Stagnant Film Theory Research Articles

The counterbalance of endothelial glycocalyx and high wall shear stress to low-density lipoprotein concentration polarization in mouse ear skin arterioles

Background and aimsAtherosclerosis preferentially occurs at regions in arterial branching, curvature, and stenosis, which may be explained by the geometric predilection of low-density lipoprotein (LDL) concentration polarization that has been investigated in major arteries in previous studies. Whether this also happens in arterioles remains unknown. MethodsHerein, a radially non-uniform distribution of LDL particles and a heterogeneous endothelial glycocalyx layer in the mouse ear arterioles, as shown by fluorescein isothiocyanate labeled wheat germ agglutinin (WGA-FITC), were successfully observed by a non-invasive two-photon laser-scanning microscopy (TPLSM) technique. The stagnant film theory was applied as the fitting function to evaluate LDL concentration polarization in arterioles. ResultsThe concentration polarization rate (CPR, the ratio of the number of polarized cases to that of total cases) in the inner walls of curved and branched arterioles was 22% and 31% higher than the outer counterparts, respectively. Results from the binary logistic regression and multiple linear regression analysis showed that endothelial glycocalyx thickness increases CPR and the thickness of the concentration polarization layer (CPL). Flow field computation indicates no obvious disturbances or vortex in modeled arterioles with different geometries and the mean wall shear stress is about 7.7–9.0 Pa. ConclusionsThese findings suggest a geometric predilection of LDL concentration polarization in arterioles for the first time, and the existence of an endothelial glycocalyx, acting together with a relatively high wall shear stress in arterioles, may explain to some extent why atherosclerosis rarely occurs in these regions.

A new reactive absorption model using extents of reaction and activities. I. Application to Alkaline-salts-CO2 systems

CO2 absorption into basic aqueous solutions is widely used for CO2 separation from gas streams (e.g., for natural gas purification). CO2 loading and ionic strength increase significantly along industrial columns. In absorption modelling, deviation from ideality should then be considered. This study implements a general steady-state model for reactive gas–liquid absorption. Firstly, equilibrium relations, Nernst-Planck diffusion fluxes and reaction rates are written based on activities. Secondly, local fluxes are related by stochiometric constraints through extents of reaction. In a first case study, the model, together with an appropriate thermodynamic representation, was applied with the stagnant film theory (Whitman, 1923) to alkaline salts-water-CO2 systems. The following Arrhenius expression was found for the direct kinetic constant of reaction CO2 + HO– ↔ HCO3–: ln k (m3 mol−1 s−1) = 19.84–5248.8/T (K) – 12% overall AAD. This kinetic law can be used in any system involving this reaction (e.g., aqueous amine solutions). This part I paves the way to the further study of CO2 absorption into aqueous amine solutions.

Lip height effects on pool fire: An experimental investigation

This work studies lip height effects on the heat transfer and combustion characteristics of pool fire. Fire experiments of n-heptane and ethanol with pool diameters (D) of 0.1 m, 0.15 m and 0.2 m were carried out, in which the lip height (h) was increased from 0 until the burning could not be sustained. Results show that for both fuels, as the lip height increases, the flame enters the pool and the flame sheet becomes wrinkled and deformed. The n-heptane fire shows two distinct burning behaviors inside and outside the pool, and the burning rate decreases with the lip height due to heat feedback attenuation and air entrainment restriction. The conductive feedback rate remains almost unchanged with different lip heights for both fuels. For n-heptane, the radiative and convective heat feedback rates generally decrease with the lip height, and the convective heat feedback fraction increases as the flame enters into the pool, suggesting intensified turbulence motion. For ethanol, the radiative heat feedback rate decreases monotonically with the lip height, and the convective heat feedback rate increases slightly, followed by a decrease with h/D. A mass flux correlation based on the modified stagnant film theory is developed for the convection-dominated pool fires, which is in good agreement with the experimental data.

