Unit Mass Of Liquid Research Articles

RESEARCH OF EXTERNAL MASS TRANSFER PROCESSES FOR ADSORPTION FROM SOLUTIONS IN A APPARATUS WITH STIRRING

A study has been mode of transport-controlled mass transfer-controlled to particles suspended in a stirred vessel. The motion of particle in a fluid was examined and a method of predicting relative velocities in terms of Kolmogoroff’s theory of local isotropic turbulence for mass transfer was outlined.
 To provide a more concrete visualization of complex wave form of turbulence, the concepts of eddies, of eddy velocity, scale (or wave number) and energy spectrum, have proved convenient.
 Large scale motions of scale contain almost all of the energy and they are directly responsible for energy diffusion throughout the stirring vessel by kinetic and pressure energies. However, almost no energy is dissipated by the large-scale energy-containing eddies. A scale of motion less than is responsible for convective energy transfer to even smaller eddy sires. At still smaller eddy scales, close to a characteristic microscale, both viscous energy dissipation and convection are the rule. The last range of eddies has been termed the universal equilibrium range. It has been further divided into a low eddy size region, the viscous dissipation subrange, and a larger eddy size region, the inertial convection subrange.
 Measurements of energy spectrum in mixing vessel are shown that there is a range, where the so called -(5/3) power law is effective. Accordingly, the theory of local isotropy of Kolmogoroff can be applied because existence of the internal subrange. As the integrated value of local energy dissipation rate agrees with the power per unit mass of liquid from the impeller, almost all energy from the impeller is viscous dissipated in eddies of microscale.
 The correlation for mass transfer to particles suspended in a stirred vessel is recommended. The results of experimental study are approximately 12 % above the predicted values.

An analysis of thermodynamic properties in both traditional and enhanced geothermal systems to compare thermal efficiencies

This meta-study draws upon previous research on both Enhanced Geothermal Systems (EGS) and traditional geothermal systems (GS), using these findings to compare and investigate the thermal efficiency of each system. Efficiency calculations include reservoir enthalpy, maximum drilling well temperature, power output (per unit mass of liquid) and mass flow rate of these systems to determine whether EGS’s are viable as an alternative, more readily available renewable energy source. This meta-study suggests that EGS are more viable than naturally occurring GS in the context of future geothermal energy production as they perform with a similar average efficiency of 10-15% and, in addition, can be used in a wider range of geothermal environments.

Visualization and quantitative analysis of dispersive mixing by a helical static mixer in upward co-current gas–liquid flow

Abstract Growing interest towards process intensification in chemical industries over the last decade promotes static mixers as an attractive contactor alternative to the bubble column and mechanically stirred vessels. In the present work, the dispersion provided by a helical static mixer in a vertical pipe at turbulent gas–liquid flow conditions was studied using ultrafast electron beam X-ray tomography. Dispersive mixing was quantified upstream and downstream of three, six and nine helical static mixer elements in terms of bubble size distribution and gas holdup. Bubble breakup within the mixer elements was visualized and quantified via bubble size distribution and interfacial area density. Moreover, the power dissipation per unit mass of liquid was calculated for different number of static mixer elements and slip. The results provide a new insight into the development of the gas phase distribution within helical static mixers and a sound basis for design improvement, optimization of flow conditions and CFD validation.

Aerosolization of Water Ejected from a Full Container Impacted by Bomb Fragments

In assessing the potential collateral effects of bomb attacks on tanks of stored liquids, it is useful to separate the liquid that is aerosolized as an escaping cloud from that which remains inside the tank or rapidly falls to the nearby ground. One relationship currently in use partitions the two categories using a linear model of aerosolized fraction versus fragment energy deposited per unit mass of liquid which is based on calculations and a few test data points. Since this model is incorporated in popular programs used by an expanding number of first responders to assess potential hazards, there is a need for high-confidence test data across the parameter space of interest to improve and/or validate the model. Such a series of tests was conducted during November of 2008 in which 7.57-liter (ℓ) sized cans of water were impacted with fragments of known mass using scored cased explosive charges. Impact velocities were measured, and the remaining water in the can and on the nearby ground platform was collected and weighed. The missing water was assumed to be aerosolized. This new data establishes an S-curve as a more accurate relationship between aerosolized fraction (AF) and the fragment energy deposited per unit mass of liquid in the container.

