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International Journal of Research in Environmental Studies

ISSN:
2059-1977

Vol. 5(3), pp. 42-47, July 2018

# Problems and prospects of cake filtration theories

Obiajulu E. Udegbunam* and Joel O. Ademiluyi

Department of Civil Engineering, University of Nigeria, Nsukka, Nigeria.

*To whom correspondence should be addressed. E-mail: udegbunam4real@yahoo.com.

Received 15 July, 2017; Received in revised form 07 August, 2017; Accepted 10 August, 2017.

# Abstract

**Keywords:**

Compressibility factor, Cake filtration equation, Reduction formula.

The constant vacuum filtration equation for compressible sludge which account for hydrostatic pressure, compressibility coefficient and specific resistance as a variable parameter should be considered further since the equation obtained can only be applicable to a sludge whose Trezaghi’s compressibility coefficient is much less than one. This may be the fact that the sludge filtration equation was derived using successive reduction method. Among the three main concepts of sludge filterability, the specific resistance concept is the most popular among the three concepts but most of the equations proposed based on this concept described the specific resistance as a constant average value. This is not in agreement with many research scientists who advocate that the specific resistance parameter should be a local variable one. One of the problems in Carman’s equation is the concentration, c which is the mass of dry cake per unit volume of filtrate. This parameter is difficult to evaluate. Also there is a problem of which area to be used in Carman’s equation, some previous workers advocate effective area of funnel while another school of thought proposed total area of funnel. The equation proposed which describes specific resistance as a local variable parameter is also limited in use in its present form except the maximum value of the specific resistance is adopted to describe sludge filterability, therefore there’s need for derivation of a new sludge filtration equation using another engineering or mathematical method in order to solve the problem of compressibility attribute of sludge called compressibility coefficient or factor, problem of which area to be used and the problem of concentration, c which is the mass of dry cake per unit volume of filtrate.

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