Douglas E. Leng

Experimental and computational study of multiple impeller flows

A computational and experimental study is conducted of viscous flow in a stirred reactor with multiple impellers. The vessel is cylindrical in shape with a stack of four 45 pitched blade impellers, four rectangular side-wall baffles and an ellipsoidal shaped bottom. The flow is computed with an incompressible Navier-Stokes solver which uses the pseudocompressibility technique of coupling the velocity and pressure fields. The laminar viscous flow field is solved using an approximate steady-state technique which neglects relative motion between the impellers and baffles and solves the flow at a single impeller position in a rotating frame of reference. The resulting velocity field is spatially averaged and compared with time-averaged experimental results. Computed results for the velocity field are shown to agree very well with experimental laser Doppler velocimetry (LDV) data for two different impeller configurations. This work illustrates the utility of the numerical method for studying complex multiple impeller flows at low Reynolds number. A variety of different impeller configurations are studied numerically and the effect of relative impeller sizing, impeller spacing and baffling on flow distributions within the stirred vessel is investigated. It is shown that global circulation patterns within the tank are strongly dependent on relative impeller size and spacing. It is concluded that obtaining good global circulation and mixing performance is sensitive to relative impeller sizing and spacing. Improper impeller spacing or sizing can result in compartmentalization of the flow inside the vessel and hence poor global circulation.

An experimental study of factors which promote coalescence of two colliding drops suspended in water-I

Abstract The factors which determine whether two colliding drops will coalesce or rebound have been studied experimentally for 3.4 mm dia. anisole drops in water, using an apparatus designed to permit control of drop size, impact velocity and collision angle. Analysis of high speed movies showed that for relative approach velocities of 1.9–11.2 cm/sec, the apparent drop contact time was less than 70 msec. The probability of coalescence during this short time interval was a function of the phase and amplitude of the drop oscillations at moment of contact. The results have been analyzed using a modification of the conventional Stefan-Reynolds type film thinning equation derived for rigid interfaces. This relationship, although indicating more thinning for coalescences than rebounds, fails to predict fast enough thinning rates to validate the model. Part II gives detailed derivations for a thinning model in which interfaces are free to move, and shows how the results given in Part I can be explained by film thinning.

The mathematical formulation of hydrodynamic film thinning and its application to colliding drops suspended in a second liquid-II

Abstract Transient solutions of the Navier Stokes flow equations for Newtonian liquids are described for the escape of the suspending fluid trapped between two drops when a head-on collision is effected. The equations enable the effects of interfacial mobility, the rate of disc expansion, the force of impact, and both physical and interfacial property variables to be determined. Analysis of the results of Part I shows that the probability of drop coalescence per collision depends on the amount of film thinning accomplished within the time span of the contact. Complete mobility of the interfaces is essential to accomplish sufficient thinning in this short interval if coalescence is to occur.