DUAL-MODE LINEAR ANALYSIS OF TEMPORAL INSTABILITY FOR POWER-LAW LIQUID SHEET

A dual-mode linear analysis of temporal instability for the power-law liquid sheet moving into an inviscid gas stream is implemented to theoretically study the breakup of the sheet. Applying the linear instability theory, the dispersion equations are derived under the dual modes of antisymmetric and symmetric disturbances by linearizing the nonlinear power-law term based on some rational and necessary assumptions. The growth rate of the two disturbances and corresponding wave number are obtained by numerically solving the dispersion equations. The effects of thickness and velocity of the sheet, initial disturbance, surface tension, consistency index, flow behavior index, gas density, and gas velocity (relative velocity) on the instability of the power-law sheet are investigated. Furthermore, to evaluate the breakup time and breakup length of the sheet and the mass mean diameter of the droplets separating from the sheet, the dominant and neutral curves are plotted. Relative results indicate that the antisymmetric disturbance is the predominant mode in the instability with greater growth rate than the symmetric disturbance. The decreases of the surface tension coefficient and sheet thickness, or the increases of the sheet velocity, gas density, and relative velocity can accelerate the instability of the sheet bringing a better atomization. Enlarging consistency index and flow behavior index can resist the breakup of the sheet, but the influence will be unapparent when the two parameters exceed a certain value, respectively. Moreover, the initial disturbance dramatically just has a weak effect on the instability of the power-law sheet through linear analysis.