INSTABILITY NATURE OF THE SWIRL APPEARANCE IN LIQUID CONES

We study the nature of the swirl dynamo (the appearance of rotation in primarily nonswirling flows) that has been found in liquid conical me nisci of electrosprays. A previous theory models the phenomenon in ter ms of the conical similarity solutions of the Navier-Stokes equations and reveals the appearance of swirling secondary regimes through the s upercritical pitchfork bifurcation at threshold Reynolds number Re. T he similarity solution can approximate a real flow only outside the vi cinities of the apex and the capillary rim, i.e., in some region r(i) < r <r(0), where ris the distance from the cone apex. The problem is h ow deviations from this solution at r=r(i) and r=r(0) influence the fl ow inside that region. It is shown here that for Re <Re, the deviatio ns from the primary flow decrease far from both the boundaries, but fo r Re> Re, a swirl disturbance given at r =r(0) grows as r decreases u ntil saturation at the secondary similarity solution. The swirling reg ime is found to be stable with respect to these spatially developing, steady, rotationally symmetric disturbances in a wide range of Re. Thu s, the swirl comes from a near-capillary region, but its cumulation in side the cone occurs only for Re > Re.