Number Pe Research Articles

Cattaneo-Christov Heat Flux Model for Bio-Convective Radiative Eyring-Powell Nanofluid with Viscous-Ohmic Dissipation and Magnetic Dipole Impacts

In this work we studied the solutions of the bio-convected Eyring-Powell nanofluid involving gyrotactic micro-organisms in the presence of viscous-ohmic dissipation, double diffusion, and magnetic field over a stretched sheet under the impacts of nonlinear radiation and Arrhenius activation energy. The magneto-nanoparticles suspension in microorganisms are beneficial in nanofluid stability. Also, they have number of applications in nanosciences, biotech, pharmaceuticals, and mechanical development. The nonlinear coupled PDEs are transformed into ODEs by taking a suitable set of similarity transformations and then computationally solved with MATLAB’s bvp4c and RK4-Shooting technique. The skin friction coefficient, Nusselt number, and Sherwood number are represented in tabular form. The mass and heat transmission rate improve in the presence of gyrotactic microorganisms. The temperature as well as concentration of Eyring-Powell Nanofluid get decreased by accelerating the significant mass and thermal stratification. The concentration profile Φ(η) depreciate for higher Chemical reaction rate (σ), Schmidt number (Sc), and temperature difference (δ1) parameters but rises upon increasing values of Activation energy (Ea). Also, the microorganism concentration difference parameter (β1), bioconvection Lewis number Lb and Peclet number Pe are opposing the motile microorganism density profile.

Artificial Neural Network Modeling in the Presence of Uncertainty for Predicting Hydrogenation Degree in Continuous Nitrile Butadiene Rubber Processing

The transition from batch to continuous production in the catalytic hydrogenation of nitrile butadiene rubber (NBR) into hydrogenated NBR (HNBR) marks a significant advance for applications under demanding conditions. This study introduces a continuous process utilizing a static mixer (SM) reactor, which notably achieves a hydrogenation conversion rate exceeding 97%. We thoroughly review a mechanistic model of the SM reactor to elucidate the internal dynamics governing the hydrogenation process and address the inherent uncertainties in key parameters such as the Peclet number (Pe), dimensionless time (θτ), reaction coefficient (R), and flow rate coefficient (q). A comprehensive dataset generated from varied parameter values serves as the basis for training an artificial neural network (ANN), which is then compared against traditional models including linear regression, decision tree, and random forest in terms of efficacy. Our results clearly demonstrate the ANN’s superiority in predicting the degree of hydrogenation, achieving the lowest root mean squared error (RMSE) of 3.69 compared to 21.90 for linear regression, 4.94 for decision tree, and 7.51 for random forest. The ANN’s robust capability for modeling complex nonlinear relationships and dynamics significantly enhances decision-making, planning, and optimization of the reactor, reducing computational demands and operational costs. In other words, this approach allows users to rely on a single ML-based model instead of multiple mechanistic models for reflecting the effects of possible uncertainties. Additionally, a feature importance study validates the critical impact of time and element number on the hydrogenation process, further supporting the ANN’s predictive accuracy. These findings underscore the potential of ML-based models in streamlining and enhancing the efficiency of chemical production processes.

Comparative analysis of thermal behaviour in functionally graded material fin under convective-radiative heat transfer: Homotopy perturbation method

In this study, the thermal characteristics of a fully wet, moving longitudinal fin made from linear Functionally Graded Material (FGM) is explored. The fin response to convective-radiative heat transfer is examined through three distinct FGM scenarios namely, a Homogeneous material (HM), Functionally Graded Material I (FGM I) having greater thermal grading near the base, and Functionally Graded Material II (FGM II) having increased thermal grading towards the tip. The derived energy equation is a second-order nonlinear ordinary differential equation is solved using the Homotopy Perturbation Method (HPM) compared with results found in the existing literature. The fin thermal profile has been graphically analysed for the thermal conductivity grading parameter (β), Peclet number (Pe) and other pertinent parameters. It is found that the temperature distribution along the fin is highest for the FGM II fin and lowest for the HM fin, with the FGM I fin displaying intermediate values. Efficiency of the fin (η) is discovered to be lowest in the case of HM fin structures followed by FGM I and FGM II fin structures at the base and vice versa at the tip. The results show significant potential of HPM which benefits the manufacture and design of FGM fin structures.

