Quantitative comparison of cellular patterns of stable and unstable mixtures

Abstract

This study describes a comparison of smoked foils from five different mixtures $({\hbox {C}}_{2}{\hbox {H}}_{2}+2.5{\hbox {O}}_{2}+85\,\%{\hbox {Ar}}, 2{\hbox {H}}_{2}+{\hbox {O}}_{2}+50\,\%{\hbox {Ar}}, {\hbox {C}}_{2}{\hbox {H}}_{2}+2.5{\hbox {O}}_{2}+70\,\%{\hbox {Ar}}, \hbox {C}_{2}{\hbox {H}}_{2}+5{\hbox {N}}_{2}{\hbox {O}}$, and ${\hbox {CH}}_{4}+2{\hbox {O}}_{2})$ that produced transverse waves of regular and irregular spacing. Histograms, variance, and the autocorrelation function (ACF) were used to quantify the spacing irregularity. Each smoked foil was first digitized then separated into left-running and right-running waves for subsequent analysis. The five mixtures showed different degrees of irregularity in the analysis of the histograms and the ACF of the spacing of the transverse waves. The dominant mode was readily found from the peak in the histogram and the first peak in the ACF result. The spacing of the main transverse waves provided by the histogram and the first peak of the ACF were much closer to the spacing of the transverse waves measured by eye for stable mixtures than for unstable ones due to their stronger dominant mode. In certain cases, other modes besides the dominant one were observed, such as two peaks in the histogram and other large peaks in the ACF result. Variance was used as a quantitative measurement of the cellular pattern irregularity level.