Nonuniform Collective Dissolution of Bubbles in Regular Pore Networks

Understanding the evolution of solute concentration gradients underpins the prediction of porous media processes limited by mass transfer. Here, we present the development of a mathematical model that describes the dissolution of spherical bubbles in two-dimensional regular pore networks. The model is solved numerically for lattices with up to 169 bubbles by evaluating the role of pore network connectivity, vacant lattice sites and the initial bubble size distribution. In dense lattices, diffusive shielding prolongs the average dissolution time of the lattice, and the strength of the phenomenon depends on the network connectivity. The extension of the final dissolution time relative to the unbounded (bulk) case follows the power-law function, $${B^k/\ell }$$ B k / ℓ , where the constant $$\ell$$ ℓ is the inter-bubble spacing, B is the number of bubbles, and the exponent k depends on the network connectivity. The solute concentration field is both the consequence and a factor affecting bubble dissolution or growth. The geometry of the pore network perturbs the inward propagation of the dissolution front and can generate vacant sites within the bubble lattice. This effect is enhanced by increasing the lattice size and decreasing the network connectivity, yielding strongly nonuniform solute concentration fields. Sparse bubble lattices experience decreased collective effects, but they feature a more complex evolution, because the solute concentration field is nonuniform from the outset.

Improving element uniformity and mechanical properties of Al-Mg-Si alloy fabricated by twin roll casting with superheat melt treatment

The effect of superheat melt treatment(SMT) on microstructure and properties of Al-Mg-Si alloy fabricated by twin roll casting(TRC) was analyzed using optical microscope, scanning electron microscopy, emission electron probe micro analyzer and transmission electron microscopy. SMT increased the subcooling degree of melt during TRC. The solidification microstructure with high dendrite density and small dendrite spacing was obtained. The second phase was evenly distributed between dendrites and the solute concentration gradient was decreased. Intergranular solute aggregation caused by Reynolds’ dilatancy in TRC slab was effectively suppressed. The homogeneous solute distribution of TRC slab with SMT can be realized by short-time homogenization heat treatment. The size of insoluble particles was greatly reduced. The complete decomposition of non-equilibrium eutectic phase increased the solute concentration in α-Al, which promoted the precipitation of precipitates during aging heat treatment. The tensile strength and yield strength of T6 slab were improved, while the uniform elongation are almost not decreased. The strength and uniform of slab in T4P state were both improved. The obtained results can help further shorten the production cycle of TRC slabs and improve mechanical properties.

Effects of chemical reaction, viscosity, thermal conductivity, heat source, radiation/absorption, on MHD mixed convection nano-fluids flow over an unsteady stretching sheet by HAM and numerical method

Investigations are performed for further observations of heat and mass transfer in magneto-hydrodynamic mixed-convectional nano-fluid flow with the assumption of variable viscosity and thermal-conductivity over an unsteady stretching sheet. Base fluid is Carboxy-methyl cellulose (CMC) water as a carrier fluid with different nano-particles such as [Formula: see text] (Titanium), Ag (Silver), [Formula: see text] (Aluminum), and Cu (Copper). Flow contains different physical parameters, such as heat source, chemical reaction effect, Schmidt number, and radiation absorptions effects are observed to be significant in the presences of magnetic field. Obtained equations are solved by numerically BVP4C-package (shooting method) and analytically by BVPh2.0-package (Homotopy Analysis Method “HAM”). Interested physical quantities are, viscosity-parameter ( A), Thermal-conductivity parameter ( N),Thermocapillary-number ( M), Hartmann-number (Ma), Prandtl-number (Pr), 4-nano-particles ([Formula: see text]), temperature Grashof number ([Formula: see text]), and mass Grashof number ([Formula: see text]) are the focus to the velocity, temperature, and solute concentration profiles. It is concluded that, Solute concentration of ([Formula: see text])-water has higher than the other 3-nano-fluids. Mass flux, heat flux, and Skin friction of fluids are direct functions of magnetic force, while inverse function of temperature. Magnetic force also decreased the speed of fluids and hence mass flux reduced which implies that, the temperature reduces. [Formula: see text] has also inverse relation with mass flux, heat flux, and skin friction, while direct relation with the speed of fluids. Similarly, [Formula: see text] has inverse relation with [Formula: see text], [Formula: see text], and [Formula: see text], but direct relation with [Formula: see text]. Different results are shown in graphical and tabular form.

Numerical Solutions of Space-Fractional Advection–Diffusion–Reaction Equations

Background: solute transport in highly heterogeneous media and even neutron diffusion in nuclear environments are among the numerous applications of fractional differential equations (FDEs), being demonstrated by field experiments that solute concentration profiles exhibit anomalous non-Fickian growth rates and so-called “heavy tails”. Methods: a nonlinear-coupled 3D fractional hydro-mechanical model accounting for anomalous diffusion (FD) and advection–dispersion (FAD) for solute flux is described, accounting for a Riesz derivative treated through the Grünwald–Letnikow definition. Results: a long-tailed solute contaminant distribution is displayed due to the variation of flow velocity in both time and distance. Conclusions: a finite difference approximation is proposed to solve the problem in 1D domains, and subsequently, two scenarios are considered for numerical computations.