Supervised Stochastic Approach for computational analysis of convectively heated magnetized nanofluid flow with bioconvection aspects

Our study delves into the dynamics of a convective Magneto-Hydrodynamic Bioconvective Nanofluid model (MHD-BCNFM) flowing over a convectively heated stretched sheet. To accomplish this, we utilize the distinctive capabilities of the Supervised Stochastic Approach for Computational Analysis (SSACA). By integrating similarity transformations, we convert the partial differential equations (PDEs) governing the system into coupled ordinary differential equations (ODEs). We generate the dataset for our approach using the Adam numerical technique specifically tailored for the (MHD-BCNFM). Achieving this involves systematic modulation of parameters such as λ, bioconvection Péclet number Pe, Bioconvection constant σ, Brownian motion parameter Nb, and thermophoresis parameter Nt. "Moreover, we utilize a reference dataset to compute numerical values of various physical quantities in the (MHD-BCNFM) employing SSACA-based Artificial Intelligence methods. The effectiveness of our devised SSACA approach is demonstrated by a negligible mean squared error, ranging from approximately 10−8 to 10−10. Histograms exhibit a maximum error range of 10−5, closely aligning with optimal correlation/regression measures. Outstanding performance metrics in terms of Mean Squared Error (MSE) are attained at levels such as l 9.93E−12, 1.07E−11, 6.28E−10, 1.43E−11, 2.09E−09, 3.65E−11, 2.97E−11, and 2.80E−13 against 320, 430, 209, 85, 356, 295, 66, and 136 epochs. A comparative study between the proposed and reference datasets underscores the authenticity and precision of SSACA, supported by error analyses ranging from E-05 to E-09 across all scenarios.

Rate-limiting factors in thin-film evaporative heat transfer processes

In this paper, we present a theoretical study aimed at investigating the rate-limiting factors in thin-film evaporative heat transfer processes, considering the finite-rate evaporation kinetics. The problems of evaporation of a flat thin-film in either pure vapours or vapour-inert-gas mixtures are analysed based on the non-dimensionalised macroscopic transport equations for continuum fluids, coupled with out-of-equilibrium kinetic boundary conditions. Both the full numerical solutions and asymptotic analytical solutions at slow evaporation limit are provided and applied to analyse thin water film evaporation. Existing solutions, assuming negligible heat transfer in the gas domain, or negligible temperature jump across the non-equilibrium kinetic layer, or more boldly a thermodynamically equilibrial interface (i.e. its temperature is at the saturation temperature), can be fully recovered from the more general solutions presented here. Our results show that while these assumptions hold in special cases, they can lead to significant errors in many conditions, especially when the film thickness δ is reduced to a few micrometers or thinner. We show that the conventional views that the rate-limiting factors in thin-film evaporative heat transfer is either the heat diffusion through the liquid film or the mass transfer in the gas domain only apply to thick film (i.e. δ≫λ where λ is the mean free path in the vapour phase). As δ decreases to a few micrometer or smaller (more precisely when the Knudsen number Kn increases beyond O(1) in an pure vapour environment or when the kinetic Peclet number Pe is reduced below O(1) in inert gases), the interfacial thermal resistance due to the evaporation kinetics can be on the same orders of magnitude as the thermal resistance in the liquid film. The analysis also allow us to compare the heat transfer processes during the evaporation of a thin-film in pure vapours to those in inert gases, providing deeper insight into the effectiveness of various strategies for exploring the evaporation process in practical thermal management.

Emergent gauge symmetry in active Brownian matter.

We investigate a two-dimensional system of interacting active Brownian particles. Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we built up the generating functional for correlation functions. We study in detail the hydrodynamic regime with a constant density stationary state. Our findings reveal that, within a small density fluctuations regime, an emergent U(1) gauge symmetry arises, originated from the conservation of fluid vorticity. Consequently, the interaction between the orientational order parameter and density fluctuations can be cast into a gauge theory, where the concept of "electric charge density" aligns with the local vorticity of the original fluid. We study in detail the case of a microscopic local two-body interaction. We show that, upon integrating out the gauge fields, the stationary states of the rotational degrees of freedom satisfy a nonlocal Frank free energy for a nematic fluid. We give explicit expressions for the splay and bend elastic constants as a function of the Péclet number (Pe) and the diffusion interaction constant (k_{d}).

