Dimensionless Mass Transfer Rate Research Articles

External mass transfer from/to a single sphere in a nonlinear uniaxial extensional creeping flow

This work systematically simulates the external mass transfer from/to a spherical drop and solid particle suspended in a nonlinear uniaxial extensional creeping flow. The mass transfer problem is governed by three dimensionless parameters: the viscosity ratio ( λ ), the Peclet number ( Pe ), and the nonlinear intensity of the flow ( E ). The existing mass transfer theory, valid for very large Peclet numbers only, is expanded, by numerical simulations, to include a much larger range of Peclet numbers (1 ≤ Pe ≤ 10 5 ). The simulation results show that the dimensionless mass transfer rate, expressed as the Sherwood number ( Sh ), agrees well with the theoretical results at the convection-dominated regime ( P e > 10 3 ). Only when E > 5/4, the simulated Sh for a solid sphere in the nonlinear uniaxial extensional flow is larger than theoretical results because the theory neglects the effect of the vortex formed outside the particle on the rate of mass transfer. Empirical correlations are proposed to predict the influence of the dimensionless governing parameters ( λ , Pe , E ) on the Sherwood number ( Sh ). The maximum deviations of all empirical correlations are less than 15% when compared to the numerical simulated results.

Computational Analyses of Cavitating Flows in Cryogenic Liquid Hydrogen

The objective of this study is to analyze the fundamental characteristics and the thermodynamic effects of cavitating flows in liquid hydrogen. For this purpose, numerical simulation of cavitating flows are conducted over a three dimensional hydrofoil in liquid hydrogen. Firstly, the efficiency of this computational methodology is validated through comparing the simulation results with the experimental measurements of pressure and temperature. Secondly, after analysing the cavitating flows in liquid hydrogen and water, the characteristics under cryogenic conditions are highlighted. The results show that the thermodynamic effects play a significant role in the cavity structure and the mass transfer, the dimensionless mass transfer rate of liquid hydrogen is much larger, and the peak value is about ninety times as high as water at room temperature. Furthermore, a parametric study of cavitating flows on hydrofoil is conducted by considering different cavitation number and dimensionless thermodynamic coefficient. The obtained results provide an insight into the thermodynamic effect on the cavitating flows.

Estimation of boundary-layer flow of a nanofluid past a stretching sheet: A revised model

The previous model for the boundary layer nanofluid flow past a stretching surface with a specified nanoparticle volume fraction on the surface is revisited. The major limitation of the previous model is the active control of the nanoparticle volume fraction on the surface. In a revised model proposed in this paper, the nanoparticle volume fraction on the surface is passively controlled, which accounts for the effects of both the Brownian motion and the thermophoresis under the boundary condition, whereas the Buongiorno's model considers both effects in the governing equations. The assumption of zero nanoparticle flux on the surface makes the model physically more realistic. In the revised model, the dimensionless heat transfer rates are found to be higher whereas the dimensionless mass transfer rates are identically zero due to the passive boundary condition. It is also found that the Brownian motion parameter has a negligible effect on the Nusselt number.

Turbulent mass transfer through a flat shear-free surface

Mass transfer through the flat shear-free surface of a turbulent open-channel flow is investigated over a wide range of Schmidt number (1 ≤ Sc ≤ 200) by means of large-eddy simulations using a dynamic subgrid-scale model. In contrast with situations previously analysed using direct numerical simulation, the turbulent Reynolds number Re is high enough for the near-surface turbulence to be fairly close to isotropy and almost independent of the structure of the flow in the bottom region (the statistics of the velocity field are identical to those described by I. Calmet & J. Magnaudet J. Fluid Mech. vol. 474, 2003, p. 355). The main statistical features of the concentration field are analysed in connection with the structure of the turbulent motion below the free surface, characterized by a velocity macroscale u and an integral length scale L. All near-surface statistical profiles are found to be Sc-independent when plotted vs. the dimensionless coordinate Sc 1/2 yu/v (y is the distance to the surface and v is the kinematic viscosity). Mean concentration profiles are observed to be linear throughout an inner diffusive sublayer whose thickness is about one Batchelor microscale, i.e. LSc -1/2 Re -3/4 . In contrast, the concentration fluctuations are found to reach their maximum near the edge of the outer diffusive layer which scales as LSc -1/2 Re -1/2 . Instantaneous views of the near-surface isovalues of the concentration and vertical velocity are used to reveal the influence of the Schmidt number. In particular, it is observed that at high Schmidt number, the tiny concentration fluctuations that subsist in the diffusive sublayer just mirror the divergence of the two-component surface velocity field. Co-spectra of concentration and vertical velocity fluctuations indicate that the main contribution to the turbulent mass flux is provided by eddies whose horizontal size is close to L, which strongly supports the view that the mass transfer is governed by large-scale structures. The dimensionless mass transfer rate is observed to be proportional to Sc -1/2 over the whole range of Schmidt number. Based on a frequency analysis of the concentration equation and on the Sc -1/2 Re -3/4 scaling of the diffusive sublayer, it is shown that the mass transfer rate at a given Sc is proportional to 1/4 , being the variance of the divergence of the surface velocity field. This yields dimensionless mass transfer rates of the form αSc -1/2 Re -1/4 , where the value of a is shown to result from both the kinematic blocking of the vertical velocity and the viscous damping of the horizontal vorticity components induced by the free surface.

