Page 342 - Process Modelling and Simulation With Finite Element Methods

Electrokinetic Flow 329

0
Pc '

Figure 9.6. The simple network considered.
The 'Y' junction domain is computed in detail with algebraic relations
linking to the known boundary conditions at reservoirs A, B and C to provide the
boundary conditions at a, b and c. In the case of non-uniform composition in
channel segment C, a one-dimensional pie must be solved for the species
composition to provide the link to downstream conditions.
The boundary conditions at the junction flow boundaries a, b and c come
from the network flow equations linking junction boundary conditions to the
known conditions of the reservoirs connected up to the network. In the simple
case considered here (where R = A = l), the linking equations for boundary a are

and

(9.1

where Q, and I, are the flow rates at boundary a given in terms of computed
conditions on that boundary by

Precisely similar relations result at boundaries b and c.