Transitions between different estuarine states in a low-inflow estuary of arid coasts (Mond Estuary, Persian Gulf) with a focus on freshwater lenses

This study shows that the Mond Estuary, Persian Gulf experiences notable time-dependent longitudinal salinity variations. Monthly-seasonal variability in salinity changes from a positive estuarine system in wintertime to inverse and salt-plug estuaries during summertime. A highly unsteady state (time scale of hours-days) occurs in the wintertime named the freshwater lens estuary (FLE), in which a low-salinity water mass (lens) is confined by both marine and riverine saltwater sources. Here, FLE dynamics is investigated using realistic and idealized numerical models and two 25-hour data sets collected immediately before a hypersaline runoff (weak FLE condition) and during another one (strong FLE condition). The Péclet Number (Pe) reveals a much stronger advective transports than diffusive one (Pe>5.7) throughout the estuary. An exception from this behavior (stronger mixing with Pe=0.8) is observed at the estuary downstream, where a significant amount of freshwater mixes with seawater during the weak FLE conditions. Also, the minimum hypersaline runoff of ∼400 m3/s estimated by the numerical model can dampen tidal waves at the head of the estuary. In an idealized basin, the model shows that FLE longitudinal flows form two cells of positive estuarine circulation separated by a maximum mixing zone (the potential energy anomaly <0.75 J/m3). In the Mond Estuary, a sea-level rise of 20 cm increases salinity in the FLE state and the positive estuary during winter. Conversely, it decreases salinity in the inverse and salt-plug estuaries in summer.

Diffusive wave model in a finite length channel with a concentrated lateral inflow subject to different types of boundary conditions

The diffusive wave model is one of the simplified forms of Saint-Venant equations, and it is often used instead of the full model. In this paper, we present an analytical solution for the linearized diffusive wave model represented by a simultaneous system of two first-order partial differential equations focused on spatial variation of a lateral inflow in a finite channel. A concentrated lateral inflow from a small-width tributary is considered through the Dirac delta function. We use the Laplace transform method to solve these equations analytically. Two types of upstream boundaries are considered here in the form of a flow-discharge hydrograph and a flow-depth hydrograph, while keeping a flow-depth hydrograph as the downstream boundary. Using unit-step responses of the lateral inflow, the effect of different boundaries on the flow-depth responses and the flow-discharge responses is studied for different values of the Peclet number (Pe). The flow depth is observed to be more sensitive to the downstream boundary and other parameters used in this work. Consideration of the flow depth as the upstream boundary reflects the effect of all the parameters on the unit-step responses presented. These responses are compared with the available semi-infinite channel responses, which are found to be an inappropriate substitute for the finite channel responses for Pe&amp;lt;5 which implies that the downstream boundary cannot be ignored for these cases. However, for the case Pe&amp;gt;5, although the semi-infinite channel responses are found to satisfactorily estimate the discharge along the entire channel, they can approximate the flow depth at the locations closer to the upstream boundary only.

Numerical comparison of nonlinear thermal radiation and chemically reactive bio-convection flow of Casson-Carreau nano-liquid with gyro-tactic microorganisms: Lie group theoretic approach

