Measured Sherwood Numbers Research Articles

Investigation of mass transfer in milli-channels using high-resolution microfocus X-ray imaging

In this work, the absorption rate of a single Taylor bubble of carbon dioxide in water was investigated within vertical capillaries using high resolution X-ray imaging. The liquid side mass transfer coefficient was calculated from the changes in the size of the bubble at constant pressure obtained from the high-resolution X-ray images by image processing. The bubbles were continuously monitored by holding the bubble stationary in a downward flow of liquid. The processed images, which give the volume of the bubble with high accuracy as a function of time, were processed to evaluate the liquid side mass transfer coefficient between bubble and liquid using the mass conservation equation.The experiments covered a large range of initial Taylor bubble length varying from 5 to 22mm. The results show that the measured Sherwood numbers depend strongly on the bubble length and also equivalent diameter, which is the same trend as in previously reported results for larger pipe sizes. However the values of measured Sherwood numbers could not be predicted by available correlations. As a result a new mass transfer coefficient in the form of Sherwood number and as a function of Peclet number as well as the ratio of bubble equivalent diameter to capillary diameter (deq/D) is presented. The proposed correlation is applicable for a large range of the ratio deq/D that varies from 0.8 to 1.6. The average relative error between measured Sherwood number and the one calculated with the new correlation is less than 9.6%.

Absorption and Chemisorption of Small Levitated Single Bubbles in Aqueous Solutions

The absorption and chemisorption of small bubbles with N2 or CO2 were investigated experimentally in aqueous and alkaline solutions. Different bubble sizes were studied ranging from 0.1 to 2.5 mm in alkaline concentrations of 0.1 mM to 1 M NaOH. The experiments were conducted in a device consisting of a converging microchannel with a down flowing liquid. Levitation positions of single bubbles were optically characterized. A correlation was developed for the drag force coefficient, CD, including wall effects based on the force equilibrium. A linear decrease of bubble diameters was identified with and without chemical reaction, which is referred to as a rigid bubble surface area. Measured Sherwood numbers agree well with the literature values for the investigated Reynolds number range.

Mass transfer from a bubble in a vertical pipe

Mass transfer from single carbon dioxide bubbles in vertical pipes is measured using a stereoscopic image processing method to develop a mass transfer correlation applicable to a wide range of bubble diameters in standard pipe sizes. The diameters of pipes used are 12.5, 18.2, and 25.0mm and the bubble diameter ranges from 5 to 26mm. The ratio, λ, of the bubble diameter to the pipe diameter is varied from 0.2 to 1.8, which covers various bubble shapes such as spheroidal, wobbling, cap, and Taylor bubbles. Measured Sherwood numbers, Sh, strongly depend on bubble shape, i.e., Sh of Taylor bubbles differs from that of spheroidal and wobbling bubbles. The Sherwood numbers are correlated in terms of the Peclet number Pe and λ. The applicability of the proposed correlation to long-term bubble dissolution process is examined through comparisons between measured and predicted dissolution processes. The predictions are carried out by solving mass conservation equations not only for carbon dioxide but also for nitrogen and oxygen. Good agreements are obtained in the dissolution processes for various bubble sizes and the three pipe diameters.

Buoyancy Driven Mass Transfer in a Liquid Desiccant Storage Tank

A new concept for long-term solar thermal storage is based on the absorption properties of aqueous calcium chloride. Water, diluted and concentrated calcium chloride solutions are stored in a single tank. An immersed heat exchanger and stratification manifold are used to preserve long-term sorption storage, and to achieve thermal stratification. The feasibility of sensible heating the tank via large-scale natural convection without mixing salt solutions is demonstrated via measurements of velocity, CaCl2 mass fraction, and temperature in a 1500 l prototype tank. Experiments are conducted over a practical range of the relevant dimensionless parameters. For Rayleigh numbers from 3.4 × 108 to 5.6 × 1010 and buoyancy ratios from 0.8 to 46.2, measured Sherwood numbers are 11 ± 2 to 62 ± 9, and the tank is thermally stratified. Convective mixing between salt layers is inhibited by the presence of a steep density gradient at the interface between regions of differing mass fraction. The predicted storage time scales based on mixing via natural convection for the reported Sherwood numbers are 160–902 days.

