rotation is increased the fluid will move around the siphon to fill the next chamber.
A number of these siphon valves can be placed in series to delay the introduction of
different reagents to a reaction chamber [ 11 , 12 , 21 ] (Fig.5.6).
Both the time taken to prime a siphon valve and the burst frequency for each
capillary valve can be calculated in order to create simple changes in the speed of
rotation to allow the addition of reagents in an automated manner, the time of each
speed of rotation can be elongated in order to allow time for specific reactions to
take place, as well as mixing of reagents [ 4 , 20 ]. The time needed to prime each
valve
t¼4 ηl^2
dσcos θð 5 : 9 ÞDepends on the surface tension, the contact angleθand the viscosityη, the length
of the liquid plugland the channel diameterd. The equation
v¼1
πffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
σ(^) cos θ
ρrΔrd
s
ð 5 : 10 Þ
provides the capillary burst frequency.
Fig. 5.6 Siphon valves build upon the principle of capillary action as previously described, the
walls of the siphon channels draw the liquid from the reagent reservoir back towards the centre of
rotation however at a high frequency of rotation (Image (a)) the liquid is held back by the
counteracting centrifugal force, this causes the liquid to reach “Hydrostatic Equilibrium” at a
point beneath the height of the siphon crest. As the frequency of rotation is reduced the adhesive
interactions between the liquid and the channel walls begin to dominate over the centrifugal force
causing the liquid to advance around the siphon crest and down towards the reaction chamber
(Image (b)). It is at this point that the siphon is “Primed”, the liquid will now flow towards the
furthest average radial point from the centre of rotation (Image (c) and (d))
5 The Centrifugal Microfluidic: Lab-on-a-Disc Platform 123