Solute Transport Control at Channel Junctions Using Adjoint Sensitivity

Water quality control and the control of contaminant spill in water in particular are becoming a primary need today. Gradient descent sensitivity methods based on the adjoint formulation have proved to be encouraging techniques in this context for river and channel flows. Taking into account that most channels and rivers include junctions with other branches, the objective of this study is to explore the adjoint technique on a channel network to reconstruct the upstream boundary condition of the convection-reaction equation. For this purpose, the one-dimensional shallow water equations and the transport equation for a reactive solute are considered. The control is formulated through the gradient-descent technique supplied with a first-order iterative process. Both the physical and the adjoint equations are supplied with suitable internal boundary conditions at the junction and are numerically solved using a finite volume upwind scheme. The results reveal that the adjoint technique is capable of reconstructing the inlet solute concentration boundary condition in an acceptable number of iterations for both steady state and transient configurations using a downstream measurement location. It was also observed that the reconstruction of the boundary condition tends to be less effective the further away the measurement station is from the target.

A quadratic analytical solution of root pressure generation provides insights about bamboo and other species

We derived a steady-state model of whole root pressure generation through the combined action of all parallel segments of fine roots. This may be the first complete analytical solution for root pressure, which can be applied to complex roots/shoots. The osmotic volume of a single root is equal to that of the vessel lumen in fine roots and adjacent apoplastic spaces. Water uptake occurs via passive osmosis and active solute uptake (J_s^*, osmol s-1), resulting in the osmolal concentration Cr (mol·kg-1 of water) at a fixed osmotic volume. Solute loss occurs via two passive processes: radial diffusion of solute Km (Cr-Csoil), where Km is the diffusional constant and Csoil is the soil-solute concentration) from fine roots to soil and mass flow of solute and water into the whole plant from the end of the fine roots. The proposed model predicts the quadratic function of root pressure P_r^2+bP_r+c=0, where b and c are the functions of plant hydraulic resistance, soil water potential, solute flux, and gravitational potential. The present study investigates the theoretical dependencies of Pr on the factors detailed above and demonstrates the root pressure-mediated distribution of water through the hydraulic architecture of a 6.8-m-tall bamboo shoot.

Process simulation of modelled reverse osmosis for desalination of seawater

Model equations for prediction of process parameters of reverse osmosis for desalination of seawater were developed via mathematical derivation from basic equations for reverse osmosis process. A model equation relating the interfacial solute concentration () with the process pressure difference () was developed. Taking the of a reverse osmosis as the basic independent variable, further model equations relating other process parameters such as the solute concentration polarity , water flux , osmotic pressure , water output rate (q), power density (Pd) and specific energy consumption (SEC) were developed. Simulation of a hypothetical reverse osmosis data using Microsoft Excel Worksheet and a Microsoft Windows 10 on a 64-bit operating system was carried out. Simulation results showed that the optimum fluid bulk concentration was = 0.0004 mole/cm3. The optimum rate of increase in the solute rejection factor per unit rise in ΔP was 0.45%. The optimum solute rejection factor was 97.6%. The optimum water output rate, specific energy consumption and power density were 103.2 L/h, 3.65 kWh/m3 and 6.09 W/m2, respectively.

Computational Fluid Dynamics Modeling of Hollow Membrane Filtration for Concentration Polarization

Based on CFD and film theory, filtration’s two-dimensional CFD model of the hollow membrane was established by integrating the mass transformation and the hydrodynamic transportation. Parameters of concentration polarization in the membrane channel (i.e., solute mass concentration, concentration polarization factors, and concentration polarization layer thickness) were estimated under different hydraulic conditions. In addition, the algorithm for the thickness of the concentration polarization layer has been improved. The results showed that decreasing the feed Reynolds number or increasing the transmembrane pressure can enhance the concentration polarization phenomena. Concentration polarization parameters increased sharply at the initial place (X/H < 25, where H is the entrance width, X is the distance from entrance) and then flatten out (X/H > 25) along the membrane channel; solute concentration and concentration polarization factors were arranged in a U-shape in the membrane channel’s cross-section. The improved algorithm could match well with cross section data, δ2H at X/H = 1, 25, and 200 are 0.038, 0.11, and 0.25, respectively, which can reasonably reflect the distribution of the concentration polarization phenomenon in the membrane channel.

Solubility and Crystallization of Piroxicam from Different Solvents in Evaporative and Cooling Crystallization

In this work, the solubility of a non-steroidal anti-inflammatory drug (NSAID), piroxicam, is investigated. The polymorphic form II, which is the most stable form at room temperature, was investigated in seven different solvents with various polarities. It has been found that the solubility of piroxicam in the solvents is in the following order: chloroform > dichloromethane > acetone > ethyl acetate > acetonitrile > acetic acid > methanol > hexane. Crystallization of piroxicam from different solvents has been performed with evaporative crystallization and cooling crystallization; the effects of solvent evaporation rate and solute concentration have also been studied. Both form I and form II could be produced in cooling and evaporative crystallization, and no simple link can be identified between the operating parameters and the polymorphic outcome. Results obtained in the present work showed the stochastic nature of the nucleation of different polymorphs as well as the complexity of the crystallization of a polymorphic system.