Aerosolization of Water Ejected from a Full Container Impacted by Bomb Fragments

In assessing the potential collateral effects of bomb attacks on tanks of stored liquids, it is useful to separate the liquid that is aerosolized as an escaping cloud from that which remains inside the tank or rapidly falls to the nearby ground. One relationship currently in use partitions the two categories using a linear model of aerosolized fraction versus fragment energy deposited per unit mass of liquid which is based on calculations and a few test data points. Since this model is incorporated in popular programs used by an expanding number of first responders to assess potential hazards, there is a need for high-confidence test data across the parameter space of interest to improve and/or validate the model. Such a series of tests was conducted during November of 2008 in which 7.57-liter (l) sized cans of water were impacted with fragments of known mass using scored cased explosive charges. Impact velocities were measured, and the remaining water in the can and on the nearby ground platform was collected and weighed. The missing water was assumed to be aerosolized. This new data establishes an S-curve as a more accurate relationship between aerosolized fraction (AF) and the fragment energy deposited per unit mass of liquid in the container.

Wall-to-liquid mass transfer in a gas–slurry transport bed

In the present study, we measured the surface-to-liquid mass transfer coefficient, K w , for the wall and the immersed vertical cylinder electrodes in the slurry (liquid–solid) and gas–slurry (three-phase) transport beds for controlled solid concentrations in the slurry using the limiting current method. The slurry contained 0.1 mm inert glass beads and the solid fraction in the slurry was varied from 0% to 10% by volume. The gas holdup and the solid concentration in the slurry were also measured for the use in correlating the mass transfer coefficients. A unified dimensionless equation with an error of 20.0% in terms of the Sherwood number, the Schmidt number and the specific power group including the energy dissipation rate per unit mass of liquid was obtained for correlating the surface-to-liquid mass transfer coefficients in both transport bed systems.

Heat Transfer from Immersed Vertical Cylinders in Gas-Liquid and Gas-Liquid-Solid Fluidized Beds

The heat transfer coefficient, h, was measured using a cylindrical heater vertically immersed in liquid-solid and gas-liquid-solid fluidized beds. The gas used was air and the liquids used were water and 0.7 and 1.5 wt% carboxymethylcellulose (CMC) aqueous solutions. The fluidized particles were sieved glass beads with 0.25, 0.5, 1.1, 2.6, and 5.2 mm average diameters. We tried to obtain unified dimensionless correlations for the cylinder surface-to-liquid heat transfer coefficients in the liquid-solid and gas-liquid-solid fluidized beds. In the first approach, the heat transfer coefficients were successfully correlated in a unified formula in terms of a modified j H -factor and the modified liquid Reynolds number considering the effect of spatial expansion for the fluidized bed within an error of 36.1%. In the second approach, the heat transfer coefficients were also correlated in a unified formula in terms of the dimensionless quantities, Nu/Pr 1/3 , and the specific power group including energy dissipation rate per unit mass of liquid, E 1/3 D 4/3 /ν l , within a smaller error of 24.7%. It is also confirmed that a good analogy exists between they surface-to-liquid heat transfer and mass transfer on the immersed cylinder in the liquid-solid and gas-liquid-solid fluidization systems.

Effects of the Stirred Tank's Design on Power Consumption and Mixing Time in Liquid Phase

The influence of the stirrer type and of the geometrical parameters of both tank and agitator (clearance of an impeller from tank bottom, impeller diameter, draft tube and geometry of the tank bottom) on power consumption and mixing time in liquid phase under turbulent regime conditions (Re > 104) have been studied. Different types of agitators have been used, namely Rushton turbine, 45° pitched-blade turbine, MIXEL TT and TTP propellers and 1-stage or 2-stage EKATO-INTERMIG propellers. All these stirrers were tested with the same power consumption per unit mass of liquid. On the basis of measured power consumption per unit mass, which is required to achieve the same degree of mixing, the results obtained in the present work show that the TTP propeller is the most efficient in liquid phase. Recommendations on the optimum geometric configuration have been made for each type of stirrer.

