nonnewtonian fluid
Dear all, could you recommend me a book about nonnewtonian fluids? I wonder how I can write NavierStokes Equations for a nonnewtonian fluid. a paper which gives governing equation is also welcome. thanks in advance

Re: nonnewtonian fluid
What sort of nonnewtonian fluid? In the most general case, the viscosity becomes a rank 4 tensor which is a function of the velocity and perhaps strain. The weak form looks like is find <code>(u,p) \in V \times P</code> such that
\int_\Omega \Big[ \rho v \cdot (u \cdot \nabla u) + \eta \DD v : \DD u  p \nabla\cdot v  q \nabla\cdot u  v \cdot \bm f \Big] + \int_{\Gamma} v \cdot (p I  \eta \DD u) \cdot n = 0 for all <code>(v,q) \in V_0\times P</code> where <code>\DD u = \frac 1 2 (\nabla u + (\nabla u)^T)</code> is symmetric gradient, <code>\rho</code> is density, <code>\eta</code> is viscosity (a rank 4 tensor in the most general case, often a scalar). The boundary integral is over the nonDirichlet portion of the boundary and is usually replaced by a boundary condition, although it's admissible as an outflow condition (this has nothing to do with nonNewtonian flows). A good book on viscoelastics is @book{owens2002cr, title={{Computational Rheology}}, author={Owens, R.G. and Phillips, T.N.}, year={2002}, publisher={Imperial College Press} } I'm not aware of any good books on anisotropy, examples of powerlaw fluids (arguably the most common nonNewtonian fluids) include the earth's mantle, ice, blood, and paint. Polymers are the usual viscoelastic fluid. 
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