Some liquids, usually those with more complex molecular structure, do not obey the
Newton's law as stated in Fig.D-5. They are called
non-newtonian fluids. As an example, the case of macromolecular organic liquids may be
cited: these usually exhibit decrease of effective viscosity
with increasing magnitude of the gradient
. This is due to originally intertangled
molecules becoming ordered with increasing shear into parallel structures
- which can move, relatively to each other, much more smoothly.
The phenomenon is known as pseudoplasticity. In at least some weak form it
is encountered
in almost all lubricating oils. Some of viscoplastic liquids are, moreover,
thixotropic: the decrease of effective viscosity is time-dependent (the effect is the
more pronounced the longer the shear is allowed to act). Thixotropy may be reversible
or irreversible (molecules retain their ordered arrangement). On the other hand, there are
liquids called dilatant in which the resistance to mutual motion of layers
increases during flow - this is often encountered in some suspensions of solid particles.
The problems of non-newtonian behaviour are important in the field of chemical and food machinery, where the
range of suspensions and polymers, the flow of which is strudied, is necessarily very
large and flow studied sometimes border with processes of plastic deformation.
Let us also note that many liquids encountered in living organisms - such as e.g. blood -
often exhibit pronounced non-newtonian behaviour.
In evaluations of the
friction loss coefficient, the viscosity
is almost always encountered
in a dimensionless complex together with velocity
and some
characteristic dimension of the flowfield - usually with the pipe diameter
. The importance of this complex was
discovered in 1883 by O. Reynolds, professor of physics on Manchester.
Because it is a value without dimension,
a mere number, it is called Reynolds number :
For a given flow rate of air, Fig.D-8 may be used to make
a rough estimate of the Reynolds
number magnitude.
Reynolds has also dicovered an even more interesting
property of this
Osborn Reynolds, 1842-1912
number. He has established that there are
two different possible flow regimes
and it is the magnitude of the Reynolds number which determines which
of them takes place. One of this regimes is called laminar.
It is characterised by smooth
sliding of imagined fluid layers.
In the classical Reynolds experiment, with
some colouring agent added to fluid to make possible flow visualisation,
the color in the laminar regime forms smooth undisturbed filament.
In the other regime, the turbulent one
(from latin word "turbo" , meaning "eddy"), which prevails
at larger velocities, the clour agent leaves a compicated, chaotic trace. This is
caused by variations in time due to action of nonperiodic vortex motion (in some arrangements of the experiment,
intensive turbulent mixing leads to virtual disappearance of the
colour filament).
The transition from the laminar flow into the turbulent one takes place at a critical value
of Reynolds number. As a rough guide, it is possible to say that flow will be turbulent above . The transition process is
a consequence of instability of laminar flow. The uncertainty of the critical
value is due to the fact that processes
near their stability limits are easily destabilised even by
minute disturbance effects (such as noise of the machinery that is used to generate flow).
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This is page Nr. D04 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS" Any comments and suggestions concerning this text may be mailed to the author
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