  We discuss a pure hyperbolic alternative to the Navier-Stokes equations,
which are of parabolic type. As a result of the substitution of the concept of
the viscosity coefficient by a microphysics-based temporal characteristic,
particle settled life (PSL) time, it becomes possible to formulate a model for
viscous fluids in a form of first order hyperbolic partial differential
equations. Moreover, the concept of PSL time allows the use of the same model
for flows of viscous fluids (Newtonian or non-Newtonian) as well as
irreversible deformation of solids. In the theory presented, a continuum is
interpreted as a system of material particles connected by bonds; the internal
resistance to flow is interpreted as elastic stretching of the particle bonds;
and a flow is a result of bond destructions and rearrangements of particles.
Finally, we examine the model for simple shear flows, arbitrary incompressible
and compressible flows of Newtonian fluids and demonstrate that Newton's
viscous law can be obtained in the framework of the developed hyperbolic theory
as a steady-state limit. A basic relation between the viscosity coefficient,
PSL time, and the shear sound velocity is also obtained.