Comparison of different ED stack conceptions when applied for drinking water production from brackish waters

Three types of electrodialysis (ED) and electrodeionization (EDI) stacks are studied when treating NaCl solutions in the range of concentrations from 10 − 5 to 3 × 10 − 2 M: (1) with a non-conducting network spacer, (2) with a mixed ion-exchange monolayer bed, (3) with profiled membranes. The Sherwood number characterizing the desalination rate is measured in recirculation regime when the concentration of feed solution is slowly decreasing in time. The data obtained are compared with the results calculated and measured for “empty” desalination channels not containing any filling. It was established that the measured Sherwood numbers at overlimiting currents in stacks with filling are higher than that in “empty” channel under the same potential drop, while the latter, in turn, are higher than the Sherwood numbers calculated for limiting current density. The mass transfer rate in several cases (under 2.5 V par cell pair in diluted, < 10 − 4 M, solutions and high flow rates, > 7 dm 3 h − 1 dm − 1 , a stack with profiled membranes) may be 4 times higher than that in “empty” channel at limiting current density. The stacks with profiled membranes are shown to be effective in the overall range of concentrations. The stacks with non-conducting spacer can be used if the feed solution concentration is not too low, > 2 × 10 − 3 M in our experiments. The stacks with ion-exchange resins are more preferable in the case of treatment of strongly diluted solutions (e.g. at the second stage following an ED with profiled membranes), as well as in the cases where it is necessary to use a compact unit characterized by a low flow velocity, though the power consumption is slightly higher.

Single-Droplet Evaporation Kinetics and Particle Formation in an Acoustic Levitator. Part 1: Evaporation of Water Microdroplets Assessed Using Boundary-Layer and Acoustic Levitation Theories

The suitability of a single droplet drying acoustic levitator as a model for the spray drying of aqueous, pharmaceutically-relevant solutes used to produce protein-loaded particles has been examined. The acoustic levitator was initially evaluated by measuring the drying rates of droplets of pure water in dependence of drying-air temperature and flow rate. The measured drying rates were higher than those predicted by boundary layer theory because of the effects of primary acoustic streaming. Sherwood numbers of 2.6, 3.6, and 4.4 at drying-air temperatures of 25 degrees C, 40 degrees C, and 60 degrees C were determined, respectively. Acoustic levitation theory could predict the measured drying rates and Sherwood numbers only when a forced-convection drying-air stream was used to neuralize the retarding effect of secondary acoustic streaming on evaporation rate. At still higher drying-air flow rates, the Ranz-Marshall correlation accurately predicts Sherwood number, provided a stable droplet position in the standing acoustic wave is maintained. The measured Sherwood numbers and droplet Reynolds numbers show that experiments performed in the levitator in still air are taking place effectively under conditions of substantial forced convection. The similitude of these values to those occurring in spray dryers is fortuitous for the suitability of the acoustic levitator as a droplet evaporation model for spray drying.

A new viscous sublayer influx (VSI) concept for near-wall turbulent momentum, heat and mass transfer

