A novel numerical approach to find the optimal frequency of Rayleigh–Plateau instability in laminar jet breakup for uniform droplet generation

One of the key aspects of studying Rayleigh-Plateau instability and laminar jet breakup is identifying the optimal disturbance wavelength. By inducing artificial disturbances with an optimal frequency or wavelength in a laminar jet, uniformly sized droplets can be produced. Most existing methods for calculating the optimal wavelength in Rayleigh-Plateau instability rely on analytical approaches with significant simplifications, leading to various limitations. The main goal of this study is to develop an effective numerical method to identify the optimal frequency in Rayleigh-Plateau instability. First, the numerical results are validated with experimental data. Then, a systematic method for calculating the optimal frequency using simulated data and the discrete Fourier transform (DFT) is proposed. This method serves as an alternative to common trial-and-error methods and inaccurate analytical approaches, providing a low-cost and highly accurate prediction of the optimal frequency. This method is applied to determine the optimal frequency for different flow conditions ($Weber\left(We\right)=6;0.013\le Ohnesorge\left(Oh\right)<0.219$). Finally, the impact of two parameters, including the inner to outer diameter ratio ($b={D_I/D}_O$) and the contact angle, on the optimal frequency is examined. The results show that increasing $b$ can increase the optimal frequency by up to 70 %. Additionally, increasing the contact angle from ${30}^{°}$ to ${120}^{°}$ raises the optimal frequency from $160Hz$ to $192Hz$ while $\mathrm{Oh}=0.013$ and $b=0.56$.