substances over a membrane against a concentration gradient exist; thereby,
passage of these substances through a tissue will be greatly hindered.
5.4 RECAPITULATION
Rheologists study the relations between stress (force per unit area) and
strain (relative deformation) of a material, generally as a function of time
scale or rate of strain. For elastic solids the modulus, i.e., stress over strain,
is a characteristic parameter; for pure liquids it is the viscosity, i.e., the ratio
of stress over strain rate. An elastic solid regains its original shape after the
stress is released and the mechanical energy used to deform it is regained; a
pure liquid retains the shape attained and the mechanical energy is
dissipated into heat.
Flow. Liquids thus flow when a stress is applied. The flow is laminar
if the streamlines are straight lines or smooth curves. The flow is
characterized by its velocity gradient (which equals the strain rate) and
the type of flow. Flow type can e.g. be rotational or elongational. Best
known is simple shear flow (parallel streamlines), which has an elongational
and a rotational component. In elongational flow, the velocity gradient is in
the direction of flow, in simple shear, normal to the direction of flow. The
elongational viscosity is larger than the common or shear viscosity. The flow
exerts a frictional stress on particles or other objects; this stress equals
viscosity times velocity gradient. The stress can cause particles to rotate and
to become deformed.
In turbulent flow, the streamlines are erratic and eddies occur. This
leads to a strong mixing effect and to a greater energy dissipation rate. Flow
is turbulent if the Reynolds number (proportional to flow velocity, channel
dimension, and the inverse of viscosity) is greater than a critical value.
Because of Bernoulli’s law, which states that the sum of pressure and kinetic
energy is constant, the strong velocity fluctuations in turbulent flow induce
pressure fluctuations. These cause, in turn, inertial forces to act on any
particles present.
Viscosity. The viscosity of liquids varies among molecular
configurations and generally increases with molar mass; it decreases with
increasing temperature. The addition of particles or of a solute leads to an
increased viscosity, the more so for a higher volume fraction. The increase is
generally (almost) independent of particle size, but it does depend on
particle shape and on the inclusion of solvent by the particles, particle
aggregates, or polymer molecules, since these variables affect the effective