197
Chapter 8
Contaminant
and sediment transport
by advection and diffusion
8.1 INTRODUCTION TO MATHEMATICAL
MODELLING OF TRANSPORT PROCESSES
8.1.1 General concepts
In nature, matter is transported exclusively by means of a moving fluid.
Thus, in geophysical systems pollutants are transported either by moving water or moving air. Without those fluids, any pollution source would
remain local. The transport of matter is achieved in two ways:
1. In solution, when the matter is dissolved in the fluid. In this case,
the molecules of the matter are mixed with the molecules of the fluid
and retained in that condition, due to electrochemical forces acting
at molecular scale. Any difference of density between the matter
and the carrying fluid is not important for concentrations less than
1% (weight or volume of dissolved matter per unit volume of the
solution).
2. In suspension, when the matter is in particulate form. The particles,
being much bigger than the molecules of the fluid, are suspended
within the fluid mass. In this case the suspension process is controlled
by the density of the matter relative to the suspending fluid, and the
driving force is the gravity rather than the electrochemical molecular
forces. Suspended matter can either be subject to settling (sedimentation), for particles with density larger than that of water, or floating
(flotation due to buoyancy), for particles with density smaller than the
water density.
In both cases, the amount of the matter in the fluid is expressed by its
concentration, that is, the ratio of the volume (or mass) of the matter over
the volume (or mass) of the mixture (in dissolved or suspended state). The
units are usually milligrams per litre (mg/L) or a dimensionless number.
In general, the concentration, c, is a function of space and time, c(x,y,z,t).
Chapter 8
Contaminant
and sediment transport
by advection and diffusion
8.1 INTRODUCTION TO MATHEMATICAL
MODELLING OF TRANSPORT PROCESSES
8.1.1 General concepts
In nature, matter is transported exclusively by means of a moving fluid.
Thus, in geophysical systems pollutants are transported either by moving water or moving air. Without those fluids, any pollution source would
remain local. The transport of matter is achieved in two ways:
1. In solution, when the matter is dissolved in the fluid. In this case,
the molecules of the matter are mixed with the molecules of the fluid
and retained in that condition, due to electrochemical forces acting
at molecular scale. Any difference of density between the matter
and the carrying fluid is not important for concentrations less than
1% (weight or volume of dissolved matter per unit volume of the
solution).
2. In suspension, when the matter is in particulate form. The particles,
being much bigger than the molecules of the fluid, are suspended
within the fluid mass. In this case the suspension process is controlled
by the density of the matter relative to the suspending fluid, and the
driving force is the gravity rather than the electrochemical molecular
forces. Suspended matter can either be subject to settling (sedimentation), for particles with density larger than that of water, or floating
(flotation due to buoyancy), for particles with density smaller than the
water density.
In both cases, the amount of the matter in the fluid is expressed by its
concentration, that is, the ratio of the volume (or mass) of the matter over
the volume (or mass) of the mixture (in dissolved or suspended state). The
units are usually milligrams per litre (mg/L) or a dimensionless number.
In general, the concentration, c, is a function of space and time, c(x,y,z,t).