Numerical study of drop spreading over saturated pores

Numerical study of the dual effect of pores in liquid spreading over porous surface (flat and spherical) whereby liquid movement is facilitated as well as restricted (visualised by Khanna and Nigam [Khanna and Nigam, Chem. Eng. Sci. 57, 3401–3405 (2002)]) is presented to improve the present understanding of wetting. Using the volume of fluid (VOF) method in a two‐dimensional solution domain, the influence of various parameters viz. drop volume, pore density, surface wettability and liquid properties on the liquid spreading over 2D pellets with saturated pores was numerically investigated. Simulation results were found to capture the key features of the liquid spreading over non‐porous and porous surfaces qualitatively. The variation of spread factor and the apex height of liquid film with time were in a good qualitative agreement with the concept of dual action of pores. The liquid spreading was observed to have a direct proportionality with the pore density, that is, higher the number of pores, better was the liquid spreading. It was also observed that the influence of the pores on the liquid spreading was reduced with decrease in the surface wettability. It is expected that this numerical analysis of the liquid droplet spreading over saturated porous surface will be useful for better understanding of the physics of drop and pore (saturated) interactions.     

The liquid spreading on porous solids: Dual action of pores

Experimental observation of the dual effect of pores in liquid spreading over porous substrates, whereby liquid movement is facilitated as well as restricted is presented based on spreading of micro-liter-sized liquid drops on substrates that have saturated (filled) millimeter-sized pores. The drops were put on porous and nonporous parts of solid substrate. The substrate was then rotated in vertical direction and the resulting motion of drops was recorded by a video camera. The analysis of the recorded images revealed that depending on whether the drop edge is moving toward the pore or away from the pore, the pore acts as accelerator or brake for the drop edge. This dual nature of the saturated pores can be ascribed to the attraction between the liquid in the drop and the liquid inside the pore. Qualitative changes in the morphology of the drop as it slides over saturated pores are also presented to highlight the process. This dual effect of pores is expected to play a major role in processes such as flow through a trickle bed of porous catalyst where it manifests itself in increased wetting efficiencies as well as pronounced hysteresis [Khanna, R., Nigam, K.D.P., 2002. Partial wetting in porous catalyst: wettability and wetting efficiency. Chemical Engineering Science 57, 3401-3405; Maiti et al., 2004. Enhanced liquid spreading due to porosity. Chemical Engineering Science 59, 2817-2820; 2005. Trickle-bed reactors: Porosity induced hysteresis. Industrial and Engineering Chemistry Research, in press.].     

Spreading of liquid droplets on proton exchange membrane of a direct alcohol fuel cell

Spreading of liquid droplets over solid surfaces is a fundamental process with a number of applications including electro-chemical reactions on catalyst surface in membrane electrode assembly of proton exchange membrane (PEM) fuel cell and direct alcohol fuel cell. The spreading process of droplet on the PEM porous substrate consists of two phenomena, e.g., spreading of droplet on PEM surface and imbibition of droplet into PEM porous substrate. The shrinkage of the droplet base occurs due to the suction of the liquid from the droplet into the PEM porous substrate. As a result of these two competing processes, the radius of the drop base goes through a maximum with time. The variation of droplet base and front diameter with time on the PEM porous substrate is monitored using microscope fitted with CCD camera and a PC. It is seen that the droplet base diameter goes through a maximum with time, whereas the front diameter increases continuously with time. Further, methanol droplet spreading and wetting front movement was faster than that for ethanol and deionized water. As the PEM porous substrate is wetted and imbibed well by the methanol compared to ethanol, it is expected that the cross over of methanol would be higher than that of ethanol in direct alcohol fuel cell. It should be noted that cross over of alcohol from anode side to cathode side through membrane is detrimental to the fuel cell operation. The experimental data on the variation of droplet base and wetting front diameter with time is predicted by the model available in the literature.     

Simulating a multiphase reactor with continuous phase transition

A novel multiphase fixed-bed reactor with continuous phase transition for benzene hydrogenation to cyclohexane has been presented by Cheng et al. (A.I.Ch.E. J. 47 (2001a) 1185; Chem. Eng. Sci. 56 (2001b) 6025; 57 (2002) 3407; A.I.Ch.E. J. 49 (2003) 225) which makes use of evaporation of volatile components to remove the reaction heat. This paper investigates issues related to the numerical simulation of the model for this novel fixed-bed reactor. The reactor is supposed to be divided into two parts subject to the phase transition point on the bed level, that is, the liquid-contacted zone at the lower part and the gas-contacted zone at the upper part. A steady-state mathematical model for the reactor is developed. All external mass and heat transfer resistances can be neglected in the case investigated, as well as temperature differences in the particles. The effects of feed inlet temperature, inlet benzene concentration, gas flow rate and liquid flow rate on the reactor performance are theoretically studied. Reliability of the model is verified by bench-scale experiments. The results show that dryout phenomena will occur in the reactor both on the bed-scale and on the pellet-scale under certain conditions.     