On the relationship between the composition, morphology and function of leaves

1. It is common practice to express measurements of leaf composition and morphology using dry mass as a basis. Relationships established using those measurements are difficult to interpret because the leaves may have different liquid contents or fractional air space. 2. In a previous theoretical investigation, we showed that the liquid content of leaves was important and the following hypotheses were proposed: (1) the mass of nitrogen per unit mass of liquid is relatively constant within leaves and (2) the surface area to volume ratio of leaves is proportional to leaf liquid content. That investigation also proposed that fractional air spaces were important, because they confer plasticity in construction, with apparently minimal cost in terms of CO2 uptake. In this paper we use a set of comprehensive measurements to address the above hypotheses and to assess whether the fractional air space does vary in a consistent manner. 3. We found that the specific gravity of the non‐gaseous fraction in the leaves we measured was within the range ≈ 0·9–3·0 and increased with the fractional air space in a regular manner. Consequently, the specific gravity varied over a much smaller range (≈ 0·9–1·4). The specific gravity at high liquid contents approached unity but at low liquid contents it was variable. 4. The mass of nitrogen (N) per unit mass of liquid was found to be relatively constant (0·01 ± 0·003, n = 76). 5. The surface area to volume ratio was positively correlated with the liquid content (R2 = 0·87, n = 27). 6. The mass of carbon (C) per unit dry mass was relatively constant (0·49 ± 0·04, n = 76). Because N was a constant fraction of the liquid mass but C was a constant fraction of the dry mass, the N:C ratio was positively correlated with the liquid content (R2 = 0·76, n = 27). 7. A comparison with leaf measurements from several external databases confirm that the relationships described above are widely applicable. 8. It is concluded that the composition and morphology of leaves are linked and that leaf function is a consequence of that linkage. Both the liquids and air spaces are integral to leaf function and need to be considered in analysis of experimental results.

A theoretical approach to linking the composition and morphology with the function of leaves

1. In this paper we develop a theoretical framework for describing the composition and morphology of leaves on a volumetric basis which is inclusive of both the liquids and internal air space. That framework is then used to link the composition and morphology with the function of leaves. 2. Leaves are segmented into a functional scheme named a–u–s–V (air space–solution–structure–Volume basis) and a measurement scheme named a–q–d–M (air space–liquid–dry matter–Mass basis). Measurements of mass, liquid mass, volume and fractional air space are necessary to (partially) link the two schemes. 3. The liquid content of leaves can be used to infer the mode of mechanical support and, hence, the likely values of air space, solution and structure. For example, if a leaf has a high liquid content, then it cannot have a large volumetric fraction of structure (which is largely made of dry matter) and is unlikely to have large internal air spaces. 4. Based on measurements of individual leaf components, the specific gravity of the non‐gaseous fraction in leaves would usually be in the range 1–1·3. Consequently, the specific gravity of leaves would be most sensitive to variation in fractional air space. 5. For the dimensions typical of most leaves, the surface area to volume ratio of a leaf is determined by leaf thickness (or diameter). 6. Leaf design is considered in terms of light interception and gas exchange. The requirements for each are essentially incompatible and lead to a trade‐off on leaf thickness. However, that relationship is complicated because variation in fractional air space can potentially lead to broad optima for gas exchange at any given leaf thickness. 7. The theoretical predictions have not been assessed owing to a lack of measurements of leaf density, fractional air space and liquid content. However, published data were used to develop the following hypotheses: (1) the mass of nitrogen per unit mass of liquid is relatively constant within leaves; (2) the surface area to volume ratio of leaves is proportional to leaf liquid content. These hypotheses are tested in a subsequent paper.

