Zur Berechnung mittlerer Warme- und Stoffubergangskoeffizienten an laminar und turbulent uberstromten Einzelkorpern wurde eine einheitliche Gleichung entwickelt und an Mesergebnissen von uberstromten ebenen Platten, Kugeln und querangestromten Zylindern uberpruft. Die Gleichung gibt auch die Mesergebnisse im Ubergangsgebiet zwischen laminarer und turbulenter Stromung gut wieder.

Berechnung mittlerer Wärme- und Stoffübergangskoeffizienten an laminar und turbulent überströmten Einzelkörpern mit Hilfe einer einheitlichen Gleichung

Free liquid-to-supercritical fluid mass transfer in packed beds

Knowledge of particle−liquid mass transfer coefficient (kSL) is important for a rational design of a solid−liquid/solid−liquid−gas stirred tank reactor (STR). Considerable efforts have been made by different investigators to study and correlate the behavior of kSL in STRs for a variety of geometric and operating conditions. This review attempts to put together and analyze the information available in the literature on kSL in STRs systematically. Different approaches used by researchers to correlate kSL are critically discussed. The effect of system configurations (type of the impeller, D/T, and C/T), operating parameters (impeller speed/power input, particle loading, and gas flow rate), and physical properties (dP, Dm, μ, and Δρ) on kSL have been discussed elaborately. Some new data for six-bladed impellers have been generated to determine the optimum geometric configuration and operating conditions for particle−liquid mass transfer in three-phase STRs. It is concluded that kSL in two-/three-phase STRs ca...

Particle-liquid mass transfer coefficient in two-/three-phase stirred tank reactors

While fluid flows are known to promote dissolution of materials, such processes are poorly understood due to the coupled dynamics of the flow and the receding surface. We study this moving boundary problem through experiments in which hard candy bodies dissolve in laminar high-speed water flows. We find that different initial geometries are sculpted into a similar terminal form before ultimately vanishing, suggesting convergence to a stable shape–flow state. A model linking the flow and solute concentration shows how uniform boundary-layer thickness leads to uniform dissolution, allowing us to obtain an analytical expression for the terminal geometry. Newly derived scaling laws predict that the dissolution rate increases with the square root of the flow speed and that the body volume vanishes quadratically in time, both of which are confirmed by experimental measurements.

Shape dynamics and scaling laws for a body dissolving in fluid flow

The effects of flow direction of solvent (CO{sub 2}) on the fluid-to-particle mass transfer were studied for packed beds of sintered porous pellets of two sizes (diameters of 1 and 2 cm) at conditions supercritical with respect to carbon dioxide using toluene and 1,2-dichlorobenzene as the impregnating solutes. Dynamic extraction experiments were performed in the laminar flow regime (Re = 8--90) where both free and forced convection modes of mass transfer were found to be significant. Measured mass transfer coefficients showed an almost linear dependence on the Reynolds number (Re{sup {approx}0.9}). Downflow of fluid had a strong effect on accelerating extraction rates, in particular at lower Reynolds numbers and for conditions near the critical point of CO{sub 2}, where natural convection is dominant. Experimental mass-transfer coefficients were well correlated using a single general equation that accounts for both modes of mass transfer (free and forced convection) as well as for upflow or downflow operation (i.e., with gravity opposing or assisting forced convection).

Supercritical Fluid Extraction of Packed Beds: External Mass Transfer in Upflow and Downflow Operation

Solution rates of 1/2-, 3/4-, and 1-in. cast benzoic acid spheres were measured under natural-and forced-convection conditions. Upward-flowing streams of water and aqueous propylene glycol, in laminar and turbulent flow, were used to contact single spheres in either a 1.50- or 4.00-in.- diameter column. Sphere Reynolds numbers ranged from 10 to 16,920; Schmidt numbers from 987 to 69,680; sphere- to column-diameter ratios, ds/dc, from 0.123 to 0.497; and Grashof numbers from 5,130 to 125,200.



The Sherwood number was found independent of the laminar-turbulent transition for pipe flow and the sphere- to column-diameter ratio when the Reynolds number is based on the average fluid velocity and sphere diameter.



A correlation of the data based on the additivity of the natural and forced convection processes is proposed, and statistical analyses of the new experimental data result in equations which correlate other heat and mass transfer data for single spheres immersed in bounded and free-jet streams of gases and liquids for NRe, S from 1 to 30,000 and NSe from 0.6 to 3,000, within an average deviation of about 20%.

Robert L. Steinberger

Papers

Mass transfer from a solid soluble sphere to a flowing liquid stream