2.1. Physical Parameters
13
is called the mass fraetion of component oe, and represents the mass ratio of
component oe to the fluid mixture per unit mass. Similarly, we can define the
volumetrie fraetion, VII' of component oe as the volume ratio of component oe to
the fluid mixture per unit volume. By means of spatial averaging, both roll and
VII can be transferred from the microscopic level to the macroscopic level. The
mean density of liquid phase ß in a porous medium is given by:
Pp (x) = ~( ) r pp(x') dUo,p,
Uo,p X JIUo.,(X))
(2.1.15)
where Pp is the microscopic density of the liquid phase ß and [Uo,p(x)] is the
volume of phase ß in the REV of porous media.
The speeijie gravity, y, of a fluid is defined as
y = pg,
(2.1.16)
where 9 is the gravitational acceleration. Then the mean specific gravity of
phase ß in porous media is
(2.1.17)
Solute Concentration
The eoneentration of component oe in a multicomponent fluid is actually its
density Pli' It is conventionally expressed as CII • For a binary system with only
one solute in a solvent, a single letter C can be used to express the solute
concentration. If the density of a solution is independent of the solute concentration, it is more convenient to use dimensionless eoneentration,
C
e=-,
(2.1.18)
P
which gives the mass ratio of solute to solution. From Eq. (2.1.14), we know
that eis, in fact, the mass fraction of the solute.
As to a porous medium, component oe can be either in the liquid phase, or
in the solid phase. We will use Cy,lI to denote the concentration of solute oe in
phase y. Its mean value is given by the following equation:
-
1 i
Cy,lI(x) = --(-)
Cy,lI(x')dUo,y,
UO,y x IUo.,(x))
(2.1.19)
where [UO,Y(x)] is the volume of phase y within the REV. If there will be no
misunderstanding, the subscripts y and oe may be omitted.
Fluid Viscosity
A continuous deformation of the fluid, i.e., a flow, will occur if a shear force
acts on it. The resistance ofthe fluid to such deformation is called its viseosity.
13
is called the mass fraetion of component oe, and represents the mass ratio of
component oe to the fluid mixture per unit mass. Similarly, we can define the
volumetrie fraetion, VII' of component oe as the volume ratio of component oe to
the fluid mixture per unit volume. By means of spatial averaging, both roll and
VII can be transferred from the microscopic level to the macroscopic level. The
mean density of liquid phase ß in a porous medium is given by:
Pp (x) = ~( ) r pp(x') dUo,p,
Uo,p X JIUo.,(X))
(2.1.15)
where Pp is the microscopic density of the liquid phase ß and [Uo,p(x)] is the
volume of phase ß in the REV of porous media.
The speeijie gravity, y, of a fluid is defined as
y = pg,
(2.1.16)
where 9 is the gravitational acceleration. Then the mean specific gravity of
phase ß in porous media is
(2.1.17)
Solute Concentration
The eoneentration of component oe in a multicomponent fluid is actually its
density Pli' It is conventionally expressed as CII • For a binary system with only
one solute in a solvent, a single letter C can be used to express the solute
concentration. If the density of a solution is independent of the solute concentration, it is more convenient to use dimensionless eoneentration,
C
e=-,
(2.1.18)
P
which gives the mass ratio of solute to solution. From Eq. (2.1.14), we know
that eis, in fact, the mass fraction of the solute.
As to a porous medium, component oe can be either in the liquid phase, or
in the solid phase. We will use Cy,lI to denote the concentration of solute oe in
phase y. Its mean value is given by the following equation:
-
1 i
Cy,lI(x) = --(-)
Cy,lI(x')dUo,y,
UO,y x IUo.,(x))
(2.1.19)
where [UO,Y(x)] is the volume of phase y within the REV. If there will be no
misunderstanding, the subscripts y and oe may be omitted.
Fluid Viscosity
A continuous deformation of the fluid, i.e., a flow, will occur if a shear force
acts on it. The resistance ofthe fluid to such deformation is called its viseosity.