Environmental Engineering Reference
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conservation, and one equation for fluid flow. The unknowns described in
this system are N species concentrations (
C
i
), one electric potential (Φ),
one hydraulic potential (
h
), and N unknowns for the rate of i chemical
reactions. Therefore, 2N+2 unknowns are described by N+2 differential
equations. The other N numbers of equations required for this system are
the mass balance equations for the chemical reactions (Alshawabkeh and
Acar, 1996; Cao, 1997).
5.4.1
Initial and Boundary Conditions
The general system describing mass transport needs to be supplied with
appropriate initial and boundary conditions. Initial condition and two
boundary conditions are necessary for each species present in the sys-
tem. Initial conditions can be evaluated by the initial concentration dis-
tribution, potential distribution and other values so that an equilibrium
state can be maintained at the starting point. Boundary conditions can be
obtained through employing different equations, which describe different
flow statuses at the boundaries. Generally used boundary conditions are
the Neumann boundary conditions, Dirichlet boundary conditions, and
mixed boundary conditions. When describing flow problems, a Neumann
boundary is an insulated boundary (or impermeable boundary) which
means there is no flux at the boundary, while a Dirichlet boundary indi-
cates that the value of head (potential, concentration, etc.) is constant at
the boundary.
To simplify the solution procedure, constant boundary conditions
can be implemented. However, such boundaries are not able to describe
the nature of the EK flow realistically. Due to the existence of flux at
boundaries caused by the electrode reactions and advection of fluid,
flux boundary condition is more capable of describing EO flow status.
The mixed boundary condition can also be implemented in the system.
The boundary conditions applied at the inlet and outlet of the soil must
express the equality between the flux of solute applied at the inside of
the soil boundary and the flux of solute at the immediate outside of the
porous medium.
Hydraulic head in the EK transport process is controlled either to pro-
vide constant head difference or constant flow rate and hydraulic head
boundary conditions can be easily described. In most cases, zero head dif-
ference is applied between the cathode and the anode. Boundary condi-
tions for charge conservation equations can be developed from the current
density value at the boundary and two types of boundary conditions can
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