Lecture 3 Flashcards
Newtonian fluids
Newtonian fluids maintain constant viscosity across all shear rates.
Shear thinning fluids
Shear-thinning fluids decrease in viscosity with increasing shear rate.
Shear thickening fluids
Shear-thickening fluids increase in viscosity with increasing shear rate.
Bingham plastics
Bingham plastics have a yield stress, behaving like solids until enough shear stress is applied to induce flow (then behave like fluids).
Types of reynolds flow regimes
Creeping flow Re <1: laminar, viscous driven no inertia
Laminar inertial 1<Re<2100 (inertia no turbulence)
Laminar turbulent (transitional) 2100<Re<4000
Turbulent Re >4000
Boundary conditions
Solid-liquid interface (no slip)
Interface between immiscible liquids
Liquid-gas interface
Symmetry
No slip condition
Thin layer of fluid adheres to solid surface
Fluid velocity in i-direction = Solid velocity in i-direction: (ni)solid
Whether solid is moving or stationary
Interface between immiscible fluids
– Velocity, vi, and shear stress tni are continuous at interface
(vi)fluid_1 =(vi)fluid_2
(τni)fluid_1 =(τni)fluid_2
Liquid gas interface
Shear stress of gas on a liquid is neglected
Symmetry boundary condition
Symmetry
– i.e. for flow between parallel plates
– Velocity symmetric about centerline (taken to be y=0)
– Velocity in x-direction = 0
Rheology
Deformation and flow of matter
Deborah number
De = Material relaxation time /Time scale of process
Characteristics of shear deformation of ideal solids
Instantaneous
Remain deformed state
DRAW shear
Characteristics of shear deformation of liquids
Deforms continuously under applied stress
Linear relationship between shear stress and strain rate (slope = viscocity)
DRAW IT AND EQUATIONS
Sign convention shear flux momentum
Shear is normal to N in the X direction and equals momentum flux of X in N direction which is the direction of the negative gradient from high to low velocity
Whats the difference between shear on a liquid and a solid
Although viscoelastic materials will ultimately cease all motion when a shear stress is applied, a fluid, by definition, will continue to deform when subjected to a constant shear stress
Whats the difference between dynamic viscosity and apparent viscosity
μ (dynamic) represents a constant viscosity for Newtonian fluids.
η is a generalized form of viscosity that can vary with the shear rate for non-Newtonian fluids.
