Gradual Variation of Specific Resistance in Constant-Pressure Filtration and Reformation of the Operating Equation to Meet the Case

Abstract

Listen

Translate article

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 filtration3.4), 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.