Dimensionless Transport Research Articles

Comparison of experimental and CFD mass transfer coefficient of three commercial turbulence promoters

The efficiency and performance of electrodialytic cells is based on the flow pattern and mass transfer characteristics, hence, evaluation of cell design, spacers and turbulence promoters (TP), is needed in order to obtain optimal operation. In this, work we compare the mass transfer performance of several plastic nets and cell orientation by means of experimental test and CFD simulation. Excellent agreement in terms of mass transfer was obtained between the two methods. From CFD analysis, it is possible to conclude that the electrochemical reactor design presented in this work, favors the formation of jet flow and stagnant zones in all reactor configurations affecting mass transport flux distribution; this behavior is associated with inlet design and TP orientation. Velocity fields and mass transport flux distributions visualized by CFD analysis, affect the mass transport coefficients values and of course the exact form of dimensionless mass transport correlations here obtained. Finally, 0273R oriented TP configuration seems to have the highest mass transport coefficients, attributed to high contribution of limiting current densities at jet flow zones. A low efficiency under operational conditions is expected.

Applicability of bed load transport models for mixed‐size sediments in steep streams considering macro‐roughness

AbstractIn steep mountain streams, macro‐roughness elements typically increase both flow energy dissipation and the threshold of motion compared to lower‐gradient channels, reducing the part of the flow energy available for bed load transport. Bed load transport models typically take account of these effects either by reducing the acting bed shear stress or by increasing the critical parameters for particle entrainment. Here we evaluate bed load transport models for mixed‐size sediments and models based on a median grain size using a large field data set of fractional bed load transport rates. We derive reference shear stresses and bed load transport relations based on both the total boundary shear stress and a reduced (or “effective”) shear stress that accounts for flow resistance due to macro‐roughness. When reference shear stresses are derived from the total boundary shear stress, they are closely related to channel slope, but when they are derived from the effective shear stress, they are almost invariant with channel slope. The performance of bed load transport models is generally comparable when using the total shear stress and a channel slope‐related reference shear stress, or when using the effective shear stress and a constant reference shear stress. However, dimensionless bed load transport relations are significantly steeper for the total stress approach, whereas they are similar to the commonly used fractional Wilcock and Crowe (WC) transport model for the effective stress approach. This similarity in the relations allows the WC model, developed for lower‐gradient streams, to be used in combination with an effective shear stress approach, in steep mountain streams.

Linking bed morphology changes of two sediment mixtures to sediment transport predictions in unsteady flows

AbstractFlume experiments were conducted to measure bed morphology adjustments in sand/gravel and sand/silt sediment mixtures during repeated hydrographs and to link these changes to sediment transport patterns over multiple time scales. Sediment composition and hydrograph flow magnitude greatly influenced channel morphology, which impacted sediment yield, hysteresis, and transport predictions. Bed load yields were larger and more variable for the sand/silt mixture, as gravel in the sand/gravel sediment inhibited grain entrainment, limited bed form growth, and acted to stabilize the bed. Hysteresis patterns varied due to bed form and surface structure adjustments, as well as the stabilizing effect of antecedent low flows. Using half the data set, a dimensionless fractional transport equation was derived based on excess shear stress. Dimensionless reference shear stresses were estimated in two ways: as bulk values from all transport measurements and by applying a separate limb approach in which values were estimated for each limb of each hydrograph. For the other half of the data set, transport predictions with the separate limb approach were more accurate than those from six existing transport equations and the fractional relationship applied with bulk reference shear stresses. Thus, hydrograph limb‐dependent dimensionless reference shear stress links changing bed morphology and sediment transport, providing a parameter to improve transport predictions during individual flood events and in unsteady flow regimes. This approach represents a framework with which to develop site‐specific transport relationships for varying flow regimes, particularly in cases where detailed bed morphology measurements are not feasible and heterogeneous sediment complicates bed structure over time.

