Motive Forces under Complete Mixing of a Liquid at the Contact Stage

Abstract

We have found the logarithmic and arithmetic mean motive forces and the corresponding numbers of transfer units N in the vapor and liquid phases under complete mixing of a liquid. The efficiency values expressed in terms of N have been derived. It has been proved that the numbers of transfer units are equal in the complex model and the mass-exchange variants using the conditions for the coupling of an ideal and a real plate of the Murphree and Hausen models. The relationship between the N values under complete mixing and without it has been established. Mixing of a liquid on a plate has an appreciable effect on the mass-exchange efficiency. Analysis of a complex model for the counterflow [1] and the cross flow [2] shows that under complete mixing of the liquid the calculated dependences are analogous to the respective expressions for the forward flow [3]. In particular, for the latter the concentration of the highly volatile component of the liquid before the plate from [3] in view of formula (25) of [4] is determined as(1)With the use of the material balance equationthe concentration of the highly volatile component in the vapor phase after the plate isUpon complete mixing the composition of the liquid on the plate is equal to the composition after it and is independent of the mutual direction of the vapor and the liquid. Under these conditions, the motive force expressed in terms of the liquid parameters at the vapor inlet to the plate and at its outlet is equal to

Motive Forces in a Complex Model Involving a Direct Flow and Mixing of a Liquid

“…which coincides with the data of [10] and confirms the calculations made. From expression (13) we find the value of the efficiency of liquid mixing:…”

“…The expressions for the mean motive forces with complete mixing of the liquid from Table 1 coincide with formulas (6) and (9) of [10], and in the absence of mixing they coincide with certain dependences of [11] obtained in the case where there is perfect displacement of the liquid, which confirms the validity of the calculations performed.…”

“…In [10], replacement of mean logarithmic values by arithmetic means is admitted provided that the ratio of the larger motive force to the smaller one does not exceed two. As applied to liquid mixing, this condition is formalized in the form whence…”

“…The boundary values of N for ϕ = 1 and ϕ = 0 are listed in Table 2, analysis of the data of which shows the identity between the dependences and the corresponding quantities of [10] and [11].…”