic effects, coupled with specific porosity, diminishes ionization energy, resulting in a concurrent decrease in the concentration and momentum profiles of the fluid flow. The rise in the viscous diffusion rate is attributed to escalating values of the Schmidt number, causing an augmentation in dynamic viscosity and consequently resulting in an overall reduction in the momentum of the fluid flow.

The present work shows that vortex breakdown may also occur in a bioreactor for animal cell or tissue culture. The aim is to study the effect of vortex breakdown on the fluid environment for cell growth, particularly hydrodynamic stress and mass transfer. A numerical simulation of the fluid flow and oxygen transfer in a cylindrical bioreactor is presented, in which a rotating base wall is used to generate the medium flow and mixing. The steady and laminar, axisymmetric Navier-Stokes and species equations are solved by the numerical model based on finite volume method. The hydrodynamic stress and oxygen transfer conditions are systematically studied by varying the two key parameters which determine the flow behavior: bioreactor aspect ratio H/R and a rotation Reynolds number Re=ΩR²/ν. It is found that the oxygen concentration at the attached breakdown vortex center is significantly higher than that at the main recirculation center but the hydrodynamic stress level is almost similar in the two regions. The results would provide guidance on choosing the proper operating parameters for cell or tissue culture.

Surface roughness exists in most microfluidic devices due to the microfabrication technique or particle adhesion. In this study, a numerical model based on Finite Volume Method has been developed to simulate the mass transfer in a flat-plate microchannel bioreactor with semi-circular protrusions uniformly distributed on the bottom. The results show that the mass transfer in rough channel is enhanced, as shown by lower minimum species concentration in the rough channel compared with that in smooth channel. Non-dimensional parameters such as Peclet number (Pe), Damkohler number (Da) and the roughness size ratio (β) can influence the effect of roughness greatly. However, it is important to ensure that the minimum species concentration in the rough channel is adequate for cell growth. The results would provide guidance on the perfusion requirements to avoid solute depletion or toxicity during cell culture.

Increasingly sophisticated techniques are being developed for the manufacture of functional nanomaterials. A growing interest is also developing in magnetic nanofluid coatings which contain magnetite nanoparticles suspended in a base fluid and are responsive to external magnetic fields. These nanomaterials are “smart” and their synthesis features high-temperature environments in which radiative heat transfer is present. Diffusion processes in the extruded nanomaterial sheet also feature Soret and Dufour (cross) diffusion effects. Filtration media are also utilized to control the heat, mass and momentum characteristics of extruded nanomaterials and porous media impedance effects arise. Magnetite nanofluids have also been shown to exhibit hydrodynamic wall slip which can arise due to non-adherence of the nanofluid to the boundary. Motivated by the multi-physical nature of magnetic nanomaterial manufacturing transport phenomena, in this paper, we develop a mathematical model to analyze the collective influence of hydrodynamic slip, radiative heat flux and cross-diffusion effects on transport phenomena in ferric oxide (${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$-water) magnetic nanofluid flow from a nonlinear stretching porous sheet in porous media. Hydrodynamic slip is included. Porous media drag is simulated with the Darcy model. Viscous magnetohydrodynamic theory is used to simulate Lorentzian magnetic drag effects. The Rosseland diffusion flux model is employed for thermal radiative effects. A set of appropriate similarity transformation variables are deployed to convert the original partial differential boundary value problem into an ordinary differential boundary value problem. The numerical solution of the coupled, multi-degree, nonlinear problem is achieved with an efficient shooting technique in MATLAB symbolic software. The physical influences of Hartmann (magnetic) number, Prandtl number, Richardson number, Soret (thermo-diffusive) number, permeability parameter, concentration buoyancy ratio, radiation parameter, Dufour (diffuso-thermal) parameter, momentum slip parameter and Schmidt number on transport characteristics (e.g. velocity, nanoparticle concentration and temperature profiles) are investigated, visualized and presented graphically. Flow deceleration is induced with increasing Hartmann number and wall slip, whereas flow acceleration is generated with greater Richardson number and buoyancy ratio parameter. Temperatures are elevated with increasing Dufour number and radiative parameter. Concentration magnitudes are enhanced with Soret number, whereas they are depleted with greater Schmidt number. Validation of the MATLAB computations with special cases of the general model is included. Further validation with generalized differential quadrature (GDQ) is also included.