This paper presents a new viscous sublayer influx (VSI) concept to describe near-wall turbulent momentum, heat and mass transfer. Based on visual studies, this concept takes account of a viscous sublayer adjacent to the wall, which is not directly affected by the bursts occurring in the wall region. Fluid penetrates only due to a wallward flow into this viscous sublayer. Thus, in contrast to the known surface renewal concept, the new VSI concept is consistent with visual flow studies and, in addition, makes it possible to meet the experimentally found limiting condition Sh ∼ 3√ Sc Sc→∞ for mass transfer. In this work, two models have been developed from the new VSI concept. The simplified viscous sublayer influx model follows the known models in literature and provides analytical equations for the profiles in the wall region. This model gives an explanation for the varying experimental results on the time intervals between successive bursts and predicts them in quantity by using measured Sherwood numbers at very high Schmidt numbers. The second, more detailed viscous sublayer influx model approximates the wallward flow in the viscous sublayer with a spherical stagnation point flow. The profiles are calculated from two ordinary differential equations. Using measured Sherwood numbers at very high Schmidt numbers, this model provides normal velocity fluctuations at the wall that agree well with experimental data. Furthermore, both models provide axial velocity fluctuations near the wall and Nusselt/Sherwood numbers in the range 0.5 ≤ Pr, Sc≤ 10 5 that both correspond with experimental data.

Heat transfer and flow field in a pipe with sinusoidal wavy surface—II. Experimental investigation

In Part I of this paper the heat and mass transfer in a pipe with a wavy surface was studied numerically. To validate the predictions and to close the gap in the Reynolds number range 400 < Re dm < 2000, where a numerical simulation of the transitional flow structure was not possible, an experimental investigation was performed. Applying the naphthalene sublimation technique, the local mass transfer was studied along the axis of the pipe. Using analogy functions, the measured Sherwood numbers were transformed into Nusselt numbers. In addition to the results of the mass transfer measurements this paper also presents flow visualization experiments.

Measurements of mass transfer between particles and gas in packed tubes at very low tube to particle diameter ratios

Experimental results for the mass transfer between spherical naphthalene particles and air in packed tubes of very low tube to particle diameter ratio (D/d=1.41, 1.98, and 3.77) are presented. During the experiments the Reynolds number (2.4<Re 0<1500), the bed length, and the test temperature have been varied. Data reduction has been carried out with and without accounting for axial dispersion in the model. The measured Sherwood numbers are compared with the predictions according to the correlation of Gnielinski and of Wakao/Funazkri, originally developed for large packed beds. The porosity of packings at smallD/d-ratios is discussed.

Evaporative mass transfer in turbulent forced convection duct flows

Experiments were performed to determine the mass transfer characteristics for evaporation from partially filled pans of distilled water recessed in the floor of a flat rectangular duct through which turbulent air flow was passed. During the course of the experiments, parametric variations were made of the Reynolds number of the air flow, the streamwise length of the pan, and the distance between the top of the pan and the water surface (hereafter referred to as the step height). For all of the operating conditions of the experiments, the measured Sherwood numbers were well correlated with the Reynolds number provided that the step height was used as the characteristic dimension. Guided by analytical considerations, a second correlation was constructed which provides Sherwood number predictions for operating conditions corresponding to pans longer than those used in the present experiments. By making use of the analogy between heat and mass transfer, it was shown how Nusselt numbers can be obtained from the Sherwood number correlations.

Evaporation of volatile liquids from an open‐topped, partially filled container to an air stream

AbstractExperiments were performed to measure the evaporative mass transfer from a partially filled, slot‐like container recessed in the floor of a flat rectangular duct through which turbulent air flow was passed. Toluene and cumene were used as the evaporating liquids, and systematic variations were made of the Reynolds number and of the distance between the top of the container and the surface of the evaporating liquid. The measured Sherwood numbers displayed unconventional dependences on both the Reynolds and Schmidt numbers as well as a complex dependence on the top‐to‐surface distance.

A wind-tunnel model study of forced convective heat transfer from cylindrical grain storage bins

Forced convective heat transfer from a series of model cylindrical grain storage bins has been modelled in a wind-tunnel experiment. Three model bins of similar geometry but different heights were placed in a simulated atmospheric boundary layer and their mean Sherwood numbers estimated by the naphthalene sublimation technique. The measured Sherwood numbers can be converted to Nusselt numbers by plausible hypotheses about the dependence of heat or mass transfer rate on molecular diffusivity. The transfer rates from the model walls are shown to be significantly higher than those from two-dimensional circular cylinders under the same conditions. A significant amount of the total mass transfer is found to occur from the conical roof.