'Mic drop': on estimating the size of sub-mm droplets using a simple condenser microphone

Abstract

The size distribution of aerosol droplets is a key parameter in a myriad of processes, and it is typically measured with optical aids (e.g., lasers or cameras) that require sophisticated calibration, thus making the measurement cost intensive. We developed a new method to indirectly measure the size of small droplets using off-the-shelf <\$1 electret microphones. In this method we exploit the natural oscillations that small droplets undergo after impacting a flat surface: by allowing droplets to land directly on a microphone diaphragm, we record the impact force they exert onto it and calculate the complex resonant frequencies of oscillations, from which their size can be inferred. To test this method, we recorded the impact signals of droplets of varying sizes generated by a pipette and extracted the resonant frequencies that characterize each signal. Various sources of uncertainty in the experiments led to a range of frequencies that can characterize each droplet size, and hence a data-driven approach was taken to estimate the size from each set of measured frequencies. We employed a simple setting of neural network and trained it on the frequencies we measured from impact of droplets of prescribed radius. The network was then able to predict the droplet radius in the test group with an average error of 2.7\% and a maximum of 8.6\% relative to the pipette nominal values. These results, achieved with a data set of only 320 measurements, demonstrate the potential for reliable size-distribution measurements via a simple and inexpensive method.

Figures (4)

• Figure 1: View of electret microphones such as the ones used in the experiments: untouched (right); with its fabric cover peeled off to show the small hole that exposes the diaphragm (center); machined to expose $\sim$50% of the diaphragm surface area (left).
• Figure 2: Representative signals of droplets of radii 415 (blue) and 620 ${\rm \mu m}$ (orange) impacting a microphone diagram, showing the recorded voltage as a function of time. The solid and dashed curves are the measurements and the exponential functions fitted to the data, respectively. The signals clearly show the exponentially-decaying nature of the signal at late times, i.e., far enough from the initial impact point, where the two curves (signal and fit) overlap almost entirely.
• Figure 3: Scaled resonant frequency $\omega/\omega_s$ vs. the droplet radius $R$. The red dashed line marks the mean of $\omega/\omega_s$ over the entire set of experiments; the blue dots and errorbars are the mean and range of $\omega/\omega_s$ over each set of 20 repetitions for each $R$; the black errorbars give the maximum error in estimating $\omega/\omega_s$ using $\omega_s(R)$ given the pipette maximal systematic error for $R$. The measurement range clearly dwarfs the pipette error, which indicates that measurement (and not droplet generation) errors are the main source of uncertainty.
• Figure 4: Neural network evaluation of the droplet radii on the test data against the ground-truth results. The dashed line is drawn as visual aid to assess the results. All the results lay relatively close to the line with the largest discrepancy of 42 ${\rm \mu m}$ at $R=587\,{\rm \mu m}$, and the largest relative error of 8.6% at $R=415\,{\rm \mu m}$. The inset shows the network training convergence, with the blue and red curves marking the training and validation losses, respectively.