We introduce and analyze a model for simulating the release of a drug from a polymeric matrix into the arterial tissue, with the aim to describe the phenomena that occur after the implantation of a cardiovascular drug eluting stent (DES). The main processes occurring in the polymeric matrix are drug dissolution and diffusion. Moreover, surface erosion, which consists in mass loss due to the degradation of the polymeric network, is considered as well. The drug eluted from the matrix is released in the arterial wall, modeled as a homogeneous porous medium. By consequence, we assume that drug molecules are transported by diffusion and convection. Moreover, inside the tissue the reversible reaction of the drug with specific binding sites is taken into account and the coupled problem of mass transfer between matrix and tissue is formulated. It is shown that the mass conservation principle leads to nonstandard boundary coupling conditions to describe the transfer of the drug between the matrix and the arterial wall. Then, the problem at hand is solved numerically, highlighting the importance of enforcing mass conservation and focusing on the influence of the polymer erosion on the drug release profile and drug distribution in the tissue.

Applying the microscopic nuclear physics ideas to macroscopic stellar systems, we study the evolution of the compact di-stars in mass asymmetry (transfer) coordinate. Depending on the internal structure of constituent stars, the initial mass asymmetry, total mass, and orbital angular momentum, the close di-star system can either exist in symmetric configuration or fuse into mono-star. The limitations for the formation of stable symmetric binary stars are analyzed.

The evolution of close binary stars in mass asymmetry (transfer) coordinate is considered. The conditions for the formation of stable symmetric binary stars are analyzed. The role of symmetrization of asymmetric binary star in the transformation of potential energy into internal energy of star and the release of a large amount of energy is revealed.

Applying the microscopic nuclear physics ideas for fusion reactions to macroscopic galactic systems, we study the evolution of the compact binary galaxy in mass asymmetry (transfer) coordinate. The conditions for the formation of stable symmetric binary galaxy are analyzed. The role of symmetrization of asymmetric binary galaxy in the transformation of gravitational energy into internal energy of galaxies accompanied by the release of a large amount of energy during the symmetrization process is revealed.

The evolution of contact binary star systems in mass asymmetry (transfer) coordinate is considered. The orbital period changes are explained by an evolution in mass asymmetry towards the symmetry (symmetrization of binary system). It is predicted that decreasing and increasing orbital periods are related, respectively, with the nonoverlapping and overlapping stage of the binary star during its symmetrization. A huge amount of energy $\mathrm{\Delta }U\approx 10^{41}$J is converted from the potential energy into internal energy of the stars during the symmetrization. As shown, the merger of stars in the binary systems, including KIC 9832227, is energetically an unfavorable process. The sensitivity of the calculated results to the values of total mass and orbital angular momentum is analyzed.

Based on the consideration of potential energy of the di-black-hole as a function of mass asymmetry (transfer) collective coordinate, the possibility of matter transfer between the black holes in a binary system is investigated. The sensitivity of the calculated results is studied to the value of the total mass of binary system. The conditions for the merger of two black holes are analyzed in the context of gravitational wave emission.