Submerged liquid slag injection in steel melt: scaleup study using cold model and dimensional analysis

Submerged injection of solid flux powder is used in the steel industry to eliminate impurities in an economical way. The efficiency of such an injection process is limited by the fact that only a fraction of the injected particles penetrate into the liquid melt, while the majority remain as bubble encapsulated solids, causing poor heat and mass transfer. Therefore, liquid slag injection can be considered a potential alternative technique in the refining of steel to improve the efficacy of mass transfer in such a process. In the present work, liquid slag injection in a steel melt has been simulated by means of laboratory scale cold model experiments in which, water, paraffin oil and benzoic acid have been used as low temperature analogues for liquid steel, slag and impurities, respectively. Through dimensional analysis it is observed that the modified Froude number can be considered as a criterion for scaling up such a process from a bench scale to a full scale system. A regression analysis has also been carried out to correlate the dimensionless mass transfer rate constant with the relevant dimensionless numbers, namely, dimensionless gas velocity, Froude number, aspect ratio and non-dimensional lance depth.

Deposition of Spherical Particles onto Cylindrical Solid Surfaces: II. Experimental Studies

This paper presents experimental studies of the deposition of silicone oil drops onto two different solid surfaces in an aqueous solution. A series of deposition tests were conducted to measure the dimensionless mass transfer rate (Sherwood number). The effects of three kinds of aqueous solutions and two solid surfaces on the deposition process were studied and compared with the numerical predictions based on the well-known DLVO theory. More specifically, both the experimentally measured and the numerically predicted Sherwood numbers monotonically decrease as the pH value of the aqueous solution increases. It was also found that two ionic surfactant solutions have similar influences while the electrolyte solutions have opposite effects on the deposition rate on different solid surfaces. Finally, comparison of all the experimental results for the bare glass surface with the numerical simulations shows that the deposition process of the silicone oil drops onto the hydrophilic solid surface can be satisfactorily described by the classical DLVO theory. However, the deposition data for the FC725 precoated surface are significantly larger than the numerical predictions. This fact suggests that the so-called non-DLVO attractive interaction is involved in the deposition process with the hydrophobic solid surface. This additional non-DLVO attractive interaction, which is generally called the hydrophobic interaction, still remains to be incorporated into the existing DLVO theory, if this is possible.

DOUBLE-DIFFUSIVE CONVECTION IN AN ANNULAR ENCLOSURE WITH A HOT INNER CYLINDER

Consideration is given to the convection in an electrochemical system described, which enables both opposing or aiding temperature and concentration gradients to be imposed. The flows have double-diffusive characteristics because of the large difference between the thermal and solutal diffusion rates. Complex flow patterns are observed as the parameters are varied. Under certain conditions the flow is found to become a fingering and multilayer structure in an annular enclosure. The dimensionless mass transfer rate Sh increases with increasing G,, and fixed Gr m, and Sh is higher in the aiding case than in the opposing case for the same Gr, and Gr " in the present experimental ranges.

Absorption of water vapour into falling films of aqueous lithium bromide

In this study, experiments have been performed for water vapour absorption into 50 and 60 mass% aqueous lithium bromide solution films flowing down a vertical surface to investigate the effects of liquid diffusivity values, molecular properties of the concentrated solutions and non-absorbable gases. The experimental results for wavy films over a film Reynolds number range of 15–90 indicate larger dimensionless mass transfer rates than for strictly laminar flow when the diffusivity of water in a concentrated lithium bromide solution is less than that in a dilute solution. The complete set of results shows that the physical property data for lithium bromide solutions including the diffusivities measured by Kashiwagi are sufficient to explain mass transfer behavior.

The effect of weak Shear-induced motion on brownian coagulation of aerosol particles

The coagulation rate of a dilute polydisperse aerosol dispersion of particles is considered for small Peclet number, which provides a measure of the ratio of the relative shear-induced motion to Brownian motion between two rigid spherical aerosol particles. The asymptotic form of the relative velocity of two unequal particles immersed in a simple shear flow when they are far apart is obtained. Using a singular perturbation method, a two term expansion for the dimensionless coagulation rate (Nusselt number) as function of the Peclet number is developed. In the limit of the radius of one of the two spheres becoming small, the result agrees with the dimensionless mass transfer rate to an aerosol particle at small Peclet number.

