Quantifying Uniform Droplet Formation in Microfluidics Using Variational Mode Decomposition

Abstract

Using variational mode decomposition, we analyze the signal from velocities at the center of the channel of a microfluidics drop-maker. We simulate the formation of water in oil droplets in a microfluidic device. To compare signals from different drop-makers, we choose the length of the water inlet in one drop-maker to be slightly shorter than the other. This small difference in length leads to the formation of satellite droplets and uncertainty in droplet uniformity in one of the drop-makers. By decomposing the velocity signal into only five intrinsic modes, we can fully separate the oscillatory and noisy parts of the velocity from an underlying average flow at the center of the channel. We show that the fifth intrinsic mode is solely sufficient to identify the uniform droplet formation while the other modes encompass the oscillations and noise. Mono-disperse droplets are formed consistently and as long as the fifth mode is a plateau with a local standard deviation of less than 0.02 for a normalized signal at the channel inlet. Spikes in the fifth mode appear, coinciding with fluctuations in the sizes of droplets. Interestingly, the spikes in the fifth mode indicate non-uniform droplet formation even for the velocities measured upstream in the water inlet in a region far before where droplets form. These results are not sensitive to the spatial resolution of the signal, as we decompose a velocity signal averaged over an area as wide as 40% of the channel width.