Frequency-dependent fluidic inductance and resistance in inkjet passages

Accurate analysis of the dynamic response of an inkjet is important to compare various geometries and predict the effect of potential design changes. The fluid in an inkjet typically has a low Reynolds number (i.e. viscous forces are important) and often oscillates quickly (relative to the timescale of boundary layer to development). It is well known that, when a viscous flow oscillates, the shape of the velocity profile is dependent on the passage geometry and the frequency of the oscillation. The viscous boundary layer effectively blocks part of the cross-section of the passage, changing the required pressure to accelerate (inductance) and sustain (resistance) the flow. Thus, the fluidic resistance and inductance are functions of both geometry and frequency. The resistance is least at low frequencies and increases with frequency. Inductance is highest at low frequency and decreases with frequency. The effect of inductance on impedance still increases with frequency. An analytical correlation for fluidic inductance and resistance has been developed. Frequency dependent inductance and resistance were important to accurately predict the resonant frequencies and the extent of damping in an inkjet.