Addressing a large number of electrodes with a limited number of control lines is possible if only some combinations of driven electrodes produce significant effects, or if the control signals can be time-multiplexed so that only synchronously driven combinations of electrodes produce a significant effect. In the current design we concentrate on the former.
The starting idea was to treat neighboring electrodes as alternately x- or y- connected, as shown in Fig 1, using half the IO-pins on the controlling device for x, half for y. This is related to twin addressing of positions via pairs of electrodes, e.g. in x-y strip detectors, to increase the number of addressable positions with n control channels from n to n-squared. The scheme on the left above shows this at its simplest. The middle scheme is the smallest one allowing electrode pair control of movement of material along individual channel segments. In the scheme on the right, any local cluster of 4 neighboring electrodes has independent control lines.
Alternatively, in order to create independent chains of electrode pairs, the x-y addressing can be rotated at 45° with respect to the microfluidic channels (Fig. 2).
The figure shows a variant with electrodes centrally at junctions that has advantages of equidistant electrodes, but disadvantages in microchannel flexibility (see below) and routing. The figure also shows the advantages of tricyclic connections in increasing the distance between correlated electrodes.
The simple schemes above are limited in that neighboring channel junctions show correlated electrode potentials, and hence cannot independently direct material flow. In fact, many of the channel segments and electrodes are superfluous for most types of designs, so that a judicious pruning of the dense array is feasible, reducing these local correlations. The objective is to retain maximum functional flexibility, optimize the global linear path length of chains of electrodes, maximize repetition lengths, and minimize local cross-talk while attaining a routable configuration.
A major consideration in thinned networks is how many of the different junctions one employs : e.g. using three-junctions lead to
brick-like networks. Examples of pruning schemes favoring T-junctions are shown on the right and top-left of Fig. 3 (opposite), and pruning favoring X-junctions on the bottom-right.
A mix of T- and X- junctions, with longer linear segments was considered maximally flexible, see below.
Using the basic unit shown in the center of Fig. 1, we investigated a range of thinning structures such as those shown in Fig. 4 opposite.
Small loops are advantageous for cyclic processing and flexible routing, whereas longer chains of electrodes are efficient for longer range transport.
Actually, fractal or hierarchical structures, in which the number of interconnections at various spatial scales remains the same, appear to provide the right kind of interconnection behavior. Purely tree-like structures, capable of space-filling electrodes, such as the Hamilton curves are less useful than designs where a constant number of cycles at all scales may be found.
Furthermore, it is useful for separation and transport tasks to have structures with continuous chains of electrodes along straight paths. The designs shown in Fig. 5 (opposite) shows how hiearachical schemes, extended with a minimum number of additional electrodes (in blue) can fulfill these design criteria simultaneously.
These designs have modules with four electrodes vertically or horizontally per unit. This was above the maximum number (3) that could be successfully routed with the desired space scale. So our design architecture was altered to preserve cycle-tracing flexibility, while not having more than three rows of electrodes in any second-order structure. A combination of two types of modules with filled in straight electrode chain segments both horizontally and vertically resulted in the following design (Fig. 6).
These modules can be routed with bundles of three control lines both in x and y layers (two layer routing), in which successive electrodes are connected successively to different lines. The raw-routing of part of such a structure is also shown in red and blue in fig.6.
The distance between electrodes in similar configurations, and governed by the same signal, is now significantly greater, but still not optimal. The final step prior to routing the design is to shuffle the electrodes locally between different control lines to decorrelate similar positions optimally.
The local two layer connections of the smallest 8 electrode cyclic unit is shown in Fig. 7. The blue circles are vias connecting the two layers of metallic connections (in red and blue). Only the electrode squares are exposed to the solution, all other wires being insulated with a silicon dioxide layer (SiO2). In green one can see an example of a microfluidic channel network. The X- junctions are dimensioned to both allow sufficient digital field strength across the junction, and to allow two separate microfluidic channels to utilize diagonal pairs of electrodes.
The final global electrode design is shown here.