12. Special Topics
12.1 Introduction
Fluid flows may include a broad range of additional physical phenomena that
take the subject far beyond the single-phase non-reacting flows that have been
the focus of this work up to this point. Many types of physical processes may
occur in flowing fluids. Each of these may interact with the flow to produce
an amazing range of new phenomena. Almost all of these processes occur in
important applications. Computational methods have been applied to them
with varying degrees of success.
The simplest element that can be added to a flow is a scalar quantity such
as the concentration of a soluble chemical species or temperature. The case in
which the presence of the scalar quantity does not affect the properties of the
fluid has already been treated in earlier chapters; in such a case, we speak of
a passive scalar. In a more complex case, the density and viscosity of the fluid
may be modified by the presence of the scalar and we have an active scalar.
In a simple example, the fluid properties are functions of temperature or the
concentration of the species. This field is known as heat and mass transfer.
In other cases, the presence of a dissolved scalar or the physical nature of
the fluid itself cause the fluid to behave in way that the stress in not related to
the strain rate by the simple Newtonian relationship (1.9). In some fluids, the
viscosity becomes a function of the instantaneous strain rate and we speak of
shear-thinning or shear-thickening fluids. In more complex fluids, the stress
is determined by an additional set of non-linear partial differential equations.
We then say that the fluid is viscoelastic. Many polymeric materials, including
biological ones, exhibit this kind of behavior, giving rise to unexpected flow
phenomena. This is the field of non-Newtonian fluid mechanics.
Flows may contain various kinds of interfaces. These may be due to the
presence of a solid body in the fluid. In simple cases of this kind, it is possible
to transform to a coordinate system moving with the body and the problem
is reduced to one of the kind treated earlier, albeit in a complex geometry.
In other problems, there may be bodies that move with respect to each other
and there is no choice but to introduce a moving coordinate system. A particularly important and difficult case of this kind is one in which the surface
is deformable. Surfaces of bodies of liquid are examples on this type.
12.1 Introduction
Fluid flows may include a broad range of additional physical phenomena that
take the subject far beyond the single-phase non-reacting flows that have been
the focus of this work up to this point. Many types of physical processes may
occur in flowing fluids. Each of these may interact with the flow to produce
an amazing range of new phenomena. Almost all of these processes occur in
important applications. Computational methods have been applied to them
with varying degrees of success.
The simplest element that can be added to a flow is a scalar quantity such
as the concentration of a soluble chemical species or temperature. The case in
which the presence of the scalar quantity does not affect the properties of the
fluid has already been treated in earlier chapters; in such a case, we speak of
a passive scalar. In a more complex case, the density and viscosity of the fluid
may be modified by the presence of the scalar and we have an active scalar.
In a simple example, the fluid properties are functions of temperature or the
concentration of the species. This field is known as heat and mass transfer.
In other cases, the presence of a dissolved scalar or the physical nature of
the fluid itself cause the fluid to behave in way that the stress in not related to
the strain rate by the simple Newtonian relationship (1.9). In some fluids, the
viscosity becomes a function of the instantaneous strain rate and we speak of
shear-thinning or shear-thickening fluids. In more complex fluids, the stress
is determined by an additional set of non-linear partial differential equations.
We then say that the fluid is viscoelastic. Many polymeric materials, including
biological ones, exhibit this kind of behavior, giving rise to unexpected flow
phenomena. This is the field of non-Newtonian fluid mechanics.
Flows may contain various kinds of interfaces. These may be due to the
presence of a solid body in the fluid. In simple cases of this kind, it is possible
to transform to a coordinate system moving with the body and the problem
is reduced to one of the kind treated earlier, albeit in a complex geometry.
In other problems, there may be bodies that move with respect to each other
and there is no choice but to introduce a moving coordinate system. A particularly important and difficult case of this kind is one in which the surface
is deformable. Surfaces of bodies of liquid are examples on this type.