Double-film Model Research Articles

Conjugate mass transfer from a spherical moving droplet: Direct numerical simulations of enhancement by a chemical reaction

Chemical reactions can have a significant impact on the overall rate of mass transfer in fluid–fluid applications (such as gas absorption in a liquid or liquid–liquid extraction). However, as for non reacting systems, the rate at which a solute is exchanged between the two fluids is difficult to predict accurately. Yet from a theoretical point of view, most studies address uniform diffusion transport or creeping flow, i.e. conditions enabling the derivation of analytical or simple numerical solutions of the solute transport equation, therefore neglecting the effect of convection in the case of coupled mass transfer problems. On the other hand, experimental investigations available in the literature provided correlations corresponding to flow conditions, shape and contamination of the interface which are extremely difficult to control precisely.Direct numerical simulation (DNS) is therefore a powerful tool to investigate the coupling of hydrodynamics with transfer and reaction. It was recently applied to model the internal and external resistances (or Sherwood numbers, Shi and She) prevailing during the transfer of a non reacting solute, in the general case of conjugate mass transfer from a moving spherical droplet (Godé et al., 2023; 2024). This study is complemented by considering a first order reaction that consumes the transferred solute in the continuous phase. The results indicate that the double film model, based on these last correlations for Shi and She, with She corrected by an enhancement factor allows obtaining accurate predictions of the overall mass transfer coefficient in the case of a reactive conjugate problem, thus extending the work of Juncu (2002) to flows at moderate or even high Re, as long as the droplet remains spherical and the flow axisymmetric.

A double film model and its application to the stability of liquid–liquid stratified flow

A double film model describing the finite-miscibility structure of interfaces was established. Without losing generality, the viscosity stratified flow was taken as an example in this approach. The double film model was validated by the break interface model and single film model proposed by previous researchers. The results indicate that the viscosity profile within the interface film of fluids has strong effects on the flow stability and the double film model is a universal model to describe the interface film structure of liquid–liquid flow. The interface break model and single film model are two special cases of the double film model. Furthermore, the double film model was adopted to investigate the stability of liquid–liquid stratified flow. The effect of liquid–liquid miscibility, film thickness, interface location and viscosity ratio on the stability of stratified flow was outlined.

The Stability of Finite Miscible Liquid-Liquid Stratified Microchannel Flow with Boundary Slip

ABSTRACTThe effects of boundary slip on the stability of finite miscible/immiscible liquid-liquid stratified microchannel flow were investigated. In this approach, the boundary slip was considered by Navier slip assumption and the finite-miscible liquid-liquid interface was modeled by double film model. The stability of the flow was studied by the small disturbance theory. The results indicated that the effects of boundary slip on the instability of finite miscible stratified microchannel flow with different viscosity ratio, interface location and the property of interface (i.e.thickness and viscosity distribution of mixed layer) are distinct and complex. The effect intensity of upper and lower boundary slip on flow stability is determined by viscosity ratio, interface structure (different Ns) and film thickness. When the interface changes from the channel center to the wall, the critical Re number is enhanced by boundary slip and especially markedly near the critical line and after across the critical line it suddenly decreases to a small value (even to 424). The flow stability always increased by boundary slip.

Analysis of the errors associated with typical pulverized coal char combustion modeling assumptions for oxy-fuel combustion

In CFD models of pulverized coal combustion, which often have complex, turbulent flows with millions of coal particles reacting, the char combustion sub-model needs to be computationally efficient. There are several common assumptions that are made in char combustion models that allow for a compact, computationally efficient model. In this work, oft used single- and double-film simplified models are described, and the temperature and carbon combustion rates predicted from these models are compared against a more accurate continuous-film model. Both the single- and double-film models include a description of the heterogeneous reactions of carbon with O2, CO2, and H2O, along with a Thiele based description of reactant penetration. As compared to the continuous-film model, the double-film model predicts higher temperatures and carbon consumption rates, while the single-film model gives more accurate results. A single-film model is therefore preferred to a double-film model for a simplified, yet fairly accurate description of char combustion. For particles from 65 to 135μm, in O2 concentrations ranging from 12 to 60vol.%, with either CO2 or N2 as a diluent, particle temperatures from the single-film model are expected to be accurate within 270K, and carbon consumption rate predictions should be within 16%, with greater accuracies for a CO2 diluent and at lower bulk oxygen concentrations. A single-film model that accounts for reactant penetration and both oxidation and gasification reactions is suggested as a computationally efficient sub-model for coal char combustion that is reasonably accurate over a wide range of gas environments.

