i = number of drainage surfaces [−]
L = thickness of compressed cake [m]
$ L_{1} $ = thickness of compressed cake at $ \theta_{c}=0 $ [m]
$ L_{x} $ = thickness of compressed cake at $ \theta_{c}=\infty $ [m]
$ p_{c} $ = applied expression pressure [Pa]
$ p_{f} $ = applied filtration pressure [Pa]
$ p_{p} $ = water permeation pressure [Pa]
$ p_{s} $ = local solid compressive pressure [Pa]
R = moisture content of cake on mass basis [wt%]
$ R_{e} $ = equilibrium moisture content of cake on mass basis [wt%]
$ R_{f} $ = ratio of added aluminum or polymer to solid mass in sludge [−]
s = mass fraction of solids in sludge [−]
$ U_{c} $ = average consolidation ratio [−]
v = filtrate volume per unit effective membrane area [m]

$$ \begin{array}{r l r l}{\alpha}&{{}={\mathrm{l o c a l~s p e c i f i c~f l o w~r e s i s t a n c e~o f~c o m p r e s s e d~c a k e}}}&{[{\mathrm{m/k g}}]}\\ {\varepsilon}&{{}={\mathrm{l o c a l~p o r o s i t y~o f~c a k e}}}&{[-]}\\ {\varepsilon_{1}}&{{}={\mathrm{e p i r i c a l~c o n s t a n t~i n~E q.~(2)~}}[{\mathrm{k g}^{\lambda}\cdot{\mathrm{m}}^{-\lambda}\cdot{\mathrm{s}}^{-2\lambda}}]}\\ {\varepsilon_{\mathrm{r}}}&{{}={\mathrm{e q u i l i b r i u m~p o r o s i t y~o f~c o m p r e s s e d~c a k e}}}&{[-]}\\ {\eta}&{{}={\mathrm{c r e e p~c o n s t a n t}}}&{[{\mathrm{s}}^{-1}]}\\ {\mu}&{{}={\mathrm{l i q u i d~v i s c o s i t y}}}&{[{\mathrm{P a}\cdot{\mathrm{s}}]}}\\ {\theta}&{{}={\mathrm{t i m e}}}&{[{\mathrm{s}}]}\\ {\theta_{\mathrm{c}}}&{{}={\mathrm{c o n s o l i d a t i o n~t i m e}}}&{[{\mathrm{s}}]}\\ {\lambda}&{{}={\mathrm{e p i r i c a l~c o n s t a n t~i n~E q.~(2)~}}[{-}]}\\ {\rho}&{{}={\mathrm{d e n s i t y~o f~f i l t r a t e}}}&{[{\mathrm{k g/m}^{3}}]}\\ {\rho_{\mathrm{s}}}&{{}={\mathrm{d e n s i t y~o f~s o l i d s}}}&{[{\mathrm{k g/m}^{3}}]}\\ {\omega_{0}}&{{}={\mathrm{t o t a l~s o l i d~v o l u m e~p e r~u n i t~c r o s s-s e c t i o n a l~a r e}}}&{[{\mathrm{m}}^{3}/{\mathrm{m}}^{2}]}\end{array} $$

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