Spreading of liquid drops over solid substrates: 'like wets like'

The classic hydrodynamic wetting theory leads to a linear relationship between spreading speed and the capillary force, being determined only by the surface tension of the liquid and its viscosity. Both equilibrium and dynamic processes of wetting are important in adhesion phenomena. The theory appears to be in good agreement with the results generated from experiments conducted on the spreading of poly(dimethylsiloxane) (PDMS) on soda-lime glass substrate and fails to account for the behavior of other liquids. In this study, the spreading kinetics of four different liquids (hexadecane, undecane, glycerol and water) was determined on three different solids, namely, soda-lime glass, poly(methyl methacrylate) (PMMA) and polystyrene (PS). Droplets from the same liquid allowed to spread under identical conditions on three different substrates produce distinctly different behaviors. The results show that the equilibrium contact angles are qualitatively ranked in accordance with the critical surface tension of wetting (γ _c) of the respective solid, i.e., high-γ _c solids caused the low surface tension liquids to assume the least equilibrium spreading (largest contact angle). On the other end, low-γ _c solids with the lowest surface tension liquid produce the most wetting (smallest contact angle). The results suggest that equilibrium spreading could be explained on the basis of the axiom 'like wets like'; in other words, polar surfaces tend to be wetted by polar liquids and vice versa.     

Numerical simulations of drop impact and spreading on horizontal and inclined surfaces

The phenomenon of drop spreading is important to several process engineering applications. In the present work, numerical simulations of the dynamics of drop impact and spreading on horizontal and inclined surfaces were carried out using the volume of fluid (VOF) method. For the horizontal surfaces, the dynamics of impact and spreading of glycerin drops on wax and glass surfaces was investigated for which the experimental measurements were available [Šikalo, Š., Tropea, C., Ganic, E.N., 2005a. Dynamic wetting angle of a spreading droplet. Experimental Thermal and Fluid Science 29, 795-802; Šikalo, Š., Tropea, C., Ganic, E.N., 2005b. Impact of droplets onto inclined surfaces. Journal of Colloid and Interface Science 286, 661-669]. The influence of surface wetting characteristics was investigated by using static contact angle (SCA) and dynamic contact angle (DCA) models. The dynamics of drop impact and spreading on inclined surfaces and the different regimes of drop impact and spreading process were also investigated. In particular, the effects of surface inclination, surface wetting characteristics, liquid properties and impact velocity on the dynamics of drop impact and spreading were investigated numerically and the results were verified experimentally. It was found that the SCA model can predict the drop impact and spreading behavior in quantitative agreement with the experiments for less wettable surfaces (SCA>90^°). However, for more wettable surfaces (SCA<90^°), the DCA observed at initial contact times were order of magnitude higher than SCA values and therefore the DCA model is needed for the accurate prediction of the spreading behavior.     

Fundamentals of bitumen coking processes analogous to granulations: A critical review

A number of coking processes use hot particles to heat liquid bitumen or petroleum residue to cause cracking reactions. These particles may be mineral or coke solids. Interactions of these particles, in fluid beds, moving beds and other types of contactors, are governed by the liquid films on the particle surfaces. This paper explores the analogy between granulation and coking, and suggests that the key relationships that will govern the behavior of wet particles in coking processes are the Stokes number of the particles, the thickness or the liquid films, and the diameter and surface roughness of the particles. The implications for distribution of liquid feed in the reactor, fouling, and defluidization or bogging are discussed. This analysis suggests experiments that can be performed under non‐reactive conditions with scaled variables in order to study phenomena that cannot be observed in situ in high‐temperature cracking processes.     

