Simplification of the Interface Boundary Conditions for a Thin Film

Simplification of the Interface Boundary Conditions for a Thin Film 

For the present analysis, we are considering a thin film. In this case, it was shown in the previous chapter that Vv = mAh = slch, so that 

we preserve the notation of the previous chapter. The variables without primes are dimensionless. 

Utilizing (6-16), we see that rather simpler approximations can be made for the unit normal and related quantities in the thin-film limit, namely, 

We determine the unit tangent vectors from n by applying the conditions n t, = 0, t tj = 

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