The current research presents a mathematical model to study the flow of a non-Newtonian magnetohydrodynamics (MHD) Casson-Carreau nanofluid (CCNF) over a stretching porous surface, considering mass and heat transport rates with Stefan blowing, non-linear thermal radiation, heat source-sink, chemical reaction, thermophoretic and Brownian motions, convective heating, Joule heating, motile microorganisms, and bio-convection. The presence of microorganisms is utilized to control the suspension of nanomaterials within the nanofluid. The current flow model has been rendered by the boundary layer approximation and we get the highly nonlinear partial differential equations (PDEs). These nonlinear PDEs are simplified by the novel Lie group theoretic method. The one-parameter Lie scaling method simplified the PDEs and convert it into the ordinary differential equations (ODEs). Numerical solutions for these ODEs are obtained using the bvp4c scheme built-in function in MATLAB, ensuring reliable outcomes for temperature, velocity, concentration, and motile microorganism density profiles. The numerical results are presented through graphs and compared with available data, showing good agreement. These numerical outcomes reveal several important flow characteristics. Rates of change for Nr are 0.0007 and 0.0005, and for Ω, they are −0.0754 and −0.0536, respectively. Similarly, the rate of change for Rb in both models is −0.002 and −0.0002. Analysis shows a positive impact of the bioconvection Rayleigh number in both models, notably higher for the Casson fluid compared to the Carreau fluid model. Buoyancy ratio parameter exhibits consistent rates of change, while the reduction in impact is more pronounced for the Casson fluid model in the case of the mixed bioconvection parameter. The mixed bio-convection parameter reduces momentum velocity for both Casson and Carreau fluids, whereas the Darcy parameter boosts fluid velocity. As the Newtonian heating parameter increases, the temperature velocity distribution of both fluids also increases. The concentration profile of both Casson-Carreau fluid phases declines as the heat source-sink parameter and Schmidt number increase. Microbial velocity shows a decrease with increasing R values, whereas the opposite trend is observed for the Peclet number Pe.

On the contribution of the top and bottom walls in micro-pillar array columns and related high-aspect ratio chromatography systems

We report on a steady-state based, and hence highly accurate numerical modelling study of the effect of the top and bottom wall in the current generation of micro-pillar array columns. These have a mesoporous retention layer that not only covers the pillar walls but also the bottom wall. Our results show that the performance of these columns can in general not be improved by also covering the top wall with the same layer, despite the increased column symmetry this approach would offer. The reason for this is that the local species retardation caused by a retentive layer is much stronger than the pure flow arresting effect of an uncovered wall. At least, this has a crucial impact in high aspect-ratio systems such as micro-pillar array columns because these require a small inter-pillar distance to promote mass transfer together with a large channel depth to enable a sufficiently high flow rate. On the other hand, a notable improvement could be made if micro-pillar array would be produced without having a retentive layer at the bottom. At Péclet number Pe = 50 and aspect ratio AR = 5 for flow-channels, this gain amounts up to about 4.5 h-units at a zone retention factor k’’ = 2 and 1.75 h-units at k’’ = 16 (gain scales almost linearly with Pe).To verify these results, we also considered another high aspect-ratio system with a simplified geometry: the open-tubular channel with a flat-rectangular cross-section. This led to very similar observations, thus confirming the findings for the micro-pillar array.The results produced in the present study also allow us to conclude that the classic modelling paradigm adopted in chromatography, which is based on the independency and hence additivity of the hCm- and hCs-contributions, can lead to large modelling errors in chromatographic systems with a high aspect-ratio, even when their geometry is so simple as that of a straight open-tubular channel with constant cross-section. Indeed, when both zones are treated independently, the analysis misses how the vertical diffusion through the retentive layer helps suppressing the vertical gradients in the mobile zone. The diffusion through this layer occurs in a ratio of k’’Ds/Dm (Dm being the diffusion coefficient in mobile phase zone and Ds being the diffusion coefficient in stationary phase zone), such that at high retention factors this diffusion contribution even becomes the dominant one.

Performance Analysis of Wet Porous Moving Fin under the Influence of Spherical Shaped TiO2- Ag Hybrid Nanoparticles in a Water Based Fluid

The study investigates the flow characteristics of spherical shaped TiO2 –Ag hybrid nanofluid with water as a base fluid passing through a wet porous rectangular moving fin with a focus on understanding the effects of nanoparticle concentration on the heat transfer rate. The fin under consideration are subjected to boundary conditions, insulated and convective tips. Hybrid nanofluid that combine nanoparticles with conventional base fluids have potentially enhanced thermal conductivity and heat transfer properties in engineering applications. The energy balance equation containing the parameters that effect the flow of heat transfer rate is non- dimensionalized and solved numerically using 3-stage Lobatto - IIIa formula with appropriate boundary conditions. The simulation result shows the impact of different parameters on the flow and heat transfer properties of the hybrid nanofluid obtained by mixing spherical shaped TiO2 –Ag hybrid nanoparticles with water as base fluid. It is observed that the fin shows significant heat transfer rate in a convective tip relative to an insulated tip. The findings contribute to the understanding of hybrid nanofluid flow and its potential application in the design and optimization of thermal management system. It also facilitates the ground work for research in the field of nano fluid based cooling system. The observation from the graphical illustration shows that the rise in the thermal conductivity of the base fluid by 23% increases the conduction heat transfer as well as the temperature distribution by 10%. The natural convection and radiation are the key parameters that determines the heat transfer rate from the surface to the surrounding. In our investigation, enhancing the Nc,Nr parameters by 50% and 25%, the temperature distribution profile is reduced by about 13% and 6% respectively. The increase in the Pe number by 100% results in a rise in the temperature distribution by 8%.

