Spontaneous imbibition of liquids in glass‐fiber wicks. Part I: Usefulness of a sharp‐front approach

Spontaneous imbibition of a liquid into glass‐fiber wicks is modeled using the single‐phase Darcy's law after assuming a sharp flow‐front marked by full saturation behind the front occurring in a transversely isotropic porous medium. An analytical expression for the height of the wicking flow‐front as a function of time is tested through comprehensive experiments involving using eight different wicks and one oil as the wicking liquid. A good fit with experimental data is obtained without using any fitting parameter. The contact‐angle is observed to be important for the success of the model—lower contact angle cases marked by higher capillary pressures were predicted the best. The proposed model provides a nice upper bound for all the wicks, thereby establishing its potential as a good tool to predict liquid absorption in glass‐fiber wicks. However, the sharp‐front model is unable to explain region of partial saturation, thereby necessitating the development of part II of this article series (Zarandi and Pillai, Spontaneous Imbibition of Liquid in Glass fiber wicks. Part II: Validation of a Diffuse‐Front Model. AIChE J, 64: 306–315, 2018) using Richard's equation. © 2017 American Institute of Chemical Engineers AIChE J, 63: 294–305, 2018     

Darcy's law–based numerical simulation for modeling 3D liquid absorption into porous wicks

Liquid imbibition into polymer wicks, where a clear liquid front can be seen rising during the wicking process, is modeled using the concepts of flow in porous media. The flow of liquid behind the moving liquid front is modeled using the physics of single‐phase flow in a porous medium where the Darcy's law is combined with the continuity equation and a capillary suction pressure is imposed at the liquid front. A novel numerical simulation PORE‐FLOW^© based on the finite element/control volume method is proposed to model such imbibitional flows in wicks of complex shapes. A validation of the simulation is obtained by achieving an excellent comparison of its predictions with an experimental result, an analytical solution, and the Washburn equation for the case of wicking against gravity in a cylindrical wick. The simulation is also used to predict a case of two‐dimensional (2D) wicking in the altered cylindrical wicks with two different cross‐sectional areas. Once again an excellent match is obtained with the experimental results, while analytical solutions for the single and double cross‐section cases along with the Washburn equation fail to predict the 2D wicking. Later, some other types of altered wicks with sharp changes in their cross‐sectional areas were analyzed numerically for their wicking behavior. It was observed that the height of liquid front in a vertical wick as a function of time, which is proportional to the history of liquid imbibed, is strongly dependent on the extent of reduction in the wick cross‐sectional area as well as its location vis‐à‐vis the wick entrance. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Wicking and evaporation of liquids in porous wicks: A simple analytical approach to optimization of wick design

Wicking and evaporation of volatile liquids in porous, cylindrical wicks is investigated where the goal is to model, using simple analytical expressions, the effects of variation in geometrical parameters of a wick, such as porosity, height and bead‐size, on the wicking and evaporation processes, and find optimum design conditions. An analytical sharp‐front flow model involving the single‐phase Darcy's law is combined with analytical expressions for the capillary suction pressure and wick permeability to yield a novel analytical approach for optimizing wick parameters. First, the optimum bead‐radius and porosity maximizing the wicking flow‐rate are estimated. Later, after combining the wicking model with evaporation from the wick‐top, the allowable ranges of bead‐radius, height and porosity for ensuring full saturation of the wick are calculated. The analytical results are demonstrated using some highly volatile alkanes in a polycarbonate sintered wick. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1930–1940, 2014     

Flow along and across glass‐fiber wicks: Testing of permeability models through experiments and simulations

A rigorous test of important theoretical models for permeability of glass‐fiber wicks, backed by numerical simulations, is conducted using a novel small‐scale experiment. The models include those for flow along and across aligned fibers and for flow through random fibers. The domains for numerical simulations were created by randomly distributed parallel fibers in a cube‐like unit‐cell using Geodict. Two separate simulations were considered: (1) Stokes‐flow solution using GeoDict, (2) Whitaker's closure‐formulation solution using COMSOL. The falling‐head parameter was adapted to measure the permeability along and across the fibers. Multiple measurements were conducted for each of the wicks to establish repeatability and estimate scatter. The permeabilities obtained through experiments matched with those from the theoretical and numerical methods. But numerical permeabilities for the longitudinal flow were exceptionally accurate. Also, the specialized models for longitudinal and transverse flows were more accurate than the random‐fiber models. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3491–3501, 2018     

Validation study on spatially averaged two‐fluid model for gas‐solid flows: II. Application to risers and fluidized beds

