Schwartz¹⁾ and Takasaki²⁾ etc. measured the flow distribution, as soon as the liquid ran out of the packed bed. Their methods do not give the true distribution in a packed bed. Therefore the author investigated on the flow distribution of liquid in the tower packed with fine particles.
In this experiment, 11 pairs of the platinum electrodes, 1mm in diameter and 1cm long, were placed in a packed bed as shown in Figure 1. And the flow distribution was measured by the electric current.
The velocity profile is the complicated foam and not flate or parabolic, as shown in Figures 5 and 6.
Near the wall, the velocity became large to a certain degree. And the minimum velocity occured approximately r/R 0.6-0.8.

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Fluidized bed-type air preheater, as shown by Figure 1, is a heat exchanger with multiple fluidized beds applied to air preheating, and the volumes of this unit needed for the required weights of air to be preheated are considerably small compared with other types of preheaters.
The sand (ie., heat carrier) charged in at the top of the tower is heated in the upper part of the tower by direct contact with waste gas and then is passed through a downspout to the lower part of tower, where the heat absorbed by the sand from the hot gas is given up to the air in the lower part of this unit having the conveying tube for cold sand. The subject of air preheating by means of the multiple beds of fluidized solids seems not to have been investigated so far. The purpose of this article is to report the results of the theoretical analyses which would be useful in clarifying the operation principle and predicting the performance of this unit.
Basic equations were derived from the non-linear difference equations depending on the operating lines resulting from heat balances and the equations on the equilibrium relations assuming each plate to be under ideal state. Now, we employed the mean specific heat of fluid at constant pressure, over the ranges of temperatures considered, in hopes that this procedure might lead to the soluble linear forms. Analyses which were carried out differ in respect of the two basic equations, one when the effect of radiant-heat transmission between successive plates is taken into consideration, and the other when it is neglected.
The unknown temperatures on the arbitrary i-th plate and the number of theoretical plates were given for each case (Equations (7) to (14) and Equations (21) to (31)), and the effects of radiation between successive plates and of the dimentionless ratio (K, K') upon the number of theoretical plates were shown. In order to compare with the analytical calculus, graphical solutions of this unit were illustrated in Figures 4 and 5, for practical operating conditions.
Fundamental quantitative relationships represented in this paper are not backed by the experimental work, but this unit would offer an attractive subject of means of air preheating, from a commercial point of view.

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Accurate thermodynamic date of simple gases and vapors of various kinds of hydrocarbons have been accumulated and are available nowadays in the tabulated forms; and yet the similar data for liquid state are still very scanty and so they are not available for equilibrium calculations.
Consider the gas phase and the liquid phase, both of which exist in the vaporization equilibrium as well as in the chemical equilibrium within each phase; and, furthermore, assume the ideal bechaviors of gas phase (ideal gas) and liquid phase (ideal solution); and, then, the following simple equation can be very easily derived from Rault's law.
or logK_p=logK_N(l)+logK_v.p.
Here K_p: partial pressure equilibrium constant.
K_N(l): mole fraction equilibrium constant in the liquid phase reaction.
K_v.v.: new function named vapor pressure equilibrium constant, which is expressed in the same way as the equilibrium constant, by means of vapor pressure of each component in the given reaction.
K_N(l) and Kv.p. are the unique function of temperature, and are independent of the total pressure of the reaction system.
It was found that the variation of log K_v.p. with temperature and with number of carbon atoms of reactants and products in the same kinds of reaction was rather small as exemplified in Table 1
Log K_p of the reaction can be calculated from the equilibrium constant of formation of each reactant and product in the vapor state, log K_f, and log K_v.p. from the vapor pressure datum of each liquid component concerned, and thus the values of log K_N(l) can be calculated from the available thermodynamic data.
In the case of liquid reactions under high pressure, the pressures may be replaced by fugacities and thus better results may be expected.

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Many inquiries have been made, theoretically and experimentally, into the hold-up in a wetted wall tower without gas flow. Most of the results of experimental studies are said to satisfy the theoretical relation obtained by Nusselt who analysed the flow of liquid film, but in view of the precision of measurements in these studies it is to be doubted whether this conclusion holds true or not. It should be rather noted that Kirkbride and Friedman et al. recognized the generation of waves on the surface of liquid film where Re_L>8.
On the other hand no researches have been made about a tower with gas flow because the suitable method for measurements was lacking.
The authors performed experiments with a new accurate method, the so-called balancing tower method. The towers used are shown in Table 1, and the liquids employed are water, soapless soap solution and millet-jelly solution. The results obtained are summarized as follows.
In the case without gas flow,
(i) The unsteady state parts of flow which existed at either end of the tower could be neglected when the length of the tower reached to about 250cm.
(ii) The influence of diameter on the thickness of liquid film might be represented by the term (1-2h/d)^1/3 regardless of the flow pattern.
(iii) The plot of h(1-2h/d)^1/3 vs. Re_L showed three different aspects according to the values of ReL as shown in Figs. 4 and 5. Where ReL was small the data agreed with Nusselt's theoretical line N represented by eq. (2). This region might by considered to be a complete laminar flow region. As ReL grew larger, the plots deviated downwards from the line N. In this region the generation of waves was observed and seemed to have some influence on the flow pattern, and the effects of the surface tension and viscosity of liquid were very significant. The data were well correlated with eq. (9). This region could be named a pseudo-laminar flow region. Eqs. (10) or (11) gave the criterion whether the flow was laminar or pseudo-laminar. In the region of large value of Re_L, the flow was fully turbulent and the influence of the surface tension of liquid diminished as in Fig. 6. Eq. (12) enabled one to predict the correlation in this region.
In the case with concurrent gas flow the following results were obtained.
(iv) When the liquid flows downwards in laminar film on a vertical surface, the ratio of the thickness of liquid film with countercurrent gas flow to that without gas flow, h/h₀, is theoretically given by eq. (16). The data obtained were compared with this equation as shown in Figs. 8, 9 and 10. The plots scattered on account of the low precision of measurements but mostly deviated downwards from the theoretical lines. The deviation appeared to be caused by the waves which were visible on the liquid surface, and the degree of deviation decreased with decrease of the surface tension of liquid and with increase of the viscosity. The ratio h/h₀ was expected to be smaller in turbulent flow than in laminar flow.

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The traditional approximation, brings appreciable error with a slight raising of temperature or humidity of gas. Its numerical value in the adiabatic vaporization (cooling of gas) process is shown in Fig. 1. In an example of counter-current, constant-rate drying (adiabatic cooling) process, the required contact area has been given by A₄, accompanying an error shown in Fig. 2, when ψ₂=80%. Correct one is A₁ of Eq. (6).
The authors propose the new approximation, Eq. (2) or A₂, instead of Eq. (4) or A₄, by which the error becomes smaller by one order and to be within the safety range. Their comparison can be made by Fig. 2 & 4.
This paper will have a relation to the discrussion about the accuracy of the Lewis' law, h/k'=CH. And the future precise investigation obout k_G=f(G'), will attract the researchers' attention to the conversion erfor of kG to k'.
In the case of taking kG as constant against instead of (p_s-p), Eq. (3) will be better suited.

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[in Japanese]

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