醸造醪の濾過, 圧搾に関する研究 (第3報) : 圧搾における平均比抵抗の新しい解析法

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Ruth differential equations involving empirical resistance have been the main source of formulae for practical, computational purposes. The equation has been developed using the Ruth specific filtration resistance. The coefficients must be related experimentally to the solid compressive pressure. Although in almost cases, the fluid behavior is layer flow through the filter bed, no reliable theoretical relation between permeability and porosity as determined by compressive pressure has been developed.The J factor, i.e. correction factor for filtration resistance, has been discussed by Tiller and Shirato. But this J factor is deduced from Ruth theory and it is obtained from the following two besic assumptions : (1) The compressive equilibrium state of solid layer in compressioin permeability cells obtains for minute parts of the active filtration cake.(2) The specific filtration resistance is a function only of the applied pressure.Hitherto, inorganic materials have been used in many filtration researches. When natural organic coloidal slurries are carried on, it is difficult to apply assumption (1), since the these materials swell during the compression permeability test. Furthermore, these materials form a stable emulsion system, so that no caked solids deposit proportionally to the filtrate mass in the Ruth cake filtration equation. Therefore it is necessary to establish a new theory. In this theory, the deposited cake is nearly constant, and porosity decreases proportionally to the filtrate mass; so it is considered that porosity decreases proportionally to m. (ratio of mass of wet cake to mass of dry cake)Therefore the following equation is obtained : [numerical formula] After a while, as α_c becomes nearly constant, the experimental equatioin of α_c is defined from both experimental data and equation (1).0<θ≲7 log α_c=(3.15)(10^<-1>)・P^<0.115>・θ+0.905logP+13.225 (2)7<θ≲40 log α_c=(1.1)(10^<-2>)・θ+0.945logP+13.401 (3)40<θ<400 log α_c=(2.48)(10^<-3>)・θ+logP+13.540 (4)Equations 2,3,4 indicate that α_c is a function of both θ and P. This fact of α_c is commonly accepted. Equations 2,3,4 are very accurate for experimental data. If equation 1 and equations 2,3,4 are solved, the following operational equations are obtained.0<θ≲7 ln(1-0.2775υ)=0.293P^<-0.0>(10^<-3.15×10^<-2>>・p^<0.115>・θ-1) (5)7<θ≲40 ln(1-0.2775υ)=0.548P^<0.05>(10^<-1.1×10^<-2>・θ>-1) (6)40<θ>400 ln(1-0.2775υ)=1.768(10^<-2.48×10^<-3>・θ>-1) (7)Equation 5,6,7 are accurate within a 3-4% error range. In equations 5 and 6,v is a function of both θ and P, but in equation 7,it is a function of θ only. In this case, we suggest that the cakes are in equilibrium dynamically at the applied pressure; and the state is a compression mechanism.
社団法人日本生物工学会の論文
1963-08-15

醸造醪の濾過, 圧搾に関する研究 (第3報) : 圧搾における平均比抵抗の新しい解析法

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