Time-derivatives and frame-invariance beyond Newtonian fluids

Replacing the time-derivatives with spatial gradients is a quite useful and ordinary method to work with the Chapman-Enskog expansion when dealing wit h non-uniform fluids. However, to perform the substitution, approximated ba lance equations, which are not frame invariant, are usually used. Alternati vely, frame-invariant but not frame-indifferent expansions may be derived. In this paper we analyze the possibility of deriving a Chapman-Enskog expan sion both frame-invariant and frame-indifferent. (C) 2000 Academie des scie nces/Editions scientifiques et medicales Elsevier SAS.