Basics of piezo driven inkjet print heads: Fluid