Numerical simulation of enzymatic hydrolysis in a bionic intestinal segmentation reactor

Enzymatic hydrolysis plays a critical role in the microbial conversion of lignocellulosic biomass, which has been widely performed in continuous stirred-tank reactors (CSTRs). However, low hydrolysis efficiency in CSTRs hinders the industrial application of lignocellulose to produce biofuels. A bionic intestinal segmentation reactor (BISR) was proposed for efficient enzymatic hydrolysis. In BISR, the dynamic reactor's wall with enzyme secretion led to a 2.0-fold improvement in the conversion of cellobiose as a model substrate compared to the control with a static one. Meanwhile, the reaction rate reached 0.89 mmol/l/s, which was increased by 6.7-fold. Flow fields further illustrated that secondary flow during the segmentation facilitated radial mass transfer between cellobiose and enzyme. Dimensionless secondary flow intensity Sem increased from 0.93 to 2.35 with amplitude, while decreasing from 2.86 to 2.26 with period. More importantly, the analysis of dimensionless Péclet number (Pe) and Damköhler number (Da) indicated that secondary flow could significantly enhance the hydrolysis process controlled by mass transfer.

Field-induced interfacial instabilities in a two-phase ferrofluid flow

Forming a stable ferrofluid and non-magnetic interface in a microchannel is essential for biomedical applications with two miscible aqueous solutions. Here, we report the interface profile and its instability of aqueous ferrofluid and water co-flow in a microchannel under the influence of a magnetic field. The scaling law related to diffusion width and dimensionless Pe number is introduced by solving the momentum and diffusion equation and combining the experimental results. It is found that the dimensionless number of diffusion width δ/h ∝ X/Peα, when core flow concentration cf, residual magnetic flux density Br, sheath flow and core flow ratio Qw/Qf, and core flow velocity Qf are changed, α is 0.633–1.071, α ∝ Qβ, β = −0.059,0.147, 0.019 and −0.101, respectively. Altering the core flow velocity and magnetic field intensity can quickly impact the interface's stability by improving the transport efficiency by 32.9 % and counteracting the impacts of material diffusion by 51.8 %, respectively. Elevating the proportion of sheath flow to core flow and magnetic field will impede the diffusion of core flow. This will result in a drop of 11.9 % in the magnetic convection effect and a 20.8 % counteraction of material diffusion effects.

Novel Bayesian distributed adaptive neural structure for titanium and aluminium alloy nanofluidic model with gyrotactic microorganisms

The purpose of this research study is to evaluate the solutions of Titanium and Aluminum alloy nanofluidic model with gyrotactic microorganisms (TAA-NFMGM) by applying stupendous knacks of Bayesian distributed adaptive neural structure (BDANS). The use of nanofluids containing gyrotactic microorganisms in combination with titanium and aluminum alloys have potential applications in diverse fields, including engineering, bioremediation, biomedical devices, biotechnology, and research depending on different factors like design of the system and use of certain microorganism. A dataset for BDANS is generated for the eight different events with Adam numerical technique for TAA-NFMGM by varying Prandtl number (Pr), mixed convection parameter (λ), microorganisms concentration parameter (Ω), bioconvection peclet number (Pe), and bioconvection Lewis number (Lb). The reference data set generated with Adam numerical technique is utilized for numerical calculation of different parameters on TAA-NFMGM by employing the artificial intelligence based BDANS. The accuracy and justification of the performance of BDANS is efficaciously substantiated through negligible level of MSE around 10–10 to 10–13, calculation of regression metrics and distribution of instances of error on histograms with values 10–04 to 10–09 near to reference line.