Drift-flux correlation disengagement models: Part II — Shape-based correlations for disengagement prediction via churn-turbulent drift-flux correlation

In Part I of this work the theoretical foundation was laid for predicting disengagement via volumetric gas production and an axial void fraction profile. Earlier work indicated for non-foaming systems one of the two drift-flux correlations can be chosen on the basis of viscosity. Herein, for the churn-turbulent drift-flux correlation (low-viscosity system), the dependence average void fraction and dimensionless superficial vapor velocity [1] on vessel shape (e.g., vertical cylinder, horizontal cylinder, or sphere) is explored. There is very little shape dependence and it is quantified below. A simple two-constant correlation is suggested, which satisfies the conditions at low and high dimensionless superficial vapor velocity conditions. Constants are given for vertical cylinders, horizontal cylinders, and spheres for the churnturbulent drift-flux correlation. The disengagement model is based on a constant energy generation per unit mass of liquid. Thus, the application to runaway reaction with vaporization is straightforward. The application of the correlation to reactive systems producing gas (i.e., gassy systems) and to those both producing gas and involving vaporization (i.e., hybrid systems) in non-constant cross-sectional area vessels is clarified here. Rating calculation equations are developed, and the calculations are illustrated. For a rating calculation, the maximum gas rate (based on vent capacity) is known. The calculation of maximum average void fraction (i.e., 1-fill ratio) and gas generation per unit of liquid is straightforward. Thus, the rate of reaction (i.e., gas generation) must be found to assure that the vent capacity is sufficient

Drift-flux correlation disengagement models: Part I — Theory: Analytic and numeric integration details

In the design of pressure relief systems for vessels containing liquid, the phase of the flow through the vent line is very important. Mounting the line on the top of the vessel does not necessarily guarantee all vapor flow. One must calculate whether vapor bubbles formed in the liquid will disengage before they reach the vent entrance. Disengagement can be predicted via an axial void fraction profile that is calculated based upon volumetric gas production. It is assumed that the liquid phase is continuous and that pseudo-steady state is reached. The disengagement model is based on a constant energy generation per unit mass of liquid. For non-foaming systems, one of two drift-flux correlations can be chosen on the basis of viscosity. The churn-turbulent drift-flux correlation is for low-viscosity systems, and the DIERS' viscous-bubbly drift-flux correlation is for high-viscosity system [1, 2]. This model reduces to a single ordinary differential equation (ode). Analytic integration results for this model are possible for constant cross-sectional area vessels (e.g., vertical cylinder) and non-unity distribution parameters Co [3–5]. If this calculation shows the bubbles do not disengage, either a partial differential equation model must be solved or the coupling equation must be used. The coupling equation uses the maximum void fraction (calculated from the ode) and ties together the vessel and vent models. The ode solutions relate the local and average void fractions to the dimensionless superficial vapor velocity. For the churn-turbulent drift-flux correlation, explicit relationships are presented for the first time. They validate the earlier approximation of Fauske et al. [6] (see also Ref. [3]). For the DIERS' viscous-bubbly drift-flux correlation, implicit relationships are presented for the first time in the open literature. The earlier approximation of Fauske et al. [6] (see also Ref. [7]) fit the data, but is different than these integration results. Further work is in progress to refit the data [8] and to clarify the best model to use. For non-constant cross-sectional area vessels (e.g., horizontal cylinders and spheres), the analytic integration is difficult, but numeric results have been presented [3, 7]. The details of the numeric integration are presented and discussed here. As the cross-sectional area converges (toward the top of the vessel), the vapor concentration (i.e., the void fraction) and velocity increase. The maximum local void fraction occurs at the top of the vessel. Numerical difficulties are encountered as a result of the cross-sectional area going to zero at the bottom and top of the vessel. The pseudo-steady-state model imposes void fractions of minimum and maximum at these extremes (i.e., 0 and 1/Co).

Mass Transfer between Particles and Liquid in Gas-Liquid-Solid Three-Phase Upflow through a Vertical Tube

Solid-liquid mass transfer coefficients have been obtained by measuring the ion-exchange rate in a gas-liquid-solid three-phase upflow through a vertical tube. The three phase is composed of nitrogen gas, an electrolyte solution, and cation-exchange resin beads of 941μm in diameter. Other experimental variables are slurry velocity, gas velocity, and temperature. The mass transfer coefficients increased according to increases in the slurry velocity, gas velocity, and temperature. The experimental results have been correlated by the following equation, previously proposed for a solid-liquid two-phase tube flow:Sh=2+0.47(e1/3Dp4/3/υ)0.63Sc1/360<(e1/3Dp4/3/υ)<400, 269<Sc<641, md<0.01where e, Dp, ν, and md are energy dissipation rate per unit mass of liquid, particle diameter, kinematic viscosity, and delivered concentration of particles, respectively.