Method of Moments for Computational Microemulsion Analysis and Prediction in Tertiary Oil Recovery

We discuss the application of Helfrich's surface torque density concept to microemulsion design and analysis from three different angles: (i) from the point of view of coarse-grained molecular simulations, using Dissipative Particle Dynamics, including charge interactions and added salt, (ii) using an approximate double-film model for the surface, and (iii) comparison with formulation approaches. The simulations use that the surface torque can be calculated unambiguously from the stress profile, provided the surface is tensionless. Very good agreement is found on predicting optimal salinity (or the absence of that) for a range of surfactants: dioctyl sodium sulfosuccinate, various twin-tailed sulfonates and sodium dodecyl sulfate. The simulations are very fast, on par with times for experiments, thus they could lead to a practical tool for discovery of more efficient surfactants, although much remains to be done with respect to other important variables: oil composition, surfactant mixtures, aggregation in solution, and so on. The microscopic model (second approach) is highly approximate: it is essentially based on two opposing swelling tendencies, that are both of osmotic nature. In accordance with the model, the tails are swollen by the oil and the charged head groups are confined in a salty layer in Donnan equilibrium with the salt solution. In this way, the surface interactions are purely entropic. The comparison of the film model with existing formulation approaches (third approach) covers the interfacial tension minimum, Winsor R theory, quantitative structure property relations (QSPR), hydrophilic-lipophilic deviation (HLD), HLD-net average curvature, and temperature coefficients. Using the surface torque analysis, we succeed in deriving in an ab initio way QSPR empirical coefficients that have been known for decades, but until now, have been obscure in origin.

Effectiveness–NTU relation for packed bed liquid desiccant–air contact systems with a double film model for heat and mass transfer

One-dimensional models were usually utilized to describe the coupled heat and mass transfer processes in packed bed liquid desiccant–air contact systems. In this paper, a double film model was utilized for both parallel and countercurrent flow configurations. The model considered the effects of non-unity values of Lewis factor, unequal effective heat and mass transfer areas, liquid phase heat and mass transfer resistances, changes in solution mass flow rate and concentration. Within the relatively narrow range of operating conditions usually encountered in a specified application, a linear approximation was made to find out the dependence of equilibrium humidity ratio on solution temperature and concentration. Constant approximations of some properties and coefficients were further made to render the coupled equations linear. The original differential equations were rearranged and an analytical solution was developed for a set of newly defined parameters. Analytical expressions for the tower efficiency and other effectiveness values were further developed based on the analytical solution. Comparisons were made between analytical results and numerical integration of the original differential equations and the agreement was found to be quite satisfactory.

Study of a chemical reaction in heterogeneous liquid–liquid medium producing a surfactant and a cosolvent

An experimental study of an exothermic reaction is carried out in a heterogeneous liquid–liquid reaction mixture, producing simultaneously a surfactant and a cosolvent. The mass transfer kinetic is influenced by the presence of these products, as reaction advances. The global rate of the chemical transformation is thus accelerated. The chosen reaction is the saponification of methyl benzoate with a soda solution at 2 M. The reaction is carried out in a Mettler™ RC1 calorimetric reactor. Thermal power profiles released by reaction mixture are used to estimate energetic and chemical kinetic parameters, as well as those linked with mass transfer. Mass balance uses a chemical kinetic law of second order. The quantification of mass transfer between phases is solved using double-film model.

Extraction rates of amino acids by an emulsion liquid membrane with tri-n-octylmethylammonium chloride

The extraction rates of amino acids from alkaline aqueous solution into an emulsion liquid membrane containing tri-n-octylmethylammonium chloride as a carrier and Paranox 100 as an emulsifier were measured using a stirred transfer cell. The effects of agitation speed (0·33–0·66 rev s−1), amino acid concentrations (0·5–50 mol m−3) and temperature (10–45°C) on the extraction rates were examined. The results were analyzed by a double-film model. The mass transfer coefficients of amino acids (0·26–1·58×10−5 m s−1) and their complexes (0·60–1·72×10−5 m s−1) were found to correlate well with the hydrophobicities of the amino acids. It was found that the surfactant layer influenced the mass transfer processes of both amino acids in the aqueous film and their complexes in the organic film. The permeation of amino acids with a large hydrophobicity through the emulsion liquid membrane was promoted by both high distribution and larger mass transfer rates. © 1998 Society of Chemical Industry

On the scavenging of SO2 by large and small rain drops: V. A wind tunnel and theoretical study of the desorption of SO2 from water drops containing S(IV)