Complementary Mass Transport Investigations in Open-Cell Foams: Full-Field Computational Fluid Dynamics Simulation with Random-Walk Microscopic Particle Tracking and Methane Nuclear Magnetic Resonance Displacement Measurements

Numerical simulation can provide detailed understanding of mass transport within complex structures. For this purpose, numerical tools are required that can resolve the complex morphology and consider the contribution of both convection and diffusion. Solving the Navier–Stokes equations alone, however, neglects self-diffusion. This influences the simulated displacement distribution of flow especially in porous media at low Péclet numbers (Pe < 16) and in near-wall regions where diffusion is the dominant mechanism. To address this problem, this study uses μCT-based computational fluid dynamics (CFD) simulations in OpenFOAM coupled with the random-walk particle tracking (PT) module disTrackFoam and cross-validated experimentally using pulsed-field gradient (PFG) nuclear magnetic resonance (NMR) measurements of gas flow within open-cell foams (OCFs). The results of the multi-scale simulations—with a resolution of 130–190 µm—and experimental PFG NMR data are compared in terms of diffusion propagators, which are microscopic displacement distributions of gas flows in OCFs during certain observation times. Four different flow rates with Péclet numbers in the range of 0.7–16 are studied in the laminar flow regime within 10 and 20 PPI OCFs, and axial dispersion coefficients were calculated. Cross-validation of PFG NMR measurements and CFD-PT simulations revealed a very good matching with integral differences below 0.04%, underpinning the capability of both complementary methods for multi-scale transport analysis.

Numerical study of the Marangoni effect induced by soluble surfactants and solute based on rising droplets

In this study, we present a numerical investigation into the phenomenon of rising droplets in immiscible fluids, focusing on the Marangoni effect induced by both solute and a combination of solute and soluble surfactants. We meticulously examine the interfacial behaviors of pure solute droplets and mixed droplets, with a particular interest on the intricate interplay among interfacial concentration, interfacial tension, Marangoni stress, and Marangoni convection. Our investigation provides insight into the influence of key physicochemical parameters, such as viscosity, diffusion coefficient, partition coefficient, and interfacial tension gradient, on the Marangoni instability. Furthermore, we conduct a comprehensive parametric exploration of the impact of dimensionless numbers such as the Langmuir number (La), the Damkohler number (Da), the Peclet number (Pe), and the elasticity number β on the stabilizing efficacy of surfactants. The research findings underscore the effectiveness of our numerical method in capturing the distinctive two-step acceleration characteristics of pure solute droplets and the stabilizing effect of surfactants on mixed droplets. Notably, our study reveals that the Marangoni instability may manifest even when the viscosity and diffusivity ratios of the two-phase fluids are closely matched. Partition coefficients below unity exhibit only a marginal influence on the re-acceleration time of the droplets. Systems characterized by extremely low interfacial tension gradients tend to exhibit no Marangoni instability. Moreover, an increase in La enhances the stability of mixed droplets, while a significant threshold is identified for Da to affect the stability of mixed droplets. The ascent speed of mixed droplets displays pronounced variation across varying Pe magnitudes. Finally, in scenarios involving a wide-ranging variation in β, mixed droplets transition between the states of pure solute droplets and rigid spheres, revealing a distinct-state transition point.

Collective behavior of self-steering active particles with velocity alignment and visual perception

The formation and dynamics of swarms is widespread in living systems, from bacterial biofilms to schools of fish and flocks of birds. We study this emergent collective behavior via agent-based simulations in a model of active Brownian particles with visual-perception-based steering and alignment interactions. The dynamics, shape, and internal structure of the emergent aggregates, clusters, and swarms of these intelligent active Brownian particles are determined by the maneuverabilities Ωv and Ωa, quantifying the steering based on the visual signal and polar alignment, respectively, the propulsion velocity, characterized by the Péclet number Pe, the vision angle θ, and the orientational noise. Various nonequilibrium dynamical aggregates—like motile wormlike swarms and milling, and close-packed or dispersed clusters—are obtained. Small vision angles imply the formation of small clusters, while large vision angles lead to more complex clusters. In particular, a strong polar-alignment maneuverability Ωa favors elongated wormlike swarms, which display superdiffusive motion over a much longer time range than individual ABPs, whereas a strong vision-based maneuverability Ωv favors compact, nearly immobile aggregates. Swarm trajectories show long persistent directed motion, interrupted by sharp turns. Milling rings, where a wormlike swarm bites its own tail, emerge for an intermediate regime of Pe and vision angles. Our results offer insights into the behavior of animal swarms and provide design criteria for swarming microbots. Published by the American Physical Society 2024