Algal biomass harvesting using low-grade waste heat: the effect of waste heat temperature and air speed on dewatering algal suspension

This study investigated the feasibility of evaporating water from heated algal biomass in an evaporation tank. Computational fluid dynamic (CFD) analysis was performed with Ansys Fluent, and the results were verified with experiments. The results of CFD analysis showed a positive effect on the evaporation rate. As the speed of the air stream increased from 0 to 3 m/s, the evaporation rate increased from 9 to 200 mL/h. It was also observed that the temperature of the mixture of air and water vapor decreases more rapidly, but the temperature of the liquid decreases more slowly, as the speed of the air stream increases. The liquid flow is more disturbed as the speed of the air stream increases while the air streamlines are more parallel at higher speeds. Finally, as the speed of the air stream increased from 0 to 3 m/s, the liquid pressure at the bottom of the tank decreased from 270 to 140 pa. The experimental results were compared with the calculation based on the stagnant film theory and showed excellent agreement. The CFD results underestimated the evaporation rate by 10% compared with the experimental results.

Influence of convective heat transfer modelling in CFD simulations of upward flame spread

Focusing on convective heat transfer modelling upward flame spread scenarios, different methods for calculating the convective heat fluxes are explored. These approaches involve: 1) calculating convective heat transfer based on the stagnant film theory; 2) using a simplified approach based on the stagnant film theory; 3) using Nusselt correlations for natural convection; and 4) modelling convection based on the effective (i.e., laminar plus sgs) thermal diffusivity. Large eddy simulations (LES) of a series of Single Burning Item (SBI) experiments with Medium Density Fiberboard (MDF) and plywood walls are performed. Even though discrepancies are observed, the approach which considered the sgs effects performs overall better and is able to predict both the initial flame growth period and the decay phase with reasonable accuracy (i.e., deviations in the peak HRR of approximately 5% and 34% for the MDF and plywood tests cases, respectively). The predicted total heat fluxes are, in most cases, in fairly good agreement with the experiments (i.e., deviations of up to 15% and 20% for the MDF and plywood tests cases, respectively). The predictions with the other methods are far less satisfactory. Overall, it is demonstrated that accurate convective heat transfer modelling can be important in flame spread scenarios.

Hybrid Modeling for Simultaneous Prediction of Flux, Rejection Factor and Concentration in Two-Component Crossflow Ultrafiltration

Ultrafiltration is a powerful method used in virtually every pharmaceutical bioprocess. Depending on the process stage, the product-to-impurity ratio differs. The impact of impurities on the process depends on various factors. Solely mechanistic models are currently not sufficient to entirely describe these complex interactions. We have established two hybrid models for predicting the flux evolution, the protein rejection factor and two components’ concentration during crossflow ultrafiltration. The hybrid models were compared to the standard mechanistic modeling approach based on the stagnant film theory. The hybrid models accurately predicted the flux and concentration over a wide range of process parameters and product-to-impurity ratios based on a minimum set of training experiments. Incorporating both components into the modeling approach was essential to yielding precise results. The stagnant film model exhibited larger errors and no predictions regarding the impurity could be made, since it is based on the main product only. Further, the developed hybrid models exhibit excellent interpolation properties and enable both multi-step ahead flux predictions as well as time-resolved impurity forecasts, which is considered to be a critical quality attribute in many bioprocesses. Therefore, the developed hybrid models present the basis for next generation bioprocessing when implemented as soft sensors for real-time monitoring of processes.

Grid insensitive modelling of convective heat transfer fluxes in CFD simulations of medium-scale pool fires

Focusing on convective heat transfer modelling of pool fires, different approaches for calculating the convective heat fluxes at the pool surface have been employed, namely to resolve them; model them based on Nusselt correlations for forced or natural convection; model them based on the stagnant film theory. Large eddy simulations of medium-scale, 30 cm in diameter, alcohol pool fires (methanol, ethanol and acetone) are conducted and compared against experimental convective and radiative heat flux measurements. Overall, the best approach is the one based on the stagnant film theory which is only slightly grid sensitive, and provides satisfactory predictions for all the different fuels tested. The predictions using the other approaches are highly grid dependent, due to a fuel rich region formed just above the pool surface when the grid size is refined, which greatly influence the calculation of the convective heat fluxes using the first grid cell values.