Theoretical possibilities for the spontaneous emission of fission fragments from ${}^{237-256}$Cf parents are investigated within the framework of preformed cluster decay model (PCM). The fragmentation potential exhibits a modification from dominated asymmetric fission profile to symmetric splitting with the rise in the N/Z ratio of parent nuclei. The calculated spontaneous fission (SF) half-life times of Cf isotopes find nice agreement with the experimental data, except for ${}^{256}$Cf nucleus. Within the PCM, the hydrodynamical mass transfer among the outgoing binary fragments occurs through a cylindrical vessel connecting them. For the overlapping configuration $(R<R_T$), the two classical models namely Model A and Model B (differ in the way the radius of the connecting cylinder is controlled) are used to estimate mass transfer flow of binary fragmentation. It is observed that with change in the overlapping distance, the radius of the cylindrical vessel changes in Model A, whereas the same remains fixed in Model B. In case of Model B, the effect of cylindrical radii parameter (${\alpha }_c$) is also analyzed for ${}^{237-256}$Cf parents at optimum neck-length ($\mathrm{\Delta }$R) in view of different observable such as most probable SF fragments, preformation probability, mass transfer, the SF half-lives and the results are compared with Model A calculations. The magnitude of mass transfer, preformation probability, and hence the SF half-lives gets significantly modified on switching from Model A to Model B. Further, a large amount of mass is transferred between the asymmetric fragments as compared to the symmetric ones. The SF half-lives are shown to depend strongly on the choice of classical models as well as on the cylindrical radius parameter, ${\alpha }_c$. The study infers the importance of classical models to spread further light in the understanding of the dynamical behavior of fragment formation in the fission process.

The pore geometry of porous rocks is fundamental for accurate description of stress dependence of effective permeability, which is an important parameter of mass transfer in porous rocks. An important physical assumption that porous rocks contain numerous elliptical or spherical pores has been shown to be successfully applied to many aspects of hydromechanical coupling properties of porous rocks. To investigate the detailed description of pore structures on the degree of effect on the coupled hydromechanical process, in this work, a generalized stress-dependent model for permeability of porous rocks has been proposed based on fractal geometry theory and mechanics of porous rock. The proposed model is expressed as a nonlinear function of pore structure parameters, such as aspect ratio (${\gamma }_{\sigma }$), the fractal dimensions ($D_{T,\sigma }$ and $D_{T,av}$) for tortuosity, the initial fractal dimension ($D_{f,0}$), and initial porosity (${\varphi }_0$) as well as matrix elastic constants ($E$ and $\nu$) of porous rocks without any empirical parameter. The validity of the proposed models is verified by the good agreements between available experimental data and theoretical predictions of stress-dependent permeabilities of porous rocks. Detailed discussions of the essential effects of pore structures parameters and material elastic constants of porous rocks on the dimensionless stress-dependent permeabilities are performed. It is found that the stress parameters ($E$ and ${\gamma }_0$) have remarkable effects on the dimensionless stress-dependent permeabilities compared with other parameters (${\varphi }_0$ and $\nu$). The proposed model may contribute to a better quantitative understanding of the coupled hydromechanical properties of porous rocks.

Mineral dissolution and precipitation reactions occur in a variety of porous rocks due to the deviations from a geochemical equilibrium between solid matrix and flow fluid, resulting in the alteration of the petrophysical properties of rocks. A physically-based theoretical model is proposed based on fractal theory for quantitatively assessing the temporal evolution of permeability for porous rocks undergoing mineral dissolution and precipitation reactions. The proposed model is associated with pore structure parameters, such as initial porosity $({\varphi }_0)$, the tortuosity fractal dimensions $(D_{T,t})$, the initial fractal dimension $(D_{f,0})$, and the overall dissolution rate $({\alpha }_t)$ considering the precipitation reactions in porous rocks. The proposed model provides a better prediction of the time dependence of permeability compared with the available experimental data. The essential effects of the overall dissolution rate and pore structural parameters of porous rocks on the dimensionless time-dependent permeabilities are investigated in detail. It is found that the overall dissolution rate has obvious effects on the dimensionless time dependence of permeabilities. The present model may provide useful insights into the understanding of permeability change during mineral dissolution and precipitation reactions in porous rocks.