Drying of Moist Clay A very thick slab of clay has an initia

Drying of Moist Clay. A very thick slab of clay has an initial moisture content of c0 = 14 wt %. Air is passed over the top surface to dry the clay. Assume a relative resistance of the gas at the surface of zero. The equilibrium moisture content at the surface is constant at c1 = 3.0 wt %. The diffusion of the moisture in the clay can be approximated by a diffusivity of DAB = 1.29 x 10^-8 m^2/s. After 1.0 h of drying, calculate the concentration of water at points 0.005, 0.01, and 0.02 below the surface. Assume that the clay is a semi-infinite solid and that the Y value can be represented using concentrations of wt % rather than kg mol/m^3, Plot the values versus x.

Solution

The drying follows a differential equation analogous to heat conduction.

The differential equation is given by dC/dt = D d^2C/dx^2

The boundary conditions are Cs = .14 ( initial condition equal to surface concntration)

Ci = .03 ( moisture conc initially present in the solid)

hen the solution is C(x,t) = Cs + (Ci-Cs) erf ( .5*x/(sqrt( DAB*t))

Plugging in the values for t = 1 hour = 3600 seconds, the concentrations at .005 m, .01 m and .02 metres are

obtained from erf (.005/2Sqrt(Dt)), etc

these values are .396, .7 and .962

The concentrations for these depths (.005, .01,.02) are then

Cs +( Ci-Cs)*erf( ) = .03+.11*erf( )

for x =.005 the conc at 60 mts (1 hr) = .03 + .11* .396 =.07356

for x = .01 .,conc = .03 +.11* .7 = 0.107

for x = .0, the conc =.03 +.11*.962 =.136

As the argument of the error function increases, it goes to 1, and the conc at the surface tends to Cs +(Ci-Cs)= Ci =.14