Regime II flows

The evaluation of the parameters for Regime II flows is difficult, due to the complexity of the fluid mechanics in this regime. It was because of this complexity that the model equations, Eqs. (15) and (17), were simplified by considering three special cases for these gas-liquid systems. 

The Peclet number defined for this case is unique to Regime II flows, due to the definition of kn eff given in Eq. (23). Therefore, Peu must be correlated with experimental data from Regime II flows. 

As in Section II,A, a set of steady-state mass and energy balances are formulated so that the parameters that must be evaluated can be identified. The annular flow patterns are included in Regime II, and the general equations formulated in Section II,A,2,a, require a detailed knowledge of the hydrodynamics of both continuous phases and droplet interactions. Three simplified cases were formulated, and the discussion in this section is based on Case I. The steady-state mass balances are... 

Example (corresponds roughly to River G at flow regime II and with a sandy bed) Kq = 10 3 m sr1... 

For regime I, dispersion begins to affect the initial atrazine concentration less than 1 km downstream of the spill. In contrast, for flow regime II, xini is 20 km. Thus, at x = 10 km the atrazine cloud still looks like Fig 24.7a dispersion does not yet lower Cmax. 

To summarize, in flow regime I the maximum atrazine concentation atx = 10 km is reduced to (0.20/0.63) 100% = 32% of its original value. This reduction is significantly larger than that from any other possible mechanism to reduce the concentration. In contrast, in flow regime II dispersion is not yet felt at x = 10 km. 

The attenuation decreases from the Natural Regime to Pump Regime II. This is consistent with (1), since the mean advective flow time rw is smallest for Pump Regime II. A short advective flow time increases the change of the oscillations to reach the well. 

The above experiments, if done under conditions equivalent to full scale ones with a well-mixed stirred tank reactor at steady state, give the basic rate of overall reaction plus information on what influences it. These can be used for scale-up calculations, either keeping to a stirred tank, or where appropriate, scaling up a different type of reactor, e.g. a bubble column for Regime I, a cascade of stirred tanks if plug flow is required in Regime II, or a packed tower or gas-liquid annular flow tubular reactor for Regime III or for gas-fllm controlled mass transfer. 

Consideration will now be given in turn to three particular aspects of gas-liquid flow which are of practical importance (i) flow patterns or regimes (ii) holdup, and (iii) frictional pressme gradient. 

Equations 10.46 and 10.47 can be applied only when the tip angle a, is small. Regime II is assumed not to contribute to the pressure generation and is further assumed to move forward at a rate of one lead per revolution. If the cross-sectional area of regime II is A, then the flow rate through this domain is ... 

Due to their simpler flow history, studies of processes similar to commercial fiber production are valuable for determining the fundamental relationships involved in orientation development. This has important commercial relevance since uniaxially oriented thin films and fibers are applications that capitalize on the directional properties of TLCPs. Dutta and Weiss [29], Hsu and Harrison [30], and Isayev and co-workers [31] explore such applications. The thermal and deformation history in fiber spinning relating to orientation development has been reviewed [32]. In that study, the process was divided into two regimes (i) flow within the die and (ii) flow outside of the die in the spinline. 

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