Chemical Engineering May 2023 - 25

Facts At Your Fingertips
Conceptualizing Fluid Viscosity
Department Editor: Scott Jenkins
V
iscosity is an important property
for understanding the flow
behavior of liquids, mixtures,
emulsions, slurries and other materials
in industrial processes. This onepage
reference provides a refresher
on conceptualizing viscosity.
Intermolecular forces
Viscosity is a measure of a material's
resistance to flow, and is governed by
the strength of intermolecular forces
among molecules, as well as by the
molecular shapes. In liquids, the internal
friction results from stretching
and breaking the London dispersion
forces between adjacent close-lying
molecules of the fluid. Liquid flow only
occurs if the molecules are able to
move past one another with minimal
resistance. Strong intermolecular attractive
forces make it more difficult
for liquid molecules to move with respect
to one another, leading to higher
viscosity values. London dispersion
forces increase with chain length.
A relationship also exists between
viscosity and molecular shape. Liquids
with longer, more flexible molecules
tend to have higher viscosities
than those composed of more
spherical or shorter-chain molecules.
Longer molecules can also become
entangled with one another, making
it more difficult for them to move past
one another.
'Two-plates' model
The two-plates model offers a way
to describe viscosity mathematically.
Consider two imaginary plates parallel
to each other, with fluid between them
(Figure 1). If a force (shear force) is applied
to the upper plate over a space
with area A, while the lower plate remains
stationary, the layer of fluid just
below the plate moves with it. For the
purpose of the model, it is assumed
that the fluid sample adheres to the
plates, and the flow is imagined to be
laminar, in the form of layers of fluid
without turbulence.
The force required to effect the
shearing is known as shear stress,
often expressed as the symbol tau
(τ). The units of shear stress are Pascals
(N/m2). The shear rate ( ∙γ
; ) is the
rate of deformation of the liquid as
a result of shear stress). Shear rate
(with units of s-1) is thought of as
velocity (m/s) over the distance between
the plates (h).
Shear stress: ∙γ = F / A
Shear rate: ∙γ = v / h
(1)
(2)
The ratio of applied shear stress to
the resulting rate of shear, Viscosity
units are the poise (mPa·s). A related
parameter is yield stress, the amount
of force required to get a material to
begin flowing.
Newtonian vs. non-Newtonian
Fluids that are ideally viscous (Newtonian
fluids) have constant viscosity for
all shear-rate values (Figure 2). Water
and hydrocarbons often exhibit Newtonian
behavior. For shear-dependent
fluids, on the other hand, the viscosity
varies. Because of this, the shear rate
at which the viscosity was determined
needs to be specified. This is known
as apparent viscosity.
If a fluid's apparent viscosity is not
constant at a given temperature and
pressure, but is dependent on flow
conditions, such as flow geometry,
shear rate and others, then the fluid
is said to behave in a non-Newtonian
manner. For many industrial applications,
expressions of viscosity as a
single value fail to capture the full picture
of the many factors that affect
viscosity. Non-Newtonian viscosity
behaviors include the following:
Pseudoplasticity (shear-thinning) occurs
when a fluid's viscosity decreases
with increasing shear rate. Many
emulsions, polymer melts and solutions,
paints, blood and some solid
suspensions exhibit this property.
Dilatant
show increasing
(shear-thickening) fluids
viscosity
with
increasing
shear rate. Dilatant behavior
is observed in starch suspensions in
water, quicksand and in some highmolecular-weight
polymers used in
drilling muds.
Thixotropy is a situation where a
fluid's viscosity decreases over time
under constant shear stress. Clay
CHEMICAL ENGINEERING WWW.CHEMENGONLINE.COM MAY 2023
FIGURE 1.
A force applied to the top plate will
effect shearing in the fluid below
Dilatant
(shear-thickening)
Newtonian
A
F
Fluid layers
Pseudoplastic
(shear-thinning)
Shear rate ∙γ (s-1)
FIGURE 2. Newtonian fluids show constant viscosity
for all shear-rate values, while non-Newtonian
fluids show divergence
suspensions used as drilling muds,
mayonnaise and some paints and
inks behave this way.
Rheopecty refers to a materials that
show a rise in viscosity as a result of
consistent agitation. Some lubricants
exhibit this property, as does heavy
cream. A gypsum suspension in water
is another example.
A flow curve (rheogram) is a graphical
representation of how a flowing
material behaves when subjected to
increasing or decreasing shear rates
(Figure 2). Newtonian fluids have a
linear flow curve with a slope intercept
at zero. Non-Newtonian fluids
have non-linear flow curves and often
a non-zero intercept.
n
References
1. Mezger, Thomas. " The Rheology Handbook, " Hannover, Germany:
Vincentz Network, 2020, pp. 108-121.
2. LibreText Chemistry, Intermolecular forces in action, Chapter
11.4, Open Textbook project, 2020. www.libretexts.org.
3. McGregor, R., Viscosity: the Basics, Chem. Eng., Aug. 2009,
pp. 34-39.
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Shear stress τ (Pa)
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