Residence time distribution of particles in a continuous liquid-solid classifier

Experiments were carried out in a continuous classification column of diameter 191 mm and height 1.47 m with water as the liquid and glass beads as the particles. Initial experiments were carried out with narrowly sized particles and somewhat larger tracer particles which could be separated by screening. The main experiments involved a wide distribution of particle sizes, with injected pulses of tracer particles of slightly higher density separated from samples using an organic liquid of intermediate density. The results show that the mixing behaviour is intermediate between plug flow and perfect mixing. Increasing the discharge rate of underflow product stream decreased both the mean residence time and the degree of classification significantly. At relatively low voidage, small particles settled more quickly and large particles more slowly than predicted on the basis of the approach proposed by Lockett and Al-Habbooby (Trans. Inst. Chem. Eng. 51(1973) 281-292) where each particle fraction is assumed to travel as if it were alone in a suspension of the overall solids concentration.     

Pore structure analysis of an SCR catalyst using a new method for interpreting nitrogen sorption hysteresis

Nitrogen sorption hysteresis of a selective catalytic reduction (SCR) catalyst in its “fresh” and “used” form [Catal. Today 56 (2000) 335] was analysed by employing the Corrugated Pore Structure Model (CPSM-nitrogen) reported elsewhere [Ind. Eng. Chem. Res. 39 (2000) 3747 and Ind. Eng. Chem. Res., 39 (2000) 3764]. The BET surface area and intrinsic pore volume, and surface area distributions were deduced via the CPSM fitting over the relevant hysteresis loop and compared to those obtained by applying various conventional methods. CPSM predictions of the total specific pore surface area, are in perfect agreement with BET estimates, while those calculated by the Roberts method, irrespective of the hysteresis loop branch chosen, deviate substantially. CPSM prediction of tortuosity factors (CPSM-tortuosity [Ind. Eng. Chem. Res., in press]) for the catalysts under consideration were found to be: τ_CPSM,fresh=4.6 and 4.5. These values are typical of porous catalysts and approach those determined experimentally (i.e. τ=5–6 [Appl. Catal. 10 (1996) 299]). The pore volume distribution of the latter catalyst obtained from mercury porosimetry measurements approaches that deduced by the CPSM method.     

CFD approach for simulation of bitumen froth settling process - Part I: Hindered settling of aggregates

Bitumen or heavy oil aggregates are formed when bitumen emulsions, consisting of emulsified water droplets dispersed solids and precipitated asphaltenes, are treated with aliphatic solvents. While settling, the aggregates exhibit zone settling mode with the development of a sharp oil and settling zone interface. Previous research [Long Y, Dabros T, Hamza H. Structure of water/solids/asphaltenes aggregates and effect of mixing temperature on settling rate in solvent-diluted bitumen. Fuel 2004;83:823-32] provides settling experimental data for bitumen aggregate settling and a Richardson-Zaki approximation was proposed by the authors with modified exponents for simulating the settling behavior of aggregates. However, the need for modified exponents and their dependence on aggregates and solvents used was not explained. Since the aggregates exhibit hindered settling, where the settling rate is different from that of individual particles or aggregates, numerous settling models have been proposed to correlate particle swarms to single particle via drag correlations [Richardson JF, Zaki WN. Sedimentation and fluidization: Part I. Trans Inst Chem Eng 1954;32:35-53; John G, Maan RA. Velocity-voidage relationships for fluidization and sedimentation in solid-liquid systems. Ind Eng Chem Proc Des Dev 1977;16:206-14]. The compaction zone, due to high concentrations of solids and the effect of their resultant weight during settling is also often ignored. In this work, the hindered settling behavior of bitumen aggregates is first studied in a CFD framework using two models: (a) modified Richardson-Zaki approximation by Long et al. [Richardson JF, Zaki WN. Sedimentation and fluidization: Part I. Trans Inst Chem Eng 1954;32:35-53] and (b) the Syamlal-O’Brien model [John G, Maan RA. Velocity-voidage relationships for fluidization and sedimentation in solid-liquid systems. Ind Eng Chem Proc Des Dev 1977;16:206-14]. To address the limitations of the two models, a new model is proposed that incorporates the irregular (fractal) structure of aggregates by considering the aggregates as porous liquid-filled solids that are fractal in nature. Results, from the new fractal model, are found to be in good agreement with empirical data.     

Pore network model of deactivation of immobilized glucose isomerase in packed-bed reactors II: three-dimensional simulation at the particle level

Immobilized glucose isomerase is widely used for converting glucose to fructose by enzymatic isomerization. The process takes place in a packed-bed reactor consisting of mesoporous particles with distributed pore sizes and interconnectivities. Its efficiency is, however, significantly affected by deactivation of the mesoporous particles. In this paper, we study deactivation of the mesoporous particles using a three-dimensional pore network model of the pore space with distributed pore sizes and interconnectivities, and investigate several plausible mechanisms of deactivation of the porous particles. The results of the present study, which will be used as the input for simulation of the phenomenon at the reactor level, demonstrates the strong effect of the particles’ morphology on the deactivation process.     

