The theory of elastic and viscoelastic micropolar liquids

A model of a liquid medium with couple stresses, which generalizes the theo ry of a viscous micropolar liquid to the same degree with which the constit utive 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 mediu m equipped with a director field and used to describe nematic liquid crysta ls is discussed. Problems of the equilibrium of a micropolar liquid, includ ing the problem with a free surface are considered. The equilibrium conditi ons of the phases of an elastic micropolar liquid are derived by a variatio nal 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 circ ular tube and between rotating coaxial cylinders are solved. The results ob tained may be useful in the mechanics of suspensions, magnetic and biologic al liquids, liquid crystals and other liquid media of complex structure. (C ) 2000 Elsevier Science Ltd. All rights reserved.