AbstractWe present conceptual designs of viscometers corresponding to our new exact molecular simulation method (Dayal & James, J. Mech. Phys. Solids, vol. 58 (2), 2010, pp. 145–163). The molecular simulation method is a generalization of the method of Lees & Edwards (J. Phys. C: Solid State Phys., vol. 5, 1972, p. 1921), and includes a three-parameter family of incompressible flows, as well as compressible flows and unsteady flows exhibiting vortex stretching. All fluids are allowed. The method gives a way to simulate these flows using relatively few molecules, in the absence of a constitutive relation describing the fluid. This paper presents conceptual designs for viscometers that produce large families of these flows. The basic theme of this paper is that the flows discussed here are a better way to characterize the properties of complex fluids than the currently available methods, such as those based on viscometric flows.