Pressure modes of the oscillating sessile drop

Drop-on-demand printing applications involve a drop connected to fluid reservoir between which volume can be exchanged, situation that idealized as sessile with prescribed flux across the drop/reservoir boundary. Here we compute frequency spectrum for these pressure disturbances, it depends upon static contact-angle $\alpha$ (CA) and an empirical constant $\chi$ relating either (i) pinned or (ii) free contact-lines. Mode shapes are characterized by mode number pair $[k,\ell ]$ property $k+\ell =\mathbb {Z}^{+}_{odd}$ associated symmetry properties of Rayleigh modes sphere. We report instabilities axisymmetric $[1,0]$ non-axisymmetric rocking $[2,1]$ related centre-of-mass motions, show how spectral degeneracy breaks model parameters.