An experimental and theoretical study has been carried out to investigate the rate of desorption of SO2 from water drops falling at terminal velocity in air. The experiments were carried out in the Mainz vertical wind tunnel in which water drops of various sizes containing S(IV) in various concentrations were freely suspended in the vertical airstream of the tunnel. The results of these experiments were compared with the predictions of three theoretical models, and with the experiments of Walceket al. This comparison shows that the predictions of the diffusion model of Kronig and Brink in the formulation given by Walcek and Pruppacher agree well with the experimental results for all relevant large and small rain-drop sizes, and for all considered concentrations of S(IV) inside the drops. In contrast, the predictions of the diffusion model which assumes complete internal mixing inside a drop agrees with the experimental results only if the concentration of S(IV) inside the drop is less than that equivalent of an equilibrium SO2 concentration of 15 ppbv. At larger concentrations, the theoretical predictions of the model for complete internal mixing progressively deviate from the experimental results. It is further shown that Barrie's double film model can be used to interpret the resistance to diffusion inside a drop in terms of a diffusion boundary layer inside the drop which increases in thickness with decreasing concentration of S(IV). Applying our results to the desorption of SO2 from small and large rain drops falling below an assumed cloud base, shows that for typical contents of S(IV) inside the drops substantial amounts of SO2 will desorb from these drops unless H2O2 is present in the surrounding air.

Experimentally determined overall burning rates of pulverized-coal chars in specified O 2 and CO 2 environments

Measurements of the size, temperature and velocity of individual pulverized-coal char particles are used to determine the overall burning rates of particles flowing in gaseous environments of specified O2 and CO2 contents. The overall burning rates of the char particles are essentially unaffected by the carbon dioxide content of the ambient gas. When the single film model of a burning carbon particle with CO as the sole heterogeneous reaction product is employed, the chemical reaction rate coefficients determined in gaseous environments of fixed CO2 levels but varying O2 levels exhibit the same temperature dependence. For the Missouri bituminous coal studied, a reaction rate coefficient of 28.4 exp (−2000/RT) g/cm2-s is determined for the C−O2 heterogeneous reaction. The apparent activation energy is in the range expected for burning limited by the combined effects of pore diffusion and the intrinsic chemical reactivity of the particle material. Based on the overall particle burning rates determined, the Thiele modulus estimated for each particle size is in the range which suggests little penetration of oxygen into the particle pores. The results support the single film model of a burning particle with CO as the sole reaction product for coal chars burning under typical pulverized-coal combustion conditions. The results indicate that the double film model of a burning carbon particle is not applicable for particles less than about 130 μm burning under such conditions. A reaction rate constant for the C−CO2 heterogeneous reaction a thousand times greater than the rate constants reported in the literature is required in order to get agreement between measured and calculated temperatures for a given particle size when the double film model is employed.

Mechanism of tear film rupture and formation of dry spots on cornea

The rupture of the tear film covering the cornea and the formation of dry spots is of importance in various pathological states associated with a dry eye. The purpose of this paper is to identify its mechanism and to compute the time required for such a rupture. A two-step, double-film model is proposed which accounts for the real structure of the tear film as composed of a mucous layer and an aqueous layer. The mechanism identifies the key step in the process of rupture to be the instability and eventual rupture of the mucous layer of about 200 to 500 Å thickness, which covers the epithelium, due to the dispersion interactions. This in turn exposes the aqueous layer of the tear film to the hydrophobic cornea, resulting in the observed end result of a spontaneous tear-film rupture or “beading-up.” The proposed mechanism is shown to be consistent with the range of observed breakup times and other clinically observed characteristics of the tear-film rupture. The implications of this mechanism in the normal wearing and tolerance of contact lenses are also indicated.

Intraparticle effects in char combustion II. Steady state analysis

AbstractBased on the results of an earlier paper, a model is developed to include the homogeneous reaction in the external boundary layer. It is assumed, consistent with those results, that there is no homogeneous reaction within the particle. A feasibility region is constructed using limiting cases along the lines described there. Under some conditions, the model predicted up to five steady states for a given set of ambient conditions. For large particles, a flame develops in the boundary layer and the main product is CO2. Under such conditions, the reaction locus coincides with the double film model. While for small particles, no flame develops and the major product is CO. The solution is sensitive to the type of radiative interaction which obtains. The combustion rate increases with increase in particle temperature until a certain point, then decreases with further increase in temperature, and eventually turns back and increases again. Such behavior has been observed in some rate measurement experiments.

Simultaneous heat and mass transfer between gas and liquid phases II.—Analysis of steady state transfer

The method of analysis by the double film model is extended to the general case of the air-aqueous solution system, and the relations among the transfer coefficients of gas and liquid film are derived. Furthermore, the application of the dehumidification operation to the design of the equipment is discussed.