Drop breakup in turbulent stirred‐tank contactors. Part III: Correlations for mean size and drop size distribution

Abstract

In Part 11, the extent to which dispersed-phase viscosity and interfacial tension influence equilibrium mean drop size and drop size distribution was determined for dilute suspensions produced in baffled cylindrical tanks of standard geometry equipped with six-blade Rushton turbines. Low to moderate viscosity (pd 5 0.5 Pa-s) dispersed-phase systems behaved similarly in that Sauter mean diameter could be correlated using the mechanistic arguments of Part I, and drop sizes, normalized with respect to D,z, could be correlated by a normal distribution in volume. Limited moderate viscosity data were reported in Part I but were not used to develop the correlations of Part 11. The objective of this study is to combine the low to moderate viscosity data of Parts I and I1 with those obtained by other investigators to obtain correlations of broader utility, and to extend these via mechanistic arguments so that they apply to nondilute systems. Dilute DispersionsSeveral investigators have studied the behavior of dilute liquid-liquid systems in the geometry of Parts I and I1 (see Figure 1 of Part I). Chen and Middleman (1967) conducted a detailed study of surface forced stabilized (low pd) dispersions encompassing a broad range of operating conditions. They considered dispersed phases with viscosities up to about 0.025 Pa. s but did not account for viscous resistance to breakage when correlating their data. Sprow (1967) NY.employed in these studies differed from that of Parts I and I1 in only two respects. Baffles were mounted flush to tank walls and bottom. Chen and Middleman varied the ratio of impeller to tank diameter ( L I T ) and Sprow obtained most of his data forFor dilute suspensions, coalescence rates are negligible. Equilibrium drop sizes are determined by breakup that occurs primarily in the impeller region. Small modifications in baffle placement should be relatively unimportant and the L/ T ratio should be of secondary importance. Chen and Middleman found that the effect of L/Tfell within the scatter in their data for the range 0.21 5 L / T 5 0.73. However, it should be noted that Okamot0 et al. (198 1) report that energy dissipation rates become more uniform as LIT increases. Therefore, the ratio of the maximum to mean energy dissipation rate per unit mass increases as L/ T decreases. For a given t, drops will experience higher local turbulent energy as LIT decreases, indicating that D,, should decrease with L f T. Mean drop size correlationsThe low to moderate viscosity data reported in Parts I and I1 and by the cited investigators were fit to models developed in Part 11. The range of variables investigated in each study is summarized in Table 1. The table provides Two models were fitted to the 349 data sets via nonlinear least-squares regression. These are the semitheoretical model LIT = 0.29.

Representative drop sizes and drop size distributions in A/O dispersions in continuous flow stirred tank

“…Several studies, however, have focused on stabilization due to dispersed phase viscosity (Calabrese et al, 1986a,b;Wang and Calabrese 1986). One of such studies (Calabrese et al 1986b), based on a large number of experimental data, proposes the following expression for the Sauter mean diameter:…”

Modeling interfacial area transport in multi-fluid systems

“…Experimental and empirical work on CSTR's has been done by Calabrese, Chang and Dang (Calabrese, 1986a), Wang and Calabrese (Wang, 1986) and Calabrese, Wang and Bryner (Calabrese, 1986b). They correlated their data using Kolmogoroff theory and included the effect of viscosity.…”

“…Hinze (Hinze, 1955), Shinnar and Church (Shinnar, 1960), Madden and Damerell (Madden, 1962), Howarth (Howarth, 1964(Howarth, ,1967, Chen and Middleman (Chen, 1967), Ramkrishna (Ramkrishna, 1974b), Coulaloglou and Tavlarides (Coulaloglou, 1976), Delichatsios andProbstein (Delichatsios, 1976), Verhoff, Ross, andCurl (Verhoff, 1977), Cruz-Pinto and Korchinsky (Cruz-Pinto, 198 l), Narsimhan, Nejfelt, and Ramkrishna (Narsimhan, 1984), Davies (Davies, 1983, Muralidhar andRamkrishna (Muralidhar, 1986), Calabrese, Chang, and Dang (Calabrese, 1986a), Wang and Calabrese (Wang, 1986), Calabrese, Wang, and Bryner (Calabrese, 1986b), Das and Kumar @as, 1987), Muralidhar, Ramkrishna, Das, and Kumar (Muralidhar, 1988), Tobin, Muralidhar, Wright, and Ramkrishna (Tobin, 1990), Tsouris and Tavlarides (Tsouris, 1994) and Lam, Sathyagal, Kumar, and Ramkrishna (Lam, 1996) have studied the breakage and coalescence of drops in dispersions.…”

Collective Rayleigh-Plateau Instability: A Mimic of Droplet Breakup in High Internal Phase Emulsion

“…Large-scale emulsification typically involves strong, crude shearing processes to achieve the needed throughput, but produce emulsions with high polydispersity (≳100%). 7 Fundamental understanding of emulsification under shear has been limited primarily to the breakup of isolated droplets in laminar flow. 8 Three main behaviors have been identified, depending on the shear history.…”