無限染浴における繊維内拡散係数を求める簡略式について

抄録

There are two equations to evaluate the rate of dyeing from a finite dyebath, one of which is a exponential form A=A_∞(1-e^-Kt), where A is the percentage of dye adsorbed at a time t, A^∞ the equilibrium exhaution and K a velocity constant.
In this paper, this equation is expanded to the case of an infinite dyebath, and a simple equation to obtain the diffusion coefficient within a fibre is derived.
The equation is:
-ln(1-C_t/C_∞)=5.85Dt/r²+0.346 where C_t is the amount of dye adsorbed at t, C_∞ the amount at the equilibrium, D the diffusion coefficient of dye and r the radius of the fibre.
This logarithmic equation agrees with that of the Hill's and also experimental results, provided C_t/C∞>0.5.
Applying this equation, C_∞ can be calculated from adsorption data at some arbitrary short times with an accuracy which is sufficient for most purposes.