In the previous paper⁵⁾, one of the authors pointed out the variation of the resistance coefficient of caked cloth and the constancy of the ratio, bfυ/rfυ.
In the present paper, the gradual variation of the mean specific resistance of the cake is described together with the relation between the unsteady distribution of the specific resistance in the constantpressure filtration cake and the mean value thereof.
The constant-vacuum-filtration and permeation-tests were conducted, using the experimental apparatus as shown in Fig. 1. Slurrics put to the tests were those of potato- and sweet-potato-starch for industrial use.
The Underwood's type plots of the data obtained by means of Eq. (1) concaved upward as shown in Fig. 3. The data on permeation, whose tests were carried out soon after the filtration tests without any discontinuity, held no constant rates (Cf. Figs. 2 and 3).
It is imaginable that in the cake there was some unsteady distribution of specific resistance, occurring, probably, in two different cases shown below:
(I) When the mean specific resistance is constant:
Even if the cake has certain distribution of its specific resistance along its thickness, there may be a case when the Ruth's equation holds, provided its mean specific resistance, rfυ, remains constant thronghout the filtration operation. This phenomenon may be explained as follows. Suppose a simple model of a distribution curve for the specific resistance of the cake, r, along its thickness, and its development due to the progress of the constant-pressure filtration operation may be assumed as shown in Fig. 6 (A).
In this case, the following three assumptions are being made:
(1) The specific resistance of the cake initially formed on the surface of the filter medium, rB, ismaximum and is held to be constant.
(2) The specific resistance of the cake newly formed on the surface of the already deposited cake, rs, is minimum and its variation is almost negligible.
(3) The specific resistance of the cake at any point x and any time θ, r, is given by Eq. (3). In such a case the mean specific resistance, rfυ, is given by Eq. (3') and its value is constant.
(II) When the mean specific resistance gradually increases:
In the case as shown in Fig. 6(B), the value of rfυ may vary gradually with the progress of filttation. The Underwood's type plot, in this case, naturally concaves upward. Further, there may appear a negative value of resistance coefficient of the caked cloth in the Underwood's type plot, or in the Ruth's type plot, as cited in Fig. 5. The author supposes that these are due to the gradual increase of the mean specific r sistance.
A filtration equation, Eq. (13), is proposed together with the method of determining the experimental constant in the equation. This Eq. (13) has been derived from Eqs. (11) and (12), the former of the two is a combined form of Eq. (10) and bfυ/rfυ=const5). Fig. 7 and Eqs. (4)-(10) illustrate the process taken for arriving at the conclusion, in which an assumption is made of the mechanism of cake filtration accompanied by scouring effect and standard blocking¹⁾.
The author's data on continuous vacuum filtration^3.4), are almost equal to the data on the earlier period of the constant-vacuum-batch filtration, but they are different from the succeeding ones as shown in Table 1.

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In order to study the filtration characteristics of Kaolin slurries, a number of experiments were conducted in constant-pressure filtration, and measurements of the hydraulic pressure variations within actual filter-cakes at constant-pressure filtration (using air-sealed manometers) and compression permeability experiments (using a consolidometer) were made.
The results may be summarized as follows:
(i) The Ruth's coefficients K₂₀ obtained from Eqs. (3) and (4) showed deviations of less than 10% from the actual filtration results K_20f.
(ii) The values of m obtained from Eq. (4) showed good agreement with m′ obtained from Eq. (4′), as revealed in Table 3. Consequently, it may safely be concluded that so far as Kaolin slurries are concerned, experiments in constant pressure filtration besides mere compression tests would be enough to make clear the behaviours thereof.
(iii) The specific resistance αf of the constant-pressure-filtration cakes of Kaolin slurries proved to be a function not only of P but also of s and V.
(iv) By the direct measurements of liquid pressure distribution in the cakes under constant-pressure filtration, the cake thickness L was observed to be exactly linear with the filtrate volume V, as shown in Fig. 7. m″ obtained from Eq. (10) was nearly equal to m or m′.
(v) Liquid pressure distribution as measured by using air-sealed manometers showed closer approximation to P_x vs. x′/L curve obtained from Eq. (7′) as shown in Fig. 6-1, rather than Px vs. x/L curve obtained from Eq. (7).

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Using 1/2″, 3/4″ and 1″ gas pipes, each provided with the DIN standard nozzle-flow meters with their throat area ratios of 0.96, 0.313 and 0.466, the author measured the flow rates and pressure drops, at the nozzles, of flowing boiled starch. The discharge coefficients and Reynolds numbers, calculated from these, were plotted on semi-log papers.
The results obtained are listed below:
(1) When the Reynolds numbers were smaller than 3, 000, the discharge coefficients, as measured with any of the flow meters, varied with the change in the pipe diameters, although the area ratios were the same.
(2) When the throat area ratio was 0.096 and the Reynolds numbers were larger than 4, 000, the discharge coefficients approximately coincided with each other, the deviations from the correlation line being within ±2%.
(3) When the concentration of the boiled starch was 4.96 and the throat area ratio 0.096, it was impossible to measure the pressure drops at the nozzles.
(4) when the throat area ratio was 0.313 and the Reynolds numbers were larger than 4, 000, the difference between the discharge coefficients of the boiled starch and those of water were less than 4%, and the larger the Reynolds numbers, the smaller the differences.
(5) When the throat area ratio was 0.466, the discharge coefficients of the boiled starch were larger than those of water, and the thicker the boiled starch, the larger the differences.
Further the author proposes a method of calculating the flow-rates of pseudoplastic fluids, using the correlation curves between Red/C^2-1/n and Red.

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In wetted wall columns, pure carbon dioxide was absorbed in water containing surface active agent.
With the increase in the concentration of the agent, rippling on the surface of the liquid film decreased. When the concentration of the agent exceeded a certain value, rippling almost disappeared. The effect of this change in rippling on the rate of mass transfer from gas to liquid across the interface was studied, and the results obtained are shown in Fig. 2 and 3, in which HL is plotted versus Re on logarithmic coordinates.
From these results, it appears that with the decrease in rippling, the disturbance caused by the mixing action of ripples decreases and the flow pattern of the liquid film in the pseudo-stream line flow approaches that of the liquid film in the true viscous flow.
The results obtained by the present author and the previous investigators^{3, 6)} for the case when there was no rippling, are shown in Figs. 5 and 6, respectively, as the plots of HL/z versus l/p on logarithmic coordinates. The best line through the data can be expressed by Eq. (8). This experimental line lies above the theoretical line based on the unsteady-state diffusion theory derived by Pigford⁹. The discrepancy between the theory and the experiment is probably due to the difference between the assumed and actual flow conditions for the liquid film.

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The dissolution rate of a pipe wall into a falling liquid film was measured. Systems employed for this study were iron in dilute sulfuric acid (0.01N) and zinc in aqueous iodine-potassium iodide solution (0.01N).
On the assumption that the diffusion of oxygen or iodine from the bulk of liquid to the wall surface was the controlling mechanism, the height of a liquid phase transfer unit, HL, was calculated and the result was compared with the one obtained from the theoretical equation, which the author had derived, supposing the existence of an unsteady-state diffusion and parabolic velocity distribution in the liquid film. The observed values of HL were in good agreement with the values obtained by means of the theoretical equation, as shown in Figs. 3-6.
From these results, it appears that the liquid film is formed in the viscous flow even though ripples are present at the gas-liquid interface and that the turbulence caused by the ripples remains within the thin layer near the interface.

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