AIR ENTRAPMENT DURING LIQUID INFILTRATION OF POROUS MEDIA

Some aspects of the interfacial phenomena that occur during liquid infiltration of porous media are discussed. Experimental data are presented on the critical speed at which air bubbles are trapped when a horizontal liquid surface passes (from below) across an isolated cylindrical rod or filament whose axis is horizontal. The results are correlated over a wide range of liquid viscosities and surface tensions. We observe that bubble entrapment occurs when the Capillary number exceeds a value defined by $ where γ is the so-called Property number, defined by $ The coefficients A and m depend upon the wetting characteristics of the liquid with respect to the solid (filament). A simple physical model is proposed which is in qualitative agreement with the observations.

In a porous bed of nonwoven filaments the physical phenomena that occur during wetting are different from those that occur on a single filament. Discussion of flow through such a porous medium leads to a simple model that describes recent data of others on removal of the initially entrapped air from the medium     

Some aspects of wetting/dewetting of a porous medium

Various features of wetting/dewetting of porous media are examined. The phenomenon of capillary hysteresis is illustrated by a vertical capillary tube which consists of an alternating sequence of convergent—divergent conical sections. A study of the kinetics of wetting of this tube by a liquid shows that when the velocity of the liquid/vapour meniscus is plotted against the height of penetration, it oscillates about the Washburn velocity—distance curve and performs Haines jumps. A general macroscopic equation is derived for the rate of wetting/dewetting of a porous medium having randomly distributed, finely divided particles or pores. Use is made of the Forchheimer equation, which is an extension of Darcy's equation to higher Reynolds numbers. Dissipative energy terms due to internal fluid calculaton and to irreversible movements of the meniscus strongly affect the initial rate of imbibition, but as the wetting progresses the Reynolds number decreases and Washburn's equation prevails.The application of percolation theory to wetting/dewetting phenomena in porous media is studied. The use of percolation theory by Kirkpatrick and Stinchcombe to find the electrical conductivity of inhomogeneous solid mixtures is adapted to determining the permeability of a porous medium to fluid flow. It is also shown how the relation between the “precolation probability” and the concentration of “unblocked” channels or pores can be applied in calculating the capillary pressure—desaturation curve in drainage. In particular, percolation theory predicts that a threshold pressure or break-through pressure is required before a non-wetting fluid can displace a wetting fluid in a porous medium. It is often convenient to use tree-like or branching lattice networks as models of a porous medium, because these are amenable to exact solutions in regard to percolation probability and permeability. The percolation properties of porous medium models which consist of lattice networks of cylindrical channels with a distribution of cross-sections and also of randomly packed rotund particles are examined and their relevance to wetting/dewetting phenomena discussed.     

液体与多孔固体颗粒间反应的模型研究

为探讨流休一多孔固体颗粒非催化反应模型中液固反应与气固反应的差别,本文用合成的一系列具有不同孔结构参数的多孔颗粒,考察了液固界面间的浸润现象(毛细现象)作为一种质量传递过程,对液体-多孔颗粒间的反应率～时间关系的影响,根据液体反应物在反应初始时刻进入颗粒的不同方式,定义了三类浸润条件,并对其中的两类提出了质量平衡方程和解析解.     

Modelling and experimental validation of a fluidized-bed reactor freeboard region: Application to natural gas combustion

A theoretical and experimental study of natural gas–air mixture combustion in a fluidized bed of sand particles is presented. The operating temperatures are lower than a critical temperature of 800 °C above which the combustion occurs in the vicinity of the fluidized bed. Our study focusses on the freeboard zone where most of the methane combustion takes place at such temperatures. Experimental results show the essential role of the projection zone in determining the global thermal efficiency of the reactor. The dense bed temperature, the fluidizing velocity and the mean particle diameter significantly affect the thermal behaviours.A model for natural gas–air mixture combustion in fluidized beds is proposed, counting for interactions between dense and dilute regions of the reactor [P. Pré, M. Hemati, B. Marchand, Study of natural gas combustion in fluidised beds: modelling and experimental validation, Chem. Eng. Sci. 53 (1998) (16), 2871] supplemented with the freeboard region modelling of Kunii–Levenspiel [D. Kunii, O. Levenspiel, Fluidized reactor models: 1. For bubbling beds of fines, intermediate and large particles. 2. For the lean phase: freeboard and fast fluidization, Ind. Eng. Chem. Res. 29 (1990) 1226–1234]. Thermal exchanges due to the convection between gas and particles, and due to the conduction and radiation phenomena between the gas-particle suspension and the reactor walls are counted. The kinetic scheme for the methane conversion is that proposed by Dryer and Glassman [F.L. Dryer, I. Glassman, High-temperature oxidation of CO and CH₄, Proceedings of the 14th International Symposium on Combustion, The Combustion Institute, Pittsburg (1973) 987]. Model predictions are in good agreement with the measurements.     

