Pattern Formation and Evolution of Viscous and Non-viscous Liquids on a Vertical Vibrating Surface: An Experimental Investigation

We experimentally studied the pattern formation of viscous and non-viscous Newtonian liquids on a vertically vibrating finite-size container. Experimental results show that the pattern formation in the case of water at 100 Hz and in the case of silicon oil at 20 Hz and 80 Hz has been verified from the patterns obtained in the literature, which shows excellent agreement. We investigate the physical parameters that significantly impact pattern creation, such as Faraday wave frequency, cross-over wave frequency, Faraday critical acceleration, and decay length. The study found that the Faraday critical acceleration (ac = 1.45 m/s2) is maximum for silicon oil, whereas the decay length (ld = 0.1432 m) is maximum for water at a given vibrational frequency. In addition, we also emphasize the well-known Mathieu equation to obtain the value of wavelength as well as wave vector of the generated pattern. Furthermore, the study found that at a given vibrational frequency, the wavelength (λ = 0.016 m) of pattern formation is maximum for water. Additionally, the study is carried out to investigate how driving frequency and Faraday wave frequency affect the physical characteristics of pattern formation.