81
4
The Reynolds number of a fluid differentiates between turbulent and
laminar flows.
Reynolds number = ρ
η
vd /
(4.1)
where
5 ρ = Density
5 v = Velocity
5 d = Diameter of flow
5 η = Viscosity
If the value of the Reynolds number is ≥2100, the flow is called
turbulent; otherwise, the flow is called laminar. Polymers, either in
the form of viscous resin or molten polymer, have laminar flow only
[4]. Usually, the Reynolds number for liquid resins and molten
polymers is <100.
4.1.1 Viscometry
4.1.1.1 Newtonian and Non-Newtonian Behaviour
Newton’s law of fluids states that shear stress is directly proportional
to the shear rate and the proportionality constant is called viscosity
(η)
Shear stress and shear rate
τ γ
τ ηγ
∝ =
(
)
=
dv dt
/
(4.2)
where
5 τ = Shear stress
5
γ = Shear rate
5 η = Viscosity coefficient
The viscosity coefficient, η, is known as the viscosity of a fluid. In
Newtonian fluids, the shear rate of a fluid under isothermal conditions remains directly proportional to the shear stress at any point
of consideration, as shown in . Fig. 4.1. In non-Newtonian fluids,
the shear stress is not directly proportional to the applied shear rate
such that, when the shear stress is plotted against the shear rate, the
points are not in a straight line. The Weissenberg effect is seen in
non-Newtonian fluids. In this effect, a non-Newtonian fluid climbs
up the stirrer rod when it is stirred.
4.1.1.2 Shear Flows and Deformation
Non-Newtonian fluids have different categories as discussed here.
Viscoelastic Fluids Viscoelastic fluids are those which behave as viscous liquids and elastic solids simultaneously and also exhibit partial
elastic recovery after deformation.
Point to Ponder…
Tomato sauce shows thixotropic
behaviour. It does not come out of
the bottle instantaneously. Rather,
with time its viscosity comes down
slowly when it starts flowing out of
the bottle.
4.1 · Fundamentals of Rheology
4
The Reynolds number of a fluid differentiates between turbulent and
laminar flows.
Reynolds number = ρ
η
vd /
(4.1)
where
5 ρ = Density
5 v = Velocity
5 d = Diameter of flow
5 η = Viscosity
If the value of the Reynolds number is ≥2100, the flow is called
turbulent; otherwise, the flow is called laminar. Polymers, either in
the form of viscous resin or molten polymer, have laminar flow only
[4]. Usually, the Reynolds number for liquid resins and molten
polymers is <100.
4.1.1 Viscometry
4.1.1.1 Newtonian and Non-Newtonian Behaviour
Newton’s law of fluids states that shear stress is directly proportional
to the shear rate and the proportionality constant is called viscosity
(η)
Shear stress and shear rate
τ γ
τ ηγ
∝ =
(
)
=
dv dt
/
(4.2)
where
5 τ = Shear stress
5
γ = Shear rate
5 η = Viscosity coefficient
The viscosity coefficient, η, is known as the viscosity of a fluid. In
Newtonian fluids, the shear rate of a fluid under isothermal conditions remains directly proportional to the shear stress at any point
of consideration, as shown in . Fig. 4.1. In non-Newtonian fluids,
the shear stress is not directly proportional to the applied shear rate
such that, when the shear stress is plotted against the shear rate, the
points are not in a straight line. The Weissenberg effect is seen in
non-Newtonian fluids. In this effect, a non-Newtonian fluid climbs
up the stirrer rod when it is stirred.
4.1.1.2 Shear Flows and Deformation
Non-Newtonian fluids have different categories as discussed here.
Viscoelastic Fluids Viscoelastic fluids are those which behave as viscous liquids and elastic solids simultaneously and also exhibit partial
elastic recovery after deformation.
Point to Ponder…
Tomato sauce shows thixotropic
behaviour. It does not come out of
the bottle instantaneously. Rather,
with time its viscosity comes down
slowly when it starts flowing out of
the bottle.
4.1 · Fundamentals of Rheology