document: Inspired by energy-fueled phenomena such as cortical cytoskeleton flows [46,45,32] during biological morphogenesis, the theory of active polar viscous gels has been developed [37,33]. The theory models the continuum, macroscopic mechanics of a collection of uniaxial active agents, embedded in a viscous bulk medium, in which internal stresses are induced due to dissipation of energy [41,58]. The energy-consuming uniaxial polar agents constituting the gel are modeled as unit vectors. The average of unit vectors in a small local volume at each point defines the macroscopic directionality of the agents and is described by a polarization field. The polarization field is governed by an equation of motion accounting for energy consumption and for the strain rate in the fluid. The relationship between the strain rate and the stress in the fluid is provided by a constitutive equation that accounts for anisotropic, polar agents and consumption of energy. These equations, along with conservation of momentum, provide a continuum hydrodynamic description modeling active polar viscous gels as an energy consuming, anisotropic, non-Newtonian fluid [37,33,32,41]. The resulting partial differential equations governing the hydrodynamics of active polar viscous gels are, however, in general analytically intractable.
extractive_keyphrases: active polar viscous gels biological morphogenesis constitutive equation continuum hydrodynamic description cortical cytoskeleton flows equation of motion fluid gel polarization field uniaxial active agents uniaxial polar agents viscous bulk medium
abstractive_keyphrases: energy consuming, anisotropic, non-newtonian fluid models the continuum, macroscopic mechanics polar viscous gels theory of active polar viscous gels these equations, along with conservation of momentum