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The principle underlying expression basically involves the separation of a solid from the liquid in which it is suspended by passing the mixture through a porous medium with pore sizes too small to allow the passage of the solid particles at an applied pressure. The analytical method of the finite element method has been used to determine the relationship between pressure distribution and displacement distribution along sludge cake height in a filter press expression process. The finite element formulation basically involves the properties of the sludge in question as distinguished from other solution. The solution domain was idealized as a one-dimensional quadratic shape function for the purpose of this analysis and the displacement function formulation method were employed in solving the pressure distribution. It was discovered that pressure increases with an increase in displacement of the cake at different time of expression. It was also discovered that pressure increases simultaneously with displacement as the time of expression increases. The ranges of displacement in a sludge cake height with increase time of expression increases with a decrease in sludge depth, hence impacting positively of the effective pressure. The displacement increases continuously with increase time of expression.

Effect of Displacement on Pressure Distribution in Cake Expression