Solid-liquid mass transfer in falling liquid films on single spheres

TLDR: In this article, mass transfer equations were derived and compared with dissolution experiments of C6H5COOH-H2O and Cu-H 2SO4-K2Cr2O7 systems on single spheres (6 different sizes from 3/4" to 3").

Abstract: Mass transfer equations are derived and compared with dissolution experiments of C6H5COOH-H2O and Cu-H2SO4-K2Cr2O7 systems on single spheres (6 different sizes from 3/4" to 3"). In region I (long contact time with smooth laminar film), Sh converges Sh=1.608 (GaSc/Pe*)1/3 or k=2.01 D√δ(δ: mean film thickness) and increases with decreasing volumetric flow rate Q. In region II (short contact time with smooth laminar film), Sh converges Sh=0.716 Pe*1/9(GaSc)2/9The transition from region I to II occurs around Pe*/(GaSc)1/4≤10. In region III (short contact time with wavy film surface), Sh increases with Pe* to the 1/3 - 1/2 power and is substantially higher than that in region II. A generalized short contact time equation using the measured local film thickness δ Sh=0.501 Pe*1/3{∫π0(d/δ)sinθdθ}2/3is valid in this region. Thus, main cause for enhancement in Sh is the reduction in film thickness relevant to the wave formation. The II-III transition is somewhere between wave inception and wave coverage flow rates. In the above, Sh=kd/D, Pe*=Q/dD and Ga=gd3/v2, in which k is based on a log-mean driving force.