Shear thickening, i.e. the increase of the viscosity with increasing shear rate as it occurs in dense colloidal dispersions and polymeric fluids is an intriguing phenomenon with a considerable potential for technical applications. The theoretical description of this phenomenon is patterned after the thermodynamic and mesoscopic modeling of the orientational dynamics and the flow behavior of liquid crystals in the isotropic and nematic phases, where the theoretical basis is well-established. Even there the solutions of the relevant equations recently yielded surprises: not only stable flow alignment and a periodic behavior (tumbling) are found as response to an imposed stationary shear flow but also irregular and chaotic dynamics occurs for certain parameter ranges. To treat shear-thickening fluids, a non-linear Maxwell model equation for the symmetric traceless part of the stress tensor has been proposed in analogy to the equations obeyed by the alignment tensor of nematics. The fluid-solid transition is formally analogous to the isotropic-nematic transition. In addition to shear-thickening and shear-thinning fluids, substances with yield stress can be modeled. Furthermore, periodic stick-slip-like motions and also chaotic behavior are found. In the latter cases, the instantaneous entropy production is not always positive. Yet it is comforting that its long-time average is in accord with the second law.

Shear thickening, i.e. the increase of the viscosity with increasing shear rate as it occurs in dense colloidal dispersions and polymeric fluids is an intriguing phenomenon with a considerable potential for technical applications. The theoretical description of this phenomenon is patterned after the thermodynamic and mesoscopic modeling of the orientational dynamics and the flow behavior of liquid crystals in the isotropic and nematic phases, where the theoretical basis is well-established. Even there the solutions of the relevant equations recently yielded surprises: not only stable flow alignment and a periodic behavior (tumbling) are found as response to an imposed stationary shear flow but also irregular and chaotic dynamics occurs for certain parameter ranges. To treat shear-thickening fluids, a non-linear Maxwell model equation for the symmetric traceless part of the stress tensor has been proposed in analogy to the equations obeyed by the alignment tensor of nematics. The fluid-solid transition is formally analogous to the isotropic-nematic transition. In addition to shear-thickening and shear-thinning fluids, substances with yield stress can be modeled. Furthermore, periodic stick-slip-like motions and also chaotic behavior are found. In the latter cases, the instantaneous entropy production is not always positive. Yet it is comforting that its long-time average is in accord with the second law.