Shape of adsorption wave for different isotherms

Ka is the mass transfer coefficient and / is the function describing a particular isotherm providing a relation between solute concentration in stationary phase Cs) and equilibrium composition of solute in mobile phase. Equation 8.16, 8.20, and 8.21 can be solved simultaneously with the following boundary conditions to obtain breakthrough curves C versus t) for adsorption. This is illustrated in the following example for linear isotherm. 

Example 8.2 A solution containing biological compound was fed at an interstitial velocity of 20 cms/hour to a fixed bed column. The feed composition is 4 milligrams per milliliter, low enough to have a linear adsorption isotherm given below 

The mass transfer coefficient Ka for this system is approximately equal to 105 h. The void fraction of packing is 0.66. Find the breakthrough curves for the column length 0-0.05 cms. 

Solution This is a problem where the dynamics of fixed bed result in partial differential equations given below 

These partial differential equations can be converted to ordinary differential equations nsing orthogonal collocation. For this purpose, we will use the shifted Legendre polynomials whose roots and matrices are provided below. 

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