Comparative study of chemo-electro-mechanical transport models for an electrically stimulated hydrogel

The main objective of this work is to introduce a new expression for the hydrogel’s hydration for use within the Poisson Nernst–Planck chemo electro mechanical (PNP CEM) transport models. This new contribution to the models support large deformation by considering the higher order terms in the Green–Lagrangian strain tensor. A detailed discussion of the CEM transport models using Poisson Nernst–Planck (PNP) and Poisson logarithmic Nernst–Planck (PLNP) equations for chemically and electrically stimulated hydrogels will be presented. The assumptions made to simplify both CEM transport models for electric field application in the order of 0.833 kV m−1 and a highly diluted electrolyte solution (97% is water) will be explained. This PNP CEM model has been verified accurately against experimental and numerical results. In addition, different definitions for normalizing the parameters are used to derive the dimensionless forms of both the PNP and PLNP CEM. Four models, PNP CEM, PLNP CEM, dimensionless PNP CEM and dimensionless PNLP CEM transport models were employed on an axially symmetric cylindrical hydrogel problem with an aspect ratio (diameter to thickness) of 175:3. The displacement and osmotic pressure obtained for the four models are compared against the variation of the number of elements for finite element analysis, simulation duration and solution rate when using the direct numerical solver.

Time-dependent sediment transport subjected to downward seepage

Experiments were conducted using cohesionless sand particles with median diameter of 0.48 mm to investigate the time variation of sediment transport rate under the influence of local downward seepage. The experimental results show that the bedload transport rate in terms of volumetric sediment transport rate per unit width increased rapidly with time in the presence of suction, eventually reaching a peak beyond which it started to decrease. The trend of reduction was significantly reduced beyond 8 400 s after the test started. The analytical expression was derived in terms of dimensionless sediment transport rate and dimensionless time. The hypothesized relationships were compared with the experimental data, indicating a good agreement with each other.

Downstream geomorphic variation and local bedrock influence of a steep transitional river: Blue Ridge to Piedmont, South Carolina

Spatial patterns in geomorphic variations are examined in a river transition from the Southern Blue Ridge to the Piedmont physiographic regions. Downstream hydraulic geometry (DHG), fining of bed material, and changes in reach-scale channel-bed morphology (bedforms) were sampled and analyzed. DHG power functions were well developed (r2 > 0.75 for channel area, width, and depth). Bed material showed a general downstream exponential decrease in caliber (from 940 mm to sand). However, variations within the general downstream trends reflect local variations and a rapid transition in hydraulic variables and bedforms at a key zone with substantial tributary inputs, decreases in slope, and a punctuated longitudinal profile. Structurally controlled bedrock knickpoints are associated with anomalous spatial patterns of bedforms and can be distinguished through relationships between dimensionless sediment transport capacity and sediment supply using a sediment regime diagram that is independent of drainage area. Plots of relative grain submergence (R/D84), relative form submergence (R/H), Darcy–Weisbach friction factor (f), and slope vs. area also reveal trends that suggest local factors that are missed by downstream hydraulic progressions. The findings of this study corroborate the utility of scale-independent methods, especially in mountain or transitional environments where fluvial controls may be longitudinally sporadic.

Coarsening and solidification via solvent-annealing in thin liquid films

AbstractWe examine solidification in thin liquid films produced by annealing amorphous ${\mathrm{Alq} }_{3} $ (tris-(8-hydroxyquinoline) aluminium) in methanol vapour. Micrographs acquired during annealing capture the evolution of the film: the initially-uniform film breaks up into drops that coarsen, and single crystals of ${\mathrm{Alq} }_{3} $ nucleate randomly on the substrate and grow as slender ‘needles’. The growth of these needles appears to follow power-law behaviour, where the growth exponent, $\gamma $, depends on the thickness of the deposited ${\mathrm{Alq} }_{3} $ film. The evolution of the thin film is modelled by a lubrication equation, and an advection–diffusion equation captures the transport of ${\mathrm{Alq} }_{3} $ and methanol within the film. We define a dimensionless transport parameter, $\alpha $, which is analogous to an inverse Sherwood number and quantifies the relative effects of diffusion- and coarsening-driven advection. For large $\alpha $-values, the model recovers the theory of one-dimensional, diffusion-driven solidification, such that $\gamma \rightarrow 1/ 2$. For low $\alpha $-values, the collapse of drops, i.e. coarsening, drives flow and regulates the growth of needles. Within this regime, we identify two relevant limits: needles that are small compared to the typical drop size, and those that are large. Both scaling analysis and simulations of the full model reveal that $\gamma \rightarrow 2/ 5$ for small needles and $\gamma \rightarrow 0. 29$ for large needles.

