Would someone tells me where is the error in the equation (ɛ). $\frac{d(x)}{(dt)} = \frac{(K∆P)}{φμs[ML+(1-M)x]}$ (2.14)
The velocity of the leading edge of the perturbation is given by :
$\frac{d(x+ɛ)}{(dt)} = \frac{(K∆P)}{φμs[ML+(1-M)(x+ɛ)]}$ (2.15)
By subtracting equation (2.15) from (2.14) and provided that ɛ⪡xf:
$\frac{d(ɛ)}{(dt)} = \frac{(-K∆P(1-M)ɛ)}{φμs[ML+(1-M)x]^2}$
Therefore, ɛ=e^C, where C is:
${C} = \frac{(-K∆P(1-M))}{φμs[ML+1-Mx]^2}$