koff - LEPA

5. Coating a microchannel
5.1 Iterative stop-flow with adsorption equilibrium
One way to coat a microchannel is the stop-flow method that consists in filling the channel
quickly and to allow the adsorption to take place. This process is then repeated n-times until the
surface concentration is high enough to allow a detection using, for example, a sandwich assay.
During the iterative process, the total number of molecules present after the nth fill of the
microchannel channel is equal to what was adsorb on the wall at the (n-1) fill plus the number of
molecules injected during the nth fill
n tot,N = n wall, N –1 + n in (53)
In this way, we can write for the successive iterations.
First fill:
Second fill:
n tot,1 = n in (54)
n wall, 1 = !n in (55)
ntot,2 = nwall, 1 + nin = ( 1+ ! )nin (56)
µ
ntot,2 = nwall,2 + nsolution = ! eq,2A
+ ceqV = K! maxceqA + ceqV (57)
µ
! eq,2
=
" K! max %
#
$ V + K! maxA &
' ntot,2 µ
nwall,2 = ! eq,2A
=
" K! maxA %
#
$ V + K! maxA &
' ntot,2 (58)
= ! 1+ ! ( )nin (59)
Then, at the n-th fill we have
ntot,n = nwall, n!1 + nin = 1+ ! + ! 2 +... + ! n–1
( )nin (60)
and
nwall,n = ! + ! 2 +... + ! n–1
( ) · nin (61)
Considering the properties of geometric series
n wall,N
n in
N –1
!
i=0
= ! 1"! N
= = ! ! i
( )
1"!
As illustrated in Figure 10, we have an additive filling for the values of α close to unity.
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