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Taking into account the random charge fluctuation on embedded micro spheres in low pressure gas discharge two differential equation for two-dimensional dust lattice wave is derived. 2D hexagonal crystal is investigated in this paper. The dispersion relation for both longitudinal and transverse waves in different direction is studied as well. It is in agreement between analytical results and the experimental ones reported previously. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

Nonlinear stability analysis shows that there exists a series of dimensionless breakup point parameters, (ωr/Re)b, (ωr/We)b, (ωr/Eu)b, at any axial location, under certain injected velocity and liquid sheet thicknesses. The liquid sheet will breakup when conditions of ωr/Re>=(ωrRe)b, (ωr/We>=(ωr/We)b, and ωr/Eu<=(ωr/Eu)b are satisfied. There exists a transition region, liquid wave instability from a sinuous wave to a varicose mode, and breakup lengths from a decreasing trend to an increasing one as increased injected velocity, when aspect ratio of nozzle exit is changed from larger to smaller values. [ABSTRACT FROM AUTHOR]