Transport of heat and mass between liquids and spherical particles in an agitated tank

Abstract

Data are reported for heat transfer from water to melting ice spheres and for mass transfer in the case of dissolving spheres of pivalic acid suspended in water agitated in a stirred vessel.The transport coefficients are found to depend on agitator power input but not on agitator design, in agreement with the Kolmogoroff theory. These experimental results are used with others in the literature to develop a correlation involving Nusselt and Prandtl or Schmidt numbers together with a dimensionless group involving agitation power. The correlation is essentially independent of solid-liquid density ratio in the ranqe 0.8 to 1.25, and in this range the gravity group also appears to be unimportant.Particles or drops suspended in agitated liquids are employed in various chemical processes, including crystallization, solvent extraction, polymerization, slurry catalysis, and direct-contact heat exchange. In many cases the size of the process equipment is directly related to the rate of mass or heat transfer between the particles and the liquid. Though numerous studies of the transport rates in such systems have been reported, the large number of variables involved has made it difficult to develop a full understanding of the physics of the processes of interest. Evidently the physical properties of both phases are important, as well as the nature of the turbulence in the liquid, as determined by the type of agitation and the geometry of the system.Perhaps the most widely used method of estimating transport rates in such systems is that based on the work of Harriott (12). Hariott suggested that the transport rates in a stirred tank can be estimated as a multiple of the transport which would result if the particles fell through a stagnant medium at their terminal velocity. There are, however, no reliable methods of predicting this multiple. KOLMOGORBFF'S THEORYSeveral investigators (8, 21,27) have suggested that KolmogoroFs theory of isotropic turbulence may be applied to a stirred liquid in turbulent motion and, therefore, that the transport results can be correlated with the agitation power per unit volume. However, no satisfactory correlation of transport data based upon these ideas has been developed.Kolmogoroff's theory postulates that turbuleiice results in a continuous inertial transfer of kinetic energy from the larger eddies to smaller and smaller eddies, finally resulting in viscous dissipation of the energy by the smallest eddies in the dissipation range. In a stirred tank, the impeller continually creates eddies described by a certain size and frequency distribution and also by a certain geometric orientation. The largest eddies are of the order of the size of the container and constitute the bulk flow. These large eddies transfer energy to smaller and smaller eddies through inertial interaction. As the kinetic energy is transferred from large to small eddies, the geometric orientation is lost. The large eddies interact to produce more random smaller ones and eventually, if sufficient interaction takes place, all ...

Effects of transpiration and changing diameter on heat and mass transfer to spheres

“…An analytical solution can be obtained for the case of a growing sphere, which corresponds to positive values of NpeR. Such a solution was first obtained by Frank (7); it can also be obtained from Equation ( 5 ) Equation (13) is plotted as the uppermost curve in Figure 5 in normalized coordinates analogous to those employed in Figures 3 and 4. The normalizing parameter is NN?…”

“…In solving Equation (5) numerically for spheres of changing radius, Equation (15) was used, with a constant value of a, to relate NP,R to NNu. Likewise, Equation ( 2 0 ) was used to evaluate changes in R with time.…”

Modeling and Measurement of the Dissolution Rate of Solid Particles in Aqueous Suspensions – Part II: Experimental Results and Validation

“…The computation of the particle Sherwood number is based on the Kolmogoroff theory (Harriott [3], Brian et al [4]), which for the mass transfer in agitated cells gives:…”

Evaluation of diffusional effects on kinetics of soybean lecithin hydrolysis using A₂ phospholipase

“…El transporte de sustrato por difusión molecular y convección turbulenta está expresado por el coeficiente de transferencia de masa externo Ks y puede calcularse para partículas esféricas en solución (Brian y Hales, 1969): (Ks.dp / Dso) 2 = 4 + 1,21 (dp.U / Dso) 2/3 ecuación 3 donde U = g dp 2 ∆ρ 2 18 µ ecuación 4…”