The Models Used in Predicting Steam Condensation Occurs during Nuclear Reactor Loss of Coolant Accident

The objective of this paper is to make review and comparison between the methodologies used for modeling condensation with non-condensable, in two-phase flows channel. The important state-of-the art numerical algorithms for the solution of multi-phase conservation equations are reviewed. The methodology for modeling condensation in these algorithms is based on the stagnant film theory. The methodology used in RELAP5/MOD3 that was the most accurate model is rigorously treats the coupling between the heat and mass transfer process, and gas-liquid interphase without iteration. The objective of this paper is to make review and comparison between the methodologies used for modeling condensation with non-condensable, in two-phase flows channel. The important state-of-the art numerical algorithms for the solution of multi-phase conservation equations are reviewed. The methodology for modeling condensation in these algorithms is based on the stagnant film theory. The methodology used in RELAP5/MOD3 that was the most accurate model is rigorously treats the coupling between the heat and mass transfer process, and gas-liquid interphase without iteration.

Numerical study of the coupling between reaction and mass transfer for liquid-liquid slug flow in square microchannels

While the benefits of miniaturization on processes have been widely demonstrated, its impact on microfluidics and local mechanisms such as mass transfer is still little understood. The coupling between reaction and mass transfer in microchannels is simulated for liquid-liquid slug flow. First, the extrapolation to confined flow of the classical model used to calculate interfacial mass fluxes in reactive infinite media was studied. This model consists in estimating transferred fluxes between two phases as a function of the enhancement factor E. Its expression depends on the model used to represent interfacial mass transfer. In infinite media, Lewis and Whitman's stagnant film theory is generally preferred for its simplicity and its reliability. In the case of confined slug flow, the limitation of such a model to predict interfacial fluxes is highlighted. Second, the case of liquid-liquid competitive consecutive reactions in microchannels is considered. The unfavorable impact of the length between droplets on selectivity is emphasized. This is a direct consequence of mass-transport mechanisms in microchannels. © 2010 American Institute of Chemical Engineers AIChE J, 2011

Adsorption of Amylase Enzyme on Ultrafiltration Membranes

A method to measure the static adsorption on membrane surfaces has been developed and described. The static adsorption of amylase-F has been measured on two different ultrafiltration membranes, both with a cutoff value of 10 kDa (a PES membrane and the ETNA10PP membrane, which is a surface-modified PVDF membrane). The adsorption follows the Langmuir adsorption theory. Thus, the static adsorption consists of monolayer coverage and is expressed both as a permeability drop and an adsorption resistance. From the adsorption isotherms, the maximum static permeability drops and the maximum static adsorption resistances are determined. The maximum static permeability drop for the hydrophobic PES membrane is 75%, and the maximum static adsorption resistance is 0.014 m2.h.bar/L. The maximum static permeability drop for the hydrophilic surface-modified PVDF membrane (ETNA10PP) is 23%, and the maximum static adsorption resistance is 0.0046 m2.h.bar/L. The difference in maximum static adsorption, by a factor of around 3, affects the performance during the filtration of a 5 g/L amylase-F solution at 2 bar. The two membranes behave very similarly during filtration with almost equal fluxes and retentions even though the initial water permeability of the PES membrane is around 3 times larger than the initial water permeability of the ETNA10PP membrane. This is mainly attributed to the larger maximum static adsorption of the PES membrane. The permeability drop during filtration exceeds the maximum static permeability drop, indicating that the buildup layer on the membranes during filtration exceeds monolayer coverage, which is also seen by the increase in fouling resistance during filtration. The accumulated layer on the membrane surface can be described as a continually increasing cake-layer thickness, which is independent of the membrane type. At higher concentrations of enzyme, concentration polarization effects cannot be neglected. Therefore, stagnant film theory and the osmotic pressure model can describe the relationship between flux and bulk concentration.

Mass transfer in the vicinity of a separation membrane—the applicability of the stagnant film theory

In membrane separation cells, the permeate velocity is usually predicted applying the stagnant film equation with mass transfer data from impermeable systems, Sh I. In this paper, the applicability of the stagnant film equation is discussed. Laminar momentum and solute transport equations are numerically solved in a permeable parallel plate cell and in a conical cell with a laminar jet impinging vertically to the membrane surface. Membrane surface concentration and permeate velocity predictions are applied to stagnant film equation to obtain Sh I. Sh I data are compared with Sherwood data from impermeable systems with uniform mass production at the wall, and with Sherwood data from impermeable systems with uniform concentration at the wall. This analysis is done for a wide range of the dimensionless numbers characterizing the membrane separation process: Schmidt, Reynolds (or Peclet for the parallel plate cell), Π v and Π π 0 numbers. The stagnant film equation is a quite accurate equation to predict permeate velocity, and the type of impermeable data that must be used depends on the dimensionless groups. The conclusions are identical for both cells.

