Newtonian Fluid

Model

Definition

A Newtonian Fluid is a fluid in which the viscous stresses arising from its flow, at every point, are linearly proportional to the local strain rate—the rate of change of its deformation over time.

Constitutive Relation

τij=2μeij+λ(∇⋅v)δij\tau_{ij} = 2\mu e_{ij} + \lambda(\nabla\cdot\mathbf{v})\delta_{ij} For incompressible flow (∇⋅v=0\nabla\cdot\mathbf{v}=0): τij=μ(∂vi∂xj+∂vj∂xi)\tau_{ij} = \mu \left(\frac{\partial v_i}{\partial x_j} + \frac{\partial v_j}{\partial x_i}\right)

Relationships