Large thermal transport phase lagging improves thermoelectric efficiency

A thermoelectric (TE) generator driven by fast pulse heating is theoretically analyzed using the hyperbolic transient heat conduction equation. Results show that heat leaking in the transient TE generator can be reduced due to the lagging behavior of non-Fourier heat conduction. The total energy conversion efficiency of the transient TE generator is found to exceed that of normal steady-state operation when the dimensionless non-Fourier thermal transport relaxation time, scaled by length squared over thermal diffusivity, is larger than one. These findings may emerge as a new way to improve TE efficiency.

Dissolution of Weak Acids Under Laminar Flow and Rotating Disk Hydrodynamic Conditions: Application of a Comprehensive Convection–Diffusion–Migration–Reaction Transport Model

A steady-state mass transfer model that incorporates convection, diffusion, ionic migration, and ionization reaction processes was extended to describe the dissolution of weak acids under laminar flow and a rotating disk hydrodynamics. The model accurately predicted the experimental dissolution rates of benzoic acid, 2-naphthoic acid, and naproxen in unbuffered and monoprotic buffers within the physiological pH range for both hydrodynamic systems. Simulations at various flow rates indicated a cube root dependency of dissolution rate on the flow rate for a given bulk pH value for the laminar hydrodynamic system, as proposed earlier by Shah and Nelson (1975. J Pharm Sci 64(9):1518-1520) for neutral compounds. The model has limitations in its ability to accurately predict the dissolution of weak acids under certain conditions that imposed steep concentration gradients, such as high pH values, and for polyprotic buffer systems that caused the numerical solution to be unstable, suggesting that alternative numerical techniques may be required to obtain a stable numerical solution at all conditions. The model presents many advantages, most notably the ability to successfully predict the complex process under physiological conditions without simplifying assumptions, and therefore accurately representing the system in a comprehensive manner.

Modeling of Transient Transport of Soluble Proteins in the Connecting Cilium of a Photoreceptor Cell

A minimal mathematical model describing mass transport in the connecting cilium (CC) of a photoreceptor cell in response to a suddenly increased protein concentration at the base of the CC is developed. Dimensionless governing equations and dimensionless parameters are identified. Analytical solutions are obtained for concentrations of free (diffusion-driven) and motor-driven proteins. The obtained solutions make it possible to predict mass transfer in the CC as a function of two dimensionless transport parameters involved in the model: the diffusivity of free soluble proteins and the transition rate from the diffusion-driven to the motor-driven state. Sensitivities of the obtained solutions to these two parameters are discussed.

Validation and implications of an energy‐based bedload transport equation

AbstractA recently developed bedload equation (Abrahams & Gao, 2006) has the form ib = ωG3˙4, where ib is the immersed bedload transport rate, ω is the stream power per unit area, G = 1−θc/θ, θ is the dimensionless shear stress and θc is the associated threshold value for the incipient motion of bed grains. This equation has a parsimonious form and provides good predictions of transport rate in both the saltation and sheetflow regimes (i.e. flows with low and high θ values, respectively). In this study, the equation was validated using data independent of those used for developing it. The data represent bedload of identical sizes transported in various steady, uniform, fully rough and turbulent flows over plane, mobile beds. The equation predicted ib quite well over five orders of magnitude. This equation was further compared with six classic bedload equations and showed the best performance. Its theoretical significance was subsequently examined in two ways. First, based on collision theory, the parameter G was related to the ratio of grain‐to‐grain collisions to the total collisions including both grain‐to‐grain and grain‐to‐bed collisions, Pg by Pg = G2, suggesting that G characterizes the dynamic processes of bedload transport from the perspective of granular flow, which partly accounts for the good performance of the equation. Moreover, examining the ability of two common equations to predict bedload in gravel‐bed rivers revealed that G can also be used to simplify equations for predicting transport capacities in such rivers. Second, a simple dimensionless form of the equation was created by introducing B = ib/ω. The theoretical nature of the term B was subsequently revealed by comparing this equation with both the Bagnold model and two commonly used parameters representing dimensionless bedload transport rates.

