A long flexible thread tends to align in the direction of flow but periodically
folds (as depicted) and stretches again.
Inelongational flowof the same velocity gradient, the viscous stresses
are greater: see Eq. (5.2). Anisometric solid particles become aligned in the
direction of flow; flexible particles become extended, i.e., anisometric, and
aligned. Particles that are close to each other become separated from each
other, while they can stay together in simple shear flow: a doublet of spheres
then continues rotating as one dumbbell-shaped particle.
Turbulent Flow. In Figure 5.4, flow through a tube is depicted. In
Figure 5.4a, the flow is laminar (simple shear, Poiseuille flow) and the
velocity profile is parabolic. If the flow velocity is increased, a flow profile
like that in 5.4b may develop. The streamlines become wavy and eddies
develop. This implies that the flow becomes more chaotic and is called
turbulent. Near the wall the flow is still laminar, at an increased velocity
gradient as compared to the situation in 5.4a. For still higher velocity, the
flow becomes increasingly chaotic, and the thickness of the laminar layer
near the wall decreases, as depicted in 5.4c. The flow profile drawn now gives
thetime averageof the flow velocity at various distances from the center.
Any volume element is subject to rapid fluctuations both in velocity and in
direction of flow. The average flow profile is almost block-shaped, except for
a high velocity gradient near the wall.
Eddies(vortices, whorls) are thus superimposed on the average flow
direction, and this causes a strong mixing effect. The size of the largest
eddies is of the order of the smallest dimension of the vessel (e.g., the pipe
diameter). These large eddies transfer their kinetic energy to smaller ones,
which transfer it to still smaller eddies, etc. With decreasing eddy size, the
FIGURE5.4 Streamlines of flow through a tube. In (a) the flow is laminar
(Poiseuille flow), in (b) and (c) flow is turbulent. The average flow velocity increases
from (a) to (c). In (a) a velocity profile is given, in (b) and (c), average velocity
profiles. See text.