In our prior study (Schneiderbauer, AIChE J. 2017;63(8):3544–3562), a spatially averaged two‐fluid model (SA‐TFM) was presented, where closure models for the unresolved terms were derived. These closures require constitutive relations for the turbulent kinetic energies of the gas and solids phase as well as for the subfilter variance of the solids volume fraction. We had ascertained that the filtered model do yield nearly the same time‐averaged macroscale flow behavior in bubbling fluidized beds as the underlying kinetic‐theory‐based two‐fluid model, thus verifying the SA‐TFM model approach. In the present study, a set of 3D computational simulations for validation of the SA‐TFM against the experimental data on riser flow and bubbling fluidized beds is performed. Finally, the SA‐TFM predictions are in fairly good agreement with experimental data in the case of Geldart A and B particles even though using very coarse grids. © 2018 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 64: 1606–1617, 2018     

Extending the range of COSMO‐SAC to high temperatures and high pressures

The range of the predictive Gibbs energy of solvation model, COSMO‐SAC, is extended to large ranges of density, pressure, and temperature for very nonideal mixtures by combining it with an equation of state (EOS) using the Wong‐Sandler mixing rule. The accuracy of isothermal vapor‐liquid equilibria (VLE) calculations based on using the predictive COSMO‐SAC model and separately the correlative NRTL model is compared, each combined with three different forms of the Peng‐Robinson equation of state. All the models considered require the value of the EOS mixing rule binary parameter k_ij. The NRTL model also requires three other parameters obtained from correlation low pressure VLE data. The PRSV + COSMO‐SAC model is showed, with its one adjustable parameter obtained from low temperature data leads good predictions at much higher temperatures and pressures. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1806–1813, 2018     

Model for the outer cavity of a dual‐cavity die with parameters determined by two‐dimensional finite‐element analysis

A coating die forms liquid layers of uniform thickness for application to a substrate. In a dual‐cavity coating die an outer cavity and slot improves flow distribution from an inner cavity and slot. A model for axial flow in the outer cavity must consider the ever‐present cross flow. A 1‐D equation for the pressure gradient for a power‐law liquid is obtained as a small departure from a uniform flow distribution and no axial flow. The equation contains a shape factor dependent on cavity shape, Reynolds number, and power‐law index. The shape factor for five triangular cavity shapes is obtained by finite‐element analysis and correlated for application to die design up to the onset of flow recirculation which arises at the junction of the cavity and outer slot. The performance of the combined cavity and slot is considered and the most effective design determined. © 2017 American Institute of Chemical Engineers AIChE J, 64: 708–716, 2018     

基于泡沫金属的复合毛细芯的物性测试

为改进毛细芯的传热传质性能,以泡沫金属铜或镍为骨架,在其内部填充树形金属铜粉或镍粉,通过树形金属粉末调控泡沫金属内的孔隙结构及孔径分布,制备出一种以金属泡沫为基底的复合毛细芯,并对制备的复合毛细芯的孔隙率、抽吸性能、有效热导率及蒸发率进行研究。结果表明,这种结构的复合毛细芯孔隙率较高,有效热导率为4.1?9.8 W/(m?K)。从毛细芯毛细抽吸、有效热导率和蒸发率综合来看,以金属泡沫镍为骨架、树形镍粉末与造孔剂质量比为5:5的复合毛细芯性能最好。     

On reduced modeling of mass transport in wavy falling films

In many industrial units such as packing columns, falling film reactors, etc., the liquid phase is designed as a falling film. It is well known that the mass and heat transfer in laminar wavy film flows is significantly enhanced compared to flat films. The kinetic phenomena underlying the increase in mass and heat transfer are, however, still not fully understood. For an efficient design of falling film units, computational models that account for these enhanced transport mechanisms are of key importance. In this article, we present a reduced modeling approach based on a long‐wave approximation to the fluid dynamics of the film. Furthermore, we introduce a new two‐dimensional (2D) high‐resolution laser‐induced luminescence measurement technique. Both in the numerical simulation results and in the high‐resolution 2D‐concentration measurements obtained in the experiments we observe similar patterns of high concentrations locally, especially in the areas close to the wave hump. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2265–2276, 2018     

On the steady‐state drop size distribution in stirred vessels. Part I: Effect of dispersed phase viscosity

Previous studies on emulsification have used the maximum drop size (d_max) or Sauter mean diameter ( ) to investigate the effect of viscosity on the drop size distribution (DSD), however, these parameters fall short for highly polydispersed emulsions. In this investigation (Part I), the steady‐state DSD of dilute emulsions is studied using of silicon oils with viscosities varying across six orders of magnitude at different stirring speeds. Different emulsification regimes were identified; our modeling and analysis is centered on the intermediate viscosity range where interfacial cohesive stresses can be considered negligible and drop size increases with viscosity. The bimodal frequency distributions by volume were well described using two log‐normal density functions. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3293–3302, 2018     