Optimal Taylor–Couette turbulence

AbstractStrongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of $\eta = 0. 716$ is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)$ as a function of the Taylor number $\mathit{Ta}$ and the angular velocity ratio $a= \ensuremath{-} {\omega }_{o} / {\omega }_{i} $ in the large-Taylor-number regime $1{0}^{11} \lesssim \mathit{Ta}\lesssim 1{0}^{13} $ and well off the inviscid stability borders (Rayleigh lines) $a= \ensuremath{-} {\eta }^{2} $ for co-rotation and $a= \infty $ for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)= f(a)\hspace{0.167em} {\mathit{Ta}}^{\gamma } $, with an amplitude $f(a)$ and an exponent $\gamma $. The data are consistent with one effective exponent $\gamma = 0. 39\pm 0. 03$ for all $a$, but we discuss a possible $a$ dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux $f(a)\equiv {\mathit{Nu}}_{\omega } (\mathit{Ta}, a)/ {\mathit{Ta}}^{0. 39} $ is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of ${a}_{\mathit{opt}} = 0. 33\pm 0. 04$, i.e. along the line ${\omega }_{o} = \ensuremath{-} 0. 33{\omega }_{i} $. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position ${r}_{n} $ of the neutral line, defined by $ \mathop{ \langle \omega ({r}_{n} )\rangle } \nolimits _{t} = 0$ for fixed height $z$. For these large $\mathit{Ta}$ values, the ratio $a\approx 0. 40$, which is close to ${a}_{\mathit{opt}} = 0. 33$, is distinguished by a zero angular velocity gradient $\partial \omega / \partial r= 0$ in the bulk. While for moderate counter-rotation $\ensuremath{-} 0. 40{\omega }_{i} \lesssim {\omega }_{o} \lt 0$, the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

RECTANGULAR STORM SEWER DESIGN UNDER EQUAL SEDIMENT MOBILITY

Rectangular storm sewers are conduits delivering water to outfall locations and have sizes that are typically larger than standard pipes, by which they become subject to more sediment deposits during operation and thus require higher flow strengths to maintain the bed clean. This study suggests a design procedure of self-cleansing rectangular sewers based on maintaining a lower limit of Shields stress and an upper limit of dimensionless bedload transport capacity. The lower limit of Shields stress is proposed under two considerations: to sustain equal sediment mobility at the channel bottom instead of selective transport and to avoid progressive deposition of finer grains due to low and reducing flows. The upper dimensionless bedload capacity is determined rationally and confirmed by using experimental data obtained from the literature. An existing bedload transport equation developed under equal sediment mobility is modified to provide a basis for the design method. It is shown that the proposed design procedure can practically be applied for a channel to estimate sediment concentrations by setting the required flow strength of Shields tress and particle size. Charts are given as an example for determining explicitly the channel design parameters. The study demonstrates that despite the high flows imposed, the design specifications determined according to this criterion can reasonably be achieved in practice for a given project.

Closed string transport coefficients and the membrane paradigm

I discuss a correspondence between a fictitious fluid in the black hole membrane paradigm and highly excited closed string states according to the black hole correspondence principle. I calculate the membrane transport coefficients of an electric NS-NS 2-charged black hole and transport coefficients of the highly excited closed string states which possess a Kaluza-Klein number and a winding number. Comparing both the transport coefficients at the correspondence point, I show that, except for the bulk viscosity, the membrane transport coefficients are of the same order as the transport coefficients of the closed string states on the stretched horizon. Also, I show that, except for the bulk viscosity, both the dimensionless transport coefficients, which are defined by dividing the transport coefficients by the entropy density, are exactly equal if the central charge is 6.

