Emanating Jets As Shaped by Surface Tension Forces.

We show that emanating jets can be regarded as growing liquid towers, which are shaped by the twofold action of surface tension: first the emanated fluid is being accelerated back by surface tension force, herewith creating the boundary conditions to solve the shape of the liquid tower as a solution of an equation mathematically related to the hydrostatic Young-Laplace equation, known to give solutions for the shape of pending and sessile droplets, and wherein the only relevant forces are gravity g and surface tension γ. We explain that for an emanating jet under specific constraints all mass parts with density ρ will experience a uniform time dependent acceleration a( t). An asymptotic solution is subsequently numerically derived by making the corresponding Young-Laplace type equation dimensionless and by dividing all lengths by a generalized time dependent capillary length λc ( t) = [Formula: see text]. The time dependent surface tension γ( t) can be derived by measuring both time dependent acceleration a( t) and time dependent capillary length λc ( t). Jetting experiments with water and coffee show that the dynamic surface tension behavior according to the emanating jet method and with the well-known maximum bubble pressure method are the same, herewith verifying the proposed model.