Approximating fluid response with Helmholtz resonance
Sometimes, simple tools are very useful guides to understand the behaviour of complex systems. In this example, we're going to explore aspects of the mechanical response of a fluid in an ink jet nozzle by asuming that it behaves in a manner similar to a Helmholtz resonator.
In the image below, an approximation of an inkjet nozzle is shown on the left, containing a good, bright, magenta ink at rest! We're going to perturb it by putting a square wave displacement, lasting 5 microseconds, onto the piezo element and then watch how the ink moves.
The mechanical approximation to the ink in the nozzle is shown on the right by a 2 degree of freedom spring and damper system. The mass m1 corresponds to the ink in the throttle and the mass m2 corresponds to the ink in the nozzle.
In this version of the model there is just 1 parameter that you, dear user, can alter! The geometry of the nozzle is fixed - but you can change certain material properties. Ordinarily, this would be the density and viscosity but here it is just the speed of sound.
Typically the speed of sound for a solvent ink would be about 1100 m/s, but for an aqueous ink would be about 1600 m/s. See for yourself how changing the speed of sound alters the mechanical response of the system!
If you'd like to see how changing the geometry and viscosity of the ink changes the mechanical reponse, try this model.
