Continuous sedimentation of ideal suspensions

Abstract

We formulate (Bustos, Concha and Wendland 1990, Bustos, Paiva and Wendland 1990, Concha and Bustos 1992) the mathematical model for continuous sedimentation of an ideal suspension in an ideal continuous thickener (ICT) as an initial-boundary value problem (see Chapter 6):

$$ \tfrac{{\partial \varphi }}{{\partial t}} + \tfrac{{\partial f(\varphi ,t)}}{{\partial z}} = 0{\kern 1pt} for{\kern 1pt} (z,t) \in {Q_T}$$

((8.1a))

$$ \varphi (z,0) = {\varphi _I}(z){\kern 1pt} for{\kern 1pt} z \in \Omega $$

((8.1b))

$$ \gamma \varphi (0,t) \in {\varepsilon _0}({\varphi _\infty }){\kern 1pt} for{\kern 1pt} t \in \tau $$

((8.1c))

$$ \gamma \varphi (L,t) \in {\varepsilon _L}({\varphi _L}(t)){\kern 1pt} for{\kern 1pt} t \in \tau $$

((8.1d))