Droplet microfluidics is the science and technology of systems that process and manipulate small (pico- litres) volumes of fluids, using channels of dimensions less than a millimetre. The fluid flow in the channels is in the creeping flow regime where the governing equations are linear and reversible. But experiments in the literature have shown that a network device as simple as a microfluidic loop can result in complex patterns. A droplet reaching the junction of the loop chooses one of the two branches based on the local flow rates, which depend on branch lengths and the number of drops present in the branches. This discrete decision making step makes the problem non-linear and irreversible. A train of equally spaced droplets (1 period) entering the loop device gets converted to a periodically spaced train of droplets with one, two or even chaotic periods.
This loop device can be thought of as an encoder that passively converts a signal (train of drops) into a coded signal (periodic train of drops). Then it would be interesting to understand if there could be a decoder which is a loop device or several loops in series which can essentially convert the coded signal back to the original signal. This would mean that the decoder should convert an n-period input to a single period output. We propose an analytical scheme based on continuous phase redistribution and repeatability of events to find the different possible solutions for the lengths of the branches of the decoder loop. Multiple solutions exist to a certain decoding problem, based on the sequence of occurrence of events (drops entering and exiting the loop). The number of possibilities scale up with the periodicity of the signal being decoded. However, there exists one specific sequence of events, a pattern common to all decoding solutions that can decode any periodicity to a single period in the output signal. The problem of decoding any period signal to 1 period signal now scales down to arranging for this sequence of events to occur by optimising the branch lengths. Decoding of 2 period and 3 period to 1 period using this sequence of events is demonstrated and extension to the decoding higher period signals is indicated.
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