Evaporation of a droplet on a surface

An equation is developed for the rate of evaporation of a liquid droplet sitting on or adhering to an impermeable wall bounding a gas flow. The equation applies to droplets which are small enough to be spherical segments and to lie within the linear portion of the velocity profile. A fundamental approach is taken, starting with the convervation equation for droplet vapor and applying the boundary layer approximation. For a two-dimensional droplet of small thickness, the analysis yields a solution which gives the Sherwood number, the dimensionless mass transfer rate, as a function of the Peclet number, the ratio of convection to diffusion transfer rates

Interwell Tracer Tests To Determine Residual Oil Saturation To Waterflood At Judy Creek Bhl'a'pool

Abstract This paper describes the implementation and interpretation of two successful interwell tests conducted consecutively within five months at the same location in the R5 Zone of the Judy Creek Beaverhill Lake "A" Pool to determine the residual oil saturation to waterflood. An accurate knowledge of Sam was required for the evaluation of the miscible flood performance at Judy Creek. Upon exomining all the conventional methods for Sorw determination, the interwe11 test, though still largely an unproven technique at the time, was deemed to be tire most cost-effective and technically feasible. For the two interwell tests, tritiated water (THO), tritiated n-butonol (TNB) and C-I4 tagged i-amyl alcohol (CIA) were used as tire nonpartitioning and the two partitioning tracers. A "salt-out method was developed for separating and analyzing the tracers in produced water. A chromatographic transformation technique with forced normalization was formulated for direct calculation of Sorw by comparing the separation of the tracer profiles. Since an Sorw value was estimated independently from each of the two partitioning tracers, the reliability of the method was greatly improved. From the results of the first and second tests. Sorw values were determined to be 27 ±1% and 12 ±1% respectively. These two numbers, though vastly different, were self-consistent. Therefore, it is not likely that the discrepancy came from interpretation errors, Further examination of the core analysis data, also supported by the breakthrough times, suggested that 26% of the flow was conducted through a 0.12 m thick high permeability streak, resulting in a high water frontal velocity of 64 m/d and hence a high capillary number (1.2 × 10–6). Based on the published data(29) on the capillary desaturation curve of Caddo limestone this Nc was high enough to mobilize residual oil during the five months of prolonged water flood at high rate prior to the second test. Leaching of light/water soluble components and cooling of the reservoir by the injected water only accounted for 4% PV and 2% PV declines in Sorw in the second test. As well, the close agreement between the Sorw calculated from the TNB and CIA profiles indicated that there was no detectable mobile oil during the tests; the persistent 10% oil cut registered throughout the tests came from the bottom zones (R2-R4). This argument was indirectly proved in the second test by the immediate start-up produced tracer concentrations. The constant Sorw calculated over the whole production curves for each test proves against non-equilibrium tracer transfer during the tests. Based on the data published in the literature, tracer transfer between oil and water should be fast enough to be at near equilibrium conditions. As for the tracer transfer between flowing and dead-end pores, equilibrium can be achieved both at extremely fast and slow transfer rates. Since the contact time and hence the dimensionless mass transfer rate i. e. Damkohler number (equation available in full paper) is directly proporational to the system length L, it is likely that at reservoir-scale the transfer is a fast process.

EXPERIMENTAL STUDY OF NATURAL-CONVECTION HEAT AND MASS TRANSFER IN AN ANNULAR ENCLOSURE WITH A COLD INNER CYLINDER

An experimental study of natural-convection heat and mass transfer flow of a CuS04 + H2SO4 + H2O solution in a horizontal cylindrical annulus is performed using an electrochemical system that enables both opposing or cooperating temperature and concentration gradients to be imposed. The flows have double-diffusive characteristics because of the large difference between the thermal and solutal diffusion rates. It is found that in both cases the interaction between the temperature and concentration fields causes a fingering and multilayer flow structure in the core region. The dimensionless mass transfer rate Sh increases as GrT increased for both the cooperating cases and the opposing cases in present experimental ranges.

Axisymmetric stagnation point flow and mass transfer for power-law fluids II. Moderate schmidt number correction

The theory for axisymmetric stagnation point flow of power-law fluids has been extended to include the correction terms for convective diffusion at moderate Schmidt numbers. The dimensionless mass transfer rate is expressed as an asymptotic series that is valid for Re (1 − n)/3(1 + n) Sc − 1 3 < 1. The result can be used to predict accurate diffusion coefficients for dilute species in fluids with specified power-law characteristics.