Wall-to-liquid mass transfer in packed and fluidized beds with gas-liquid concurrent upflow.

The wall-to-liquid mass transfer coefficient, kw, was measured for both surfaces of a coaxially immersed tube and a column wall in packed and fluidi/ed bed systems with gas-liquid concurrent upflow. Supplementary measurements of kw were carried out in openpipe liquid flow, gas-liquid two-phase upflow and packed and fluidized beds with single liquid flow. The value of kw in the three-phase fluidized bed increased with increasing gas flow rate, deviating from the value in the liquid-solid fluidized bed and approaching the value in the gas-liquid two-phase upflow, while it passed through a maximum value with respect to the liquid flow rate. The value of kw in the packed-bed operation increased with increasing liquid flow rate and with increasing gas flow rate. The values of kw for the inner tube and the column wall were shown to agree with each other. The values of kw in all the gas-liquid, liquid-solid and gas-liquid-solid systems examined were correlated well by a unified equation in terms of the energy dissipation rate per unit mass of liquid. An analogy existed between wall heat transfer and wall mass transfer in all the multiphase flow systems examined.

Particle-to-liquid mass transfer in gas-liquid-solid fluidization.

Mass transfer from solid particles to liquid in gas-liquid-solid fluidization was experimentally investigated by means of an electrochemical method with 7-9 particle electrodes fixed at various radial positions in a column of 82.9 mm i.d. Supplementary measurements were also conducted for the solid-to-liquid mass transfer in single liquid flow, gas-liquid two-phase upflow and liquid-solid fluidization. The effects of particle size and liquid and gas flow rates on the solid-to-liquid mass transfer coefficient, Ks, in all the systems were investigated and the mass transfer coefficient was well correlated by the following equation proposed by Ohashi et al. for Ks in a packed bed with single liquid flow. Shs = 2 + O.51(E1/3dp4/3/V1)0.06Sc1/3where E is the energy dissipation rate per unit mass of liquid, dp the particle diameter, vl the kinematic viscosity of liquid, Shs the Sherwood number and Sc the Schmidt number. The value of E was expressed by the sum of the kinetic energy supply terms due to viscous drag force across a particle and to gas agitation.

A physical interpretation of drop sizes in homogenizers and agitated tanks, including the dispersion of viscous oils

Theoretical studies include firstly, the applicability of the Kolmogoroff-Hinze theory of droplet break-up in a turbulent liquid, testing it over a range of local power dissipations per unit mass of liquid from 5 to 10 9 W kg −1. Secondly, the turbulent fluctuation velocity is related to the size and rotational speed of the impeller blades in agitated vessels. Thirdly, the influence on droplet size of the viscosity of the dispersed phase is included in a new, simple basic theory, which is tested using data on agitated tanks, static mixers and homogenizers.

TURBULENCE IN NON-BAFFLED MIXING VESSEL

Time-mean liquid velocity, RMS velocity, various scales of turbulence, and energy dissipation rate in non-baffled mixing vessel are measured. As the lateral RMS velocity is one-third to one-fourth the longitudinal RMS velocity, liquid in the vessel is in the non-isotropic turbulence field. However, the theory of local isotropy of Kolmogoroff can be applied because existence of the inertial subrange is observed. As the integrated value of local energy dissipation rate agrees with the power per unit mass of liquid from the impeller, almost all energy from the impeller is viscous dissipated in eddies of micro scale. At low impeller speed, there exist poorly turbulent portions at parts distant from the impeller or in motion of micro scale eddies in the high frequency range in spite of the fact that Re number indicates full turbulence. Turbulent diffusivities in radial direction are from 0.1 to 10 cm2/sec in this experiment and are almost proportional to impeller speed. Turbulent diffusivities in tangential direction are three to five times larger than those of radial or axial diffusivities and mixing between cylindrically rotating zone and outer quasi-free vortex zone is poor.