Model of the Wet Limestone Flue Gas Desulfurization Process for Cost Optimization

A detailed process model of the wet limestone flue gas desulfurization system has been presented. This model can be used to calculate indispensable parameters for estimating costs and next to minimize capital and operating costs. The process model describes most important stage of SO2 removal running in an absorber and a holding tank. It includes absorption of sulfur dioxide, oxidation of SO3-, dissolution of limestone, and crystallization of gypsum. An assumption of thermodynamic equilibrium in the solution has been used. SO2 removal and limestone dissolution calculation has been based on stagnant-film theory. The model has been used for predicting the SO2 removal efficiency in the spray scrubber for process parameters, e.g., L/G, droplet diameter, stoichiometric ratio Ca/S, height of the absorption section, gas velocity, concentration in liquid-phase ions of Mg2+ and Cl-, and liquid pH. This model could be used to describe a multilevel spray system, too. The results of this model are in agreement with data from flue gas desulfurization installation at the Bełchatów Power Plant (Poland).

Modeling mass transfer and substrate utilization in the boundary layer of biofilm systems

The use of microelectrodes in biofilm research allows a better understanding of intrinsic biofilm processes. Little is known about mass transfer and substrate utilization in the boundary layer of biofilm systems. One possible description of mass transfer can be obtained by mass transfer coefficients, both on the basis of the stagnant film theory or with the Sherwood number. This approach is rather formal and not quite correct when the heterogeneity of the biofilm surface structure is taken into account. It could be shown that substrate loading is a major factor in the description of the development of the density. On the other hand, the time axis is an important factor which has to be considered when concentration profiles in biofilm systems are discussed. Finally, hydrodynamic conditions become important for the development of the biofilm surface when the Reynolds number increases above the range of 3000-4000.

Modeling mass transfer and substrate utilization in the boundary layer of biofilm systems

The use of microelectrodes in biofilm research allows a better understanding of intrinsic biofilm processes. Little is known about mass transfer and substrate utilization in the boundary layer of biofilm systems. One possible description of mass transfer can be obtained by mass transfer coefficients, both on the basis of the stagnant film theory or with the Sherwood number. This approach is rather formal and not quite correct when the heterogeneity of the biofilm surface structure is taken into account. It could be shown that substrate loading is a major factor in the description of the development of the density. On the other hand, the time axis is an important factor which has to be considered when concentration profiles in biofilm systems are discussed. Finally, hydrodynamic conditions become important for the development of the biofilm surface when the Reynolds number increases above the range of 3000–4000.

Condensation of Organic Binary Mixtures Flowing Downward inside a Vertical Tube.

Both heat and mass transfer in the gas phase and heat transfer in the liquid phase are examined experimentally for turbulent film condensation of organic binary mixtures flowing downward inside a vertical tube. For average heat flux, gas-liquid interface temperature and liquid phase Nusselt number, experimental results are compared with the analytical solutions based on stagnant film theory and heat transfer relationships for turbulent film condensation of pure vapors. The experimental results regarding heat transfer agree well with the analytical solutions, except that the liquid phase Nusselt number for ethanol and water mixtures is far higer in the experimental results than in the analytical solutions. This high liquid phase Nusselt number is considered to be caused by dropwise condensation in the liquid phase.

Condensation of Organic Binary Mixtures Flowing Horizontally in Horizontal Tube Bundle.

Both heat and mass transfer in the gas phase and heat transfer in the liquid phase are examined experimentally for film condensation of organic binary mixtures such as ethanol-water and methanol-water. Experimental results on average heat flux, gas-liquid interface temperature and liquid-phase Nusselt number are compared with the analytical solutions based on a stagnant film theory and heat transfer relationships for film condensation from a pure vapor. Experimental results on heat transfer agree well with the analytical solutions, except that the liquid-phase Nusselt number in experimental results in the condition of low mass fraction of water is considerably higher than that in analytical solutions. This high value of the liquid-phase Nusselt number is considered to be caused by dropwise condensation in liquid phase. However, its effect on the tube bundle is not so remarkable compared with that in gravity-controlled condensation on a vertical surface, This is considered to be caused by the condensate inundation effect.

