The Assumption of Linear Gradients

In Sects. 6, 7, and 8 we have derived equations for the conservation of linear momentum, energy and the mass of molecular species. We now define the gradients of the related variables as k = (Vv) and a = V In T, and b, = V In n,. In general each of these gradients is a function of both position r,. and time t. It is usually adequate to assume that the higher derivatives of these variables are sufiiciently small that, over distances comparable to molecular dimensions, they may be neglected, and thus we may use the following truncated Taylor series for velocity, temperature, and concentration  

With this assumption each molecule sees only constant gradients of velocity, temperature, and concentration. 

In considering isothermal systems of constant composition, we set both a and b, equal to zero. In later discussions, however, we will sometimes assume 

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