Self-Diffusion Coefficient and Viscosity in Fluids

Rate-based models suitable for equipment or transport-reaction modeling require a capability for predicting transport coefficients over a sufficient range of temperature and pressure. This paper demonstrates a relatively simple novel approach to correlate and estimate transport coefficients for pure components over the entire fluid region.The use of Chapman-Enskog transport coefficients for reducing self-diffusion coefficient and viscosity to dimensionless form results in relatively simple mathematical relationships between component dimensionless transport coefficients and residual entropy over the entire fluid region. Dimensionless self-diffusion coefficients and viscosities were calculated from extensive molecular dynamics simulation data and experimental data on argon, methane, ethylene, ethane, propane, and n-decane. These dimensionless transport coefficients were plotted against dimensionless residual entropy calculated from highly accurate reference equations of state.Based on experimental data, the new scaling model introduced here shows promise as: (1) an equation of state-based transport coefficient correlation over the entire fluid region (liquid, gas, and critical fluid), (2) a component transport coefficient correlation for testing transport data consistency, and (3) a component transport coefficient correlation for interpolation and extrapolation of self-diffusion coefficient and viscosity.

Self-Diffusion Coefficient and Viscosity in Fluids

Rate-based models suitable for equipment or transport-reaction modeling require a capability for predicting transport coefficients over a sufficient range of temperature and pressure. This paper demonstrates a relatively simple novel approach to correlate and estimate transport coefficients for pure components over the entire fluid region.The use of Chapman-Enskog transport coefficients for reducing self-diffusion coefficient and viscosity to dimensionless form results in relatively simple mathematical relationships between component dimensionless transport coefficients and residual entropy over the entire fluid region. Dimensionless self-diffusion coefficients and viscosities were calculated from extensive molecular dynamics simulation data and experimental data on argon, methane, ethylene, ethane, propane, and n-decane. These dimensionless transport coefficients were plotted against dimensionless residual entropy calculated from highly accurate reference equations of state.Based on experimental data, the new scaling model introduced here shows promise as: (1) an equation of state-based transport coefficient correlation over the entire fluid region (liquid, gas, and critical fluid), (2) a component transport coefficient correlation for testing transport data consistency, and (3) a component transport coefficient correlation for interpolation and extrapolation of self-diffusion coefficient and viscosity.

A rational sediment transport scaling relation based on dimensionless stream power

AbstractThe concept of stream channel grade – according to which a stream channel reach will adjust its gradient, S, in order to transport the imposed sediment load having magnitude Qb and characteristic grain size Db, with the available discharge Q (Mackin, 1948, Geological Society of America Bulletin 59: 463–512; Lane, 1955, American Society of Civil Engineers, Proceedings 81: 1–17) is one of the most influential ideas in fluvial geomorphology. Herein, we derive a scaling relation that describes how externally imposed changes in either Qb or Q can be accommodated by changes in the channel configuration, described by the energy gradient, mean flow depth, characteristic grain size and a parameter describing the effect of bed surface structures on grain entrainment. One version of this scaling relation is based on the dimensionless bed material transport parameter (W*) presented by Parker and Klingeman (1982, Water Resources Research 18: 1409–1423). An equivalent version is based on a new dimensionless transport parameter (E*) using dimensionless unit stream power. This version is nearly identical to the relation based on W*, except that it is independent of flow resistance. Both versions of the scaling relation are directly comparable to Lane's original relation. In order to generate this stream power‐based scaling relation, we derived an empirical transport function relation relating E* to dimensionless stream power using data from a wide range of stable, bed load‐dominated channels: the form of that transport function is based on the understanding that, while grain entrainment is related to the forces acting on the bed (described by dimensionless shear stress), sediment transport rate is related to the transfer of momentum from the fluid to the bed material (described by dimensionless stream power). Copyright © 2010 John Wiley & Sons, Ltd.

Discussion of “Protecting Vertical-Wall Abutments with Riprap Mattresses” by A. H. Cardoso and C. M. S. Fael

