Measurement of Nanoscale Surface Disturbances on Liquid Jets Using the Mie Scattering Method

Abstract

The Plateau--Rayleigh instability of liquid jets governs a wide range of natural and industrial processes. While the classical linear stability theory accurately predicts disturbance growth rates and dominant wavelengths, it cannot quantify the amplitude and frequency spectrum of nanoscale initial surface disturbances. This critical missing information prevents accurate forecasting of breakup lengths and droplet generation. Conventional optical imaging is constrained by the diffraction limit and lacks the capability to resolve such nanoscale surface fluctuations. Here we introduce a Mie-scattering-based measurement technique to characterize nanoscale surface disturbances on liquid jets. The method employs a thin laser sheet to illuminate the jet, with scattered light captured at designated azimuthal observation angles. Based on Lorenz--Mie theory, we develop an inversion algorithm incorporating cosine similarity and cross-correlation to reconstruct jet surface disturbances from measured scattering fringes, achieving a sub-nanometer resolution for detecting diameter variations, with an overall measurement precision limited by a background noise floor of 0.18 nm RMS. Comparative analyses of forward and rainbow scattering signals further confirm that the surface disturbances become axially symmetric as the amplitude reaches a few nanometers, and thus satisfies the assumptions of the scattering model. Synchronous validations against high--speed imaging and scanning electron microscopy corroborate the quantitative accuracy of our scattering method. Applied in the near-nozzle region, the technique identifies two intrinsic signatures of initial perturbations: stochastic pulse-like fluctuations and low-frequency oscillations.