Highly efficient separation of strongly hydrophilic structurally related compounds by hydrophobic ionic solutions

The selective separation of strongly hydrophilic structurally related compounds in aqueous solutions is a long‐standing challenge due to a trade‐off between separation selectivity and capacity. This work shows a new method to separate strongly hydrophilic structurally related compounds through hydrophobic ionic solution‐based liquid‐liquid extraction, with L‐ascorbic acid 2‐glucoside (AA‐2G) and L‐ascorbic acid as model compounds. Extraordinary distribution coefficient, superb molecular selectivity, large extraction capacity and good recyclability without using strong acids and salts were all achieved, with a small consumption of phosphonium bromide ionic liquid and aprotic molecular diluent. The essence of this method is the successful combination of both strong hydrogen‐bond basicity and good hydrophobicity along with significant preferential solvation phenomena of the constructed ionic solutions. Even if at a high feed concentration of 100 mg/mL, the purity of AA‐2G could be greatly elevated from 50% to 96.2% with an ultrahigh yield of almost 100% after five‐stage countercurrent extraction. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1373–1382, 2018     

Darcy's law‐based model for wicking in paper‐like swelling porous media

The wicking of liquid into a paper‐like swelling porous medium made from cellulose and superabsorbent fibers was modeled using Darcy's law. The work is built on a previous study in which the Washburn equation, modified to account for swelling, was used to predict wicking in a composite of cellulose and superabsorbent fibers. In a new wicking model proposed here, Darcy's law for flow in porous media is coupled with the mass conservation equation containing an added sink or source term to account for matrix swelling and liquid absorption. The wicking‐rate predicted by the new model compares well with the previous experimental data, as well as the modified Washburn equation predictions. The effectiveness of various permeability models used with the new wicking model is also investigated. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Revisiting electrolyte thermodynamic models: Insights from molecular simulations

Pitzer and electrolyte nonrandom two‐liquid (eNRTL) models are the two most widely used electrolyte thermodynamic models. For aqueous sodium chloride (NaCl) solution, both models correlate the experimental mean ionic activity coefficient (γ_±) data satisfactorily up to salt saturation concentration, that is, ionic strength around 6 m. However, beyond 6 m, the model extrapolations deviate significantly and diverge from each other. We examine this divergence by calculating the mean ionic activity coefficient over a wide range of concentration based on molecular simulations and Kirkwood–Buff theory. The asymptotic behavior of the activity coefficient predicted by the eNRTL model is consistent with the molecular simulation results and supersaturation experimental data. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3728–3734, 2018     

Eulerian‐Lagrangian simulations of settling and agitated dense solid‐liquid suspensions – achieving grid convergence

Eulerian‐Lagrangian simulations of solid–liquid flow have been performed. The volume‐averaged Navier‐Stokes equations have been solved by a variant of the lattice‐Boltzmann method; the solids dynamics by integrating Newton's second law for each individual particle. Solids and liquid are coupled via mapping functions. The application is solids suspension in a mixing tank operating in the transitional regime (the impeller‐based Reynolds number is 4000), an overall solids volume fraction of 10% and a particle–liquid combination with an Archimedes number of 30. In this application, the required grid resolution is dictated by the liquid flow and we thus need freedom to choose the particle size independent of the grid spacing. Preliminary hindered settling simulations show that the proposed Eulerian‐Lagrangian mapping strategy indeed offers this independence. The subsequent mixing tank simulations generate grid‐independent results. © 2018 American Institute of Chemical Engineers AIChE J, 64: 1147–1158, 2018     

Hydrodynamics in a pilot‐scale cocurrent trickle‐bed reactor at low gas velocities

Hydrodynamic data obtained from laboratory‐scale trickle‐beds often fail to accurately represent industrial‐scale systems with high packing aspect ratios and column‐to‐particle diameter ratios. In this study, pressure drop, liquid holdup, and flow regime transition were investigated in a pilot‐scale trickle‐bed column of 33 cm ID and 2.45 m bed height packed with 1.6 mm × 8.4 ± 1.4 mm cylindrical extrudates for air‐water mass superficial velocities of 0.0023 – 0.094 kg/m²s and 4.5 – 45 kg/m²s, respectively, at atmospheric pressure. Significant deviation was observed from pressure drop and liquid holdup correlations at low liquid flows rates, corresponding to gravity‐driven flow limit. Likewise, liquid saturation is overestimated by correlations at high liquid flow rates, owing to significantly reduced wall effects. Lastly, trickle‐to‐dispersed bubble flow and trickle‐to‐pulsing flow regime transitions are reported using a combination of visual observations and analysis of the magnitude of local pressure fluctuations within the column. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2560–2569, 2018     

