| Abstract
| - It is argued in this article that the remarkable successes achieved in simulating the flow of Newtonian fluidsin complex geometries cannot currently be achieved for most important flows of complex fluids. The exampleschosen to illustrate this thesis are the processing of polymer melts, the flow of wormlike micellar surfactantfluids, the flow of suspensions, and the flow of non-Newtonian fluids in porous media. Despite the efforts ofrheologists over the past five decades, fully adequate rheological equations of state cannot be provided forany of these fluids. This can be attributed to the mesoscale structures (within the fluids viewed as continua)underlying their rheological complexity. It is concluded that simulations carried out at several scales, usingsuitable up-scaling techniques, will be necessary to provide numerical predictions at the process (continuum)level. Empiricism will continue to play a role in process engineering.
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