The theory of elastic and viscoelastic micropolar liquids

A model of a liquid medium with couple stresses, which generalizes the theory of a viscous micropolar liquid to the same degree with which the constitutive relations of a simple viscoelastic liquid generalize the equations of a state of a Newtonian liquid, is proposed. The similarity and distinction between the model of an elastic micropolar liquid and the model of a medium equipped with a director field and used to describe nematic liquid crystals is discussed. Problems of the equilibrium of a micropolar liquid, including the problem with a free surface are considered. The equilibrium conditions of the phases of an elastic micropolar liquid are derived by a variational method. Problems of the flow of a viscoelastic liquid are derived by a variational method. Problems of the flow of a viscoelastic liquid in a circular tube and between rotating coaxial cylinders are solved. The results obtained may be useful in the mechanics of suspensions, magnetic and biological liquids, liquid crystals and other liquid media of complex structure.