Residence time distribution of the liquid in gas-liquid cocurrent upflow fixed-bed reactors

The authors present an experimental investigation of the residence time distribution (RTD) of the liquid in a gas-liquid upflow fixed-bed reactor with porous and nonporous particles and air/Newtonian or non-Newtonian systems. The piston-dispersion-exchange model with Danckwerts boundary conditions was used to describe the liquid flow. In the case of porous particles, the dynamic evolution of the tracer concentration in the particles was described in terms of diffusion phenomena. An imperfect pulse method was used to estimate the model parameters directly from the experimentally nonideal input and output response.     

PORE SCALE MODEL FOR FLOW REGIME TRANSITION IN A TRICKLE BED REACTOR

The hydrodynamic modeling of gas-liquid cocurrent downflow through a trickle bed reactor based on pore scale is presented. The pore scale hydrodynamic is related to the macroscopic scale flow parameters. The two-phase flow at pore level channel is modeled similar to annular two-phase flow in tubes. Using the film instability due to shear by the gas at the pore level channel, the transition criterion for the trickle flow to pulse flow regime is obtained. The model predictions agree with the published data. A model for transition from partial wetting to complete wetting in trickling flow is presented. The model predictions are in agreement with previous models. The model indicates better wetting of the smaller size packing for the same liquid mass flux.     

Combination of a Monte Carlo approach with the contact time distribution concept for the steady-state modeling of an isothermal heterogeneous coordinated anionic ring opening polymerization reactor

In this paper, the possibility of combining a molecular level Monte Carlo simulation with a chemical engineering model of an isothermal fixed-bed reactor is demonstrated. This approach is applied to the isothermal heterogeneous coordinated anionic ring opening polymerization of ε-caprolactone. The contact time distribution (CTD) concept as defined by Orcutt et al. (Chem. Eng. Prog. Symp. Ser. 38 (58) (1962) 1), Nauman and Collinge (Chem. Eng. Sci. 23 (1968a) 1309) and Shinnar et al. (Chem. Eng. Sci. 27 (1972) 1627) is used. The contact time is the time spent by a reactant within the pores of the pellets constituting the fixed-bed. The classical monodisperse model represents the hydrodynamic and mass transfer in the reactor. The CTD is calculated from this model according to Shinnar et al. theory. From that point, the reactor outlet monomer conversion can be calculated analytically, the ε-caprolactone consumption being a first-order process. Furthermore, the molecular size distribution (MSD) of the oligomers at the reactor outlet is computed on the basis of Monte Carlo simulations. Comparisons with experimental data are given.     

Dynamics of the wetting process on dielectric barrier discharge (DBD)-treated wood surfaces

Protection and preservation of wood properties in exterior environments can only be ensured if the surface is coated with a paint or varnish. In our experiments a dielectric barrier discharge (DBD) was used as a wood surface pretreatment for improvement of the subsequent deposition of thin paint layers from solutions onto these surfaces. As the adsorption, interfacial interactions and adhesion of paints are strongly dependent on surface wettability, the dynamics of the wetting process were analyzed. The results show that the water contact angle decreases after the DBD treatment, proving a more wettable surface. Additionally, the spreading of paint solution on the DBD-treated surface is more isotropic, showing a lower tendency to elongate along the wood fiber orientation.     

PORE SCALE MODEL FOR FLOW REGIME TRANSITION IN A TRICKLE BED REACTOR

The hydrodynamic modeling of gas-liquid cocurrent downflow through a trickle bed reactor based on pore scale is presented. The pore scale hydrodynamic is related to the macroscopic scale flow parameters. The two-phase flow at pore level channel is modeled similar to annular two-phase flow in tubes. Using the film instability due to shear by the gas at the pore level channel, the transition criterion for the trickle flow to pulse flow regime is obtained. The model predictions agree with the published data. A model for transition from partial wetting to complete wetting in trickling flow is presented. The model predictions are in agreement with previous models. The model indicates better wetting of the smaller size packing for the same liquid mass flux.