Process intensification of distillation using a microwick technology to demonstrate separation of propane and propylene

Process intensification (PI) of distillation using a microchannel distillation (MCD) device successfully reduced the height of a theoretical plate (HETP) in separating propane and propylene to 1.2 cm, representing 10 theoretical stages. Mass transfer is enhanced using thin wicking structures that are 0.17 mm thick in counterflow with vapor. Liquid is segregated in the wicks by applying a siphon relative to the vapor phase, which also enables the device to operate horizontally. A scalable device containing 11 wicks was operated cryogenically in total reflux. The HETP varied between 1.2 and 4.5 cm, representing a dramatic reduction over commercial structured packings and comparable to other PI approaches. Significant improvements are expected with further development. Potential application for intensified distillation processes include distributed manufacturing and difficult separations involving close boiling compounds and meeting high purity specifications. The ultimate application is isotopic enrichment, where the number of stages required is typically multiple thousands. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3690–3699, 2018     

A study of film thickness and hydrodynamic entrance length in liquid laminar film flow along a vertical tube

The liquid film thickness and hydrodynamic entrance length in a vertical tube was studied experimentally and numerically. Measurements using distilled water, 30 wt % MEA and 40 wt % sugar solutions were carried out to investigate the effects of liquid flow rate on the formation of the liquid film. The experimental results validate the new Navier‐Stokes based equation in cylindrical coordinates (Eq. 16) and the volume of fluid (VOF) model giving a competitively high prediction of the liquid film thickness especially in the low Reynolds number region. In addition, a new empirical model and an improved minimal surface model have been first proposed for calculation of the hydrodynamic entrance length, with a relatively reasonable average absolute relative deviation (AARD) of 3.03% and 6.83%, respectively. Furthermore, the effects of the hydrodynamic entry length on the gas–liquid interfacial area calculated by the improved minimal surface model were comprehensively studied, and can be ignored if the ratio of the liquid film length (y) and the hydrodynamic entrance length (λ_E) is lower than 10. However, it should be noted that the hydrodynamic entrance length cannot be ignored in packed columns in which the liquid flow is very complex due to the packings with different structures and materials. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2078–2088, 2018     

Model fitting of sorption kinetics data: Misapplications overlooked and their rectifications

When the model fitting of sorption kinetics data was performed using linearized pseudosecond‐order rate equations based on constant Q_e corresponding to equilibrium sorption, the instantaneous driving force for sorption was underestimated, resulting in an erroneous overestimation of the rate constant. To resolve the issue, a rectification of the model fitting was proposed by accounting for the concentration dependence of Q_e in the model equation based on the fact that Q_e in the equation represents the sorption capacity at that instant as sorption proceeded with time. The rectified approach was validated with experimental data for various sorption systems reported in the literature. It was shown that the rectification yielded true sorption rate constant that characterizes the relationship between sorption rate and solute concentration, thereby resolving the issues associated with the original approach where the specific rate constant was found to depend on solute concentration and sorption time. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1793–1805, 2018     

The effect of liquid bridge model details on the dynamics of wet fluidized beds

Wet fluidized beds of particles in small periodic domains are simulated using the CFD‐DEM approach. A liquid bridge is formed upon particle‐particle collisions, which then ruptures when the particle separation exceeds a critical distance. The simulations take into account both surface tension and viscous forces due to the liquid bridge. We perform a series of simulations based on different liquid bridge formation models: (1) the static bridge model of Shi and McCarthy, (2) a simple static version of the model of Wu et al., as well as (3) the full dynamic bridge model of Wu et al. We systematically compare the differences caused by different liquid bridge formation models, as well as their sensitivity to system parameters. Finally, we provide recommendations for which systems a dynamic liquid bridge model must be used, and for which application this appears to be less important. © 2017 American Institute of Chemical Engineers AIChE J, 64: 437–456, 2018     

A lattice boltzmann approach to surfactant-laden emulsions

We present a pseudopotential lattice Boltzmann method to simulate liquid–liquid emulsions with a slightly soluble surfactant. The model is investigated in 2-D, over a wide parameter space for a single, stationary, immiscible droplet, and surface tension reduction by up to 15% is described in terms of a surfactant strength Λ (which roughly follows a Langmuir isotherm). The basic surfactant model is shown to be insufficient for arresting phase segregation—which is then achieved by changing the liquid–liquid interaction strength locally as a function of the surfactant density. 3-D spinodal decomposition (phase separation) is simulated, where the surfactant is seen to adapt rapidly to the evolving interfaces. Finally, for pendent droplet formation in an immiscible liquid, the addition of surfactant is shown to alter the droplet-size distribution and dynamics of newly formed droplets. © 2018 The Authors. AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers. AIChE J, 65: 811–828, 2019