Condensation of organic binary mixtures flowing downward inside a vertical tube

Both heat and mass transfer in the gas phase and heat transfer in the liquid phase are examined experimentally for turbulent film condensation of organic binary mixtures flowing downward inside a vertical tube. For an average heat flux, gas-liquid interface temperature and liquid-phase Nusselt number, experimental results are compared with analytical solutions based on stagnant film theory and heat transfer relationships for turbulent film condensation of pure vapors. The experimental results regarding heat transfer agree well with the analytical solutions, except that the liquid phase Nusselt number for ethanol and water mixtures is far higher for the experimental results than predicted by the analytical solutions. This high liquid phase Nusselt number is considered to be caused by dropwise condensation in the liquid phase. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 25(6): 362–381, 1996

Condensation of organic binary mixtures flowing horizontally in a horizontal tube bundle

Both heat and mass transfer in the gas phase and heat transfer in the liquid phase are examined experimentally for film condensation of organic binary mixtures such as ethanol-water and methanol-water. Experimental results on the average heat flux, vapor-liquid interface temperature and liquid-phase Nusselt number are compared with analytical solutions based on stagnant film theory and heat-transfer relationships for film condensation from a pure vapor. Experimental heat transfer results agree well with the analytical solutions, except that the experimental liquid-phase Nusselt numbers under conditions of low mass fraction of water are considerably higher than predicted by the analytical solutions. This high value of the liquid-phase Nusselt number is considered to be caused by dropwise condensation in the liquid phase. However, its effect on the tube bundle is not so remarkable compared with that in gravity-controlled condensation on a vertical surface. This is considered to be caused by the condensate inundation effect. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 25(6): 342–361, 1996

Two‐film theory of flavour release from solids

SummaryA new theory for flavour release from solid or semi‐solid foods is is proposed which uses twolayer, stagnant film theory to calculate the mass transfer coefficient for the flavour across the food‐saliva interface. The theory is applied to the simple case of flavour release from a boiled sweet. By using the colours which dye the sweet as a substitute for flavour, the theoretical predictions are compared with experiment, both for simple solution of the dye into stirred water and for the more realistic case of mass loss on sucking in the mouth. The role of changing food‐saliva interfacial area is explicitly incorporated into the theory and used as a basis for classifying flavour release from other types of food.

The surface-renewal theory of interphase transport: a stochastic treatment

The stagnant-film, boundary-layer, and surface-renewal theories have been regarded as the cornerstone of the science of interphase mass or heat transfer in turbulent environments. The stagnant-film theory has been highly popular and remains so because of its simplicity; however, it is deemed too simplistic and unrealistic. The boundary-layer theory has been derived from a fairly rigorous and self-consistent fluid mechanical theory based on the notion of continuity; nevertheless, this theory is incapable of elucidating random disturbance or chaotic bursting at the interface under turbulent conditions. The surface-renewal theory has been conceived so that the deficiencies of the first two theories can be rectified through incorporation of some statistical components into the description of interphase mass or heat transport. Numerous variants of this theory, giving rise to various mathematical models, have been proposed; still, the acceptance or popularity of the surface-renewal theory appears to lag behind the other two theories. This is probably attributable to the fact that while the mathematical formulation of the theory is abundantly couched in statistical or stochastic parlance, the methodologies and procedures followed are those of continuum mechanics and deterministic mathematics, thereby rendering the model or theory less acceptable. The present work attempts to derive a self-consistent mathematical model of the surface-renewal theory of interphase mass transfer by resorting to the theories and methodologies of stochastic processes based on the Markovian assumption. Specifically, the expression for the contact-time distribution of fluid elements or solid particles participating in the interphase transport has been derived from the stochastic population balance of these elements or particles. Moreover, the expression for the dynamic rate of transfer of molecules or microscopic components across the interface has been derived as the continuous limit of the probability balance equation of the random walks of these entities around the interface. Proper coupling of the two expressions constitutes the desired model. By analogy, this model is applicable to the turbulent interphase heat transport and plausibly to the momentum transport under certain circumstances.