The authors are to be commended for their experimental program and for the attempt to provide guidelines for safe design of scour countermeasures by means of launching aprons. This is a technical field in which the existing literature is still relatively scarce. In this discussion, some remarks will be given about the upstream width wu of the launching apron refer to Fig. 12 of the paper under discussion. The authors did not report specific experimentation in this respect. Indeed, the upstream width of the mattress has received relatively scarce attention in works on riprap countermeasures. Experimental evidence has shown that for short abutments as well, the values of the time-averaged shear stress distribution in the corner region upstream of the abutment face are lower than that in the incoming reach Rajaratnam and Nwachukwu 1983; Molinas et al. 1998; Dey and Barbhuiya 2005. If the phenomenon is modeled at threshold conditions as is typically done in clear-water scour experiments, no scour would be expected upstream of the abutment face in all the regions with stress lower than that in the upstream reach. Experimental evidence on sediment motion during the scour process at short and intermediate abutments Radice et al. 2006,2008 has shown that at the beginning of the erosion process, the particle motion is most intense at the abutment nose where scour starts. In contrast, grain motion is almost negligible at the junction between the duct and abutment walls junction region; here, an appreciable rate of scour depth is observed only after the scour hole whose point of maximum depth is typically at the obstacle nose has reached a significant transverse slope. In terms of design of scour countermeasures, protecting the sediment bed around the abutment nose might be sufficient to prevent the scouring process. An experimental test of local scour at a protected abutment was performed to check this issue. A rectangular duct with a length of 5.8 m and a width of 0.40 m was used. The recess section of the duct was filled with uniform plastic grains with a characteristic size of D = 3.6 mm and a relative density of 1.43. Water discharge was 18.5 l / s, corresponding to the threshold value for incipient particle motion in the undisturbed bed. The abutment model was a vertical plate with a length of 10 cm and a thickness of 1 cm Fig. 1. The experimental installation has been described in detail by Radice et al. 2009, who performed an identical scour experiment without abutment protection. In that study, the possibility of comparing scour data taken under freesurface and covered flows was also demonstrated. In the present experiment, the sediment bed around the abutment nose was protected by means of a square plate as shown in Fig. 1. The plate dimension was 20 cm along both the flow and transverse directions; plate thickness was 1 cm. The plate was roughened gluing on its upper surface sediments identical to those of the loose bed; thus the resulting thickness of the countermeasure was 1.4 mm. The described protection device is actually a rough collar installed at the level of the original sediment bed. However, at scour initiation the collar is likely to behave similarly to a launching apron with an elevation identical to that of the protected sediment bed. Therefore, the following observations on scour initiation should not be significantly affected by the different configuration of the countermeasure. At the beginning of the process, some sediment motion was evident in the junction region Fig. 2. In this region the timeaverage shear stress is expected to be smaller than the threshold value; it is therefore reasonable to assume the motion events as due to the peak stress values. During the motion events, the grains assumed directions opposite to that of the incoming flow, consistent with the structure of the principal vortex. The sediment particles moved downstream of the abutment passing over the protection plate. The grain motion in the junction region resulted in a weak but nonnegligible scour rate. Some particles coming from the upstream reach can be recognized. This is consistent with the definition used here of incipient particle motion, which corresponds to a weak sediment transport condition dimensionless sediment transport rate per unit width= 6 10 �5 . After about 3 min of run time Fig. 3, the junction-region scour depth exceeded the thickness of the protection plate and the sediments

Reformulation of the bed load equation of Meyer‐Peter and Müller in light of the linearity theory for alluvial channel flow

Due to a lack of sufficient theoretical relations, equations for bed load transport in alluvial channel flow have been developed using a variety of empirical assumptions. A linear relationship exhibited in the complex interactions among the three essential components of a river (channel geometry, bed load transport and flow resistance) has led this study to develop a more accurate form of the Meyer‐Peter and Müller (1948, hereafter MPM) relationship, one of the world's most widely used bed load transport equations. This study demonstrates that the application of linearity theory can significantly improve its performance. On the basis of the dataset originally used by MPM, it is shown that the applicable form of the Manning‐Strickler flow resistance relationship can be very satisfactorily determined. The MPM equation is consequently found to be expressible more accurately as Φ = 6[ητb* − 0.047]5/3, where Φ, η and τ*b are the normalized, dimensionless bed load transport rate, bed‐form correction, and flow‐strength parameters, respectively.

A general correlation for mass transfer in isotropic and anisotropic solid foams

Many open-cell foams exhibit ellipsoidal rather than spherical cells. The extent of the anisotropy of the structure typically increases with decreasing cell density. In dimensionless transport correlations, an anisotropy factor has to be introduced in order to lend them general applicability. This paper reports on such a correlation for mass transfer which has been proven to be useful for ceramic and metallic foams with pore counts between 10 and 45 ppi and porosities between 75% and 95%. Based on this novel correlation it was also possible to apply successfully the Lévêque equation which enables the prediction of mass transfer coefficients from pressure drop data.