CALCULATION OF DISTRIBUTION OF IMPURITIES IN SOLIDIFIED CONDENSATE INTO ACCOUNT OF PECLET NUMBER

The results of calculations of the distribution of impurities in the condensate obtained by condensation of vapor into a solid phase in the process of evaporation of the “base-impurity” substance are presented at the values of the equilibrium separation factor β0 in the range of 0.001…10 and the values of the diffusion Peclet number (Pe) in the range of 0.1…1∙104 . One can see the influence of both parameters on the formation of the distribution: at given values of β0 and Pe, the condensates have larger or smaller areas with a uniform distribution of impurities. The graphs of the averaged impurity concentration in the condensates are also presented depending on the degree of distillation at the same values of β0 and Pe.

Phase diagram and permeability evolution for dissolving vertical fractures in a gravity field

Rock fractures always provide the main flow pathways in geological systems. When exposed to reactive flow, mineral dissolution causes different dissolution regimes and significantly impacts permeability change. Previous studies have examined dissolution regimes and permeability evolution in horizontal geometry, but dissolution dynamics and permeability changes of vertical fractures in a gravity field remain unexplored. Here, we conduct flow-dissolution experiments combined with a pore-scale modeling approach to investigate regime transition and permeability evolution in vertical fractures. We validate the modeling approach using experimental results and illustrate the importance of gravitational effects in dissolving vertical fractures. Our 3D numerical simulations reveal the regime transition, represented by a critical Richardson number Ri, from the forced convection regime to the buoyancy-driven convection regime as the importance of gravity increases. In the buoyancy-driven regime, gravitational effects promote the development of localized dissolution/flow channels. However, gravitational effects become negligible in the forced convection regime where wormholes and uniform patterns can be separated by the critical Pe number. Using the critical Ri and Pe numbers, we establish a phase diagram of dissolution regimes for vertical fractures in a gravity field, exhibiting good agreement with experiments. By correlating this phase diagram with permeability-aperture curves, we directly estimate the power law exponent of permeability evolution for each dissolution regime. This approach extends the classic phase diagram of dissolution regimes to consider gravitational effects on vertical fractures and provides a guide to directly estimate the parameters for permeability evolution, which is essential in reactive-transport modeling at the field scale.

Intensifying the particle deposition from a colloidal solution for the purpose of liquid purification: Comparison of deposition mechanisms and rates

The deposition of particles from a layer of colloidal solution (water and microparticles) has been experimentally studied in the presence of laser heating. Instantaneous temperature and velocity fields are measured using a thermal imager and the Particle Image Velocimetry and the Particle Tracking Velocimetry methods. The unstable behavior of the velocity field in the presence of heating and a free liquid surface are assumed to be determined by the Bond number (Bo). Of interest is also an additional mechanism for the instability formation when the Peclet number (Pe) exceeds the critical value and when the ratio of characteristic velocities VT/Vavr > 1, where VT is the heat front velocity at the initial moment of laser heating, and Vavr is the average convection velocity. A new mechanism of particle deposition due to the use of local laser heating is proposed for the first time. The control over local heating and local deposition increases the particle deposition rate by 2–3 orders compared with that without convection. The particle deposition rate and the deposit area increase with increasing height of the liquid layer, reach maximum values at a critical height, and then decrease sharply with increasing height. The dependence for determining the area and mass of the deposit is proposed to take into account the deposition time, the height of the liquid layer and the rate of convection. The resulting particle deposition method and calculation method may be used in technologies related to the purification of liquid from solid impurities in small volumes, as well as in problems where deposition in a given direction is required to form an ordered nanocoating.