Cubes, mass transfer

When a liquid is dispersed into droplets the surface area is increased, which enhances the rates of heat and mass transfer. For a particular liquid dispersed at constant concentration in air the MIE varies with approximately the cube of surface average droplet diameter, hence the MIE decreases by a factor of about 8 when the surface average diameter D is halved (A-5-1.4.4). Ease of ignition is greatly enhanced for finely divided mists with D less than about 20 /rm, whose MIE approaches that of the vapor. Below 10 /rm a high flash point liquid mist (tetrahydronaphthalene) was found to behave like vapor while above about 40/rm the droplets tended to burn individually [ 142]. Since liquid mists must partially evaporate and mix with air before they ignite, the ease with which a liquid evaporates also affects MIE (Eigure 5-1.4.4). 

Sirkar and Hanratty (S13) showed, by means of refined measurements using strip electrodes at different orientations with respect to the mean flow, that transverse velocity fluctuations play a significant part in the turbulent transport very close to the wall, and that the eddy diffusivity may well be dependent on the cube of the distance y+, leading to a Sc1/3 dependence of mass-transfer correlations, which is often found experimentally. 

Dissolution time, tdi (for powder) Particle mass, m Mass transfer coefficient, k Solubility, S Particle radius, r Density, p Hixson-Crowell (cube root) equation t 1 — (tti 1 m0 )1/3 (kS/prJ... 

It is interesting that iL is independent of the viscosity of the solution note, however, that this is only true for high Schmidt numbers (thin diffusion layer). Also, iL is dependent only on the cube root of the fluid flow (cf. square root at the RDE). This lower sensitivity can result in larger errors in the determination of mass transfer and kinetic parameters. 

Oyama and Endoh (012) studied the solution of sugar in water in 6.7- and 10.8-in. baffled vessels using paddles and flat-blade turbines. They report a mass-transfer coefficient which was proportional to the cube root of the particle diameter and to the cube root of the impeller power consumption per unit mass of agitated liquid. 

Equation (13.15) shows that the steady mass-transfer-controlled flux of a reacting species is proportional to the cube root of the velocity gradient, i.e., N,- oc... 

The gas flows horizontally, contacting by downflowing liquid. The effective driving force for mass transfer is between that for counter- and cocurrent contactors. Crossflow scrubbers have low pressure drop and usually require a lower liquid/gas ratio than either counter- or cocurrent scrubbers. The time of contact between gas and liquid is relatively low, and crossflow units are not reconunended for most chemical absorptions. Design procedures follow a finite-element approach the scrubber volume is divided into cubes, each of which is assumed to reach equilibrium. 

Thus during the steady-state stage of isothermal mass transfer the cube of average radius grows linearly with time the growth rate is a function of interfacial tension, as well as of the solubility and diffusion coefficient of dispersed substance. If an admixture that is nearly insoluble in a continuous phase is introduced into the dispersion phase, a sharp decrease in recondensation rate, as well as changes in laws describing the process, may take place. 

E. M. Sparrow and A. J. Stretton, Natural Convection From Variously Oriented Cubes and From Other Bodies of Unity Aspect Ratio, Int. J. Heat Mass Transfer (28/4) 741-752,1985. 

Sugar [6]. Powdered sugar takes less time to dissolve than cube sugar when poured in hot tea. Why does this occur Sugar also dissolves faster in hot water than in cold water. From a mass transfer point of view why do you think this occurs What are the effects of stirring the cup in this example ... 

The derivation of the unsteady-state diffusion equation in one direction for mass transfer is similar to that done for heat transfer in obtaining Eq. (5.1-10). We refer to Fig. 7.1-1 where mass is diffusing in the. x direction in a cube composed of a solid, stagnant gas, or stagnant liquid and having dimensions Ax, Ay, and Az. For diffusion in the x direction we write... 

The H2S reaction is a typical gas-solid reaction. External mass transfer or diffusion of H2S through the ZnO bed could hmit the reaction rate. Novichinskii et al. [24] reported that flake- or plate-type adsorbents offer lower mass transfer limitations compared with cube- or prism-type materials. Furthermore, an optimum ZnO particle size should be chosen with regard to capacity and pressure difference. 

A much more complicated system (solid particles suspended in agitated fluids) also lends itself to analogy (Figure 11-4). Here experimental heat (10) and mass transfer (9) data all correlated with the cube root of e, the agitation power per unit mass times the particle diameter to the fourth power divided by the cube of the kinematic viscosity. In addition, the Prandtl or Schmidt number must be used for each case. 

Bialobrzewski, I., Zielinska, M., Mujumdar, A. S., Markowski, M., 2008. Heat and mass transfer during drying of a bed of shrinking particles Simulation for carrot cubes dried in a spout-fiuidised-bed drier. Int. J. Heat Mass Transfer 51 4704-4716. 

Figure 3.6. Schematic of the cube model for energy transfer ( ) of an atom/molecule of mass m incident with energy Et to the lattice represented by a cube of mass Ms. The atom/molecule adsorption well depth is W. The double arrow labeled Ts emphasizes that the cube also has initial thermal motion in the scattering.

Figures 13.10 to 13.16 present a visual explanation for the pattern of mass- and current-potential curves that is obtained in this system. They are based on a cube-system in which the three elementary steps are coupled electron/ion transfer, solvation and polymer reconfiguration. Explanation of the phenomena observed in Fig. 13.9 requires the use of two cubes, joined at the bottom front edge of one and the top back edge of the other,...

In E. coli, the complex has a mass of about 4 x 106 Da and consists of 60 polypeptide chains. In the center of the complex there is a core of eight trimers of E2 arranged in cubic symmetry (Fig. 5-10). Dimers of E3 are bound to the six faces of the cube. Finally, pairs of Et bind to each edge of the cube encircling the dehydrogenase dimers. The central position of the transacetylase (E2) allows the flexible lipoyl arms to transfer reactants from Ej to E3 or to CoA. 

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