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.

Fig.D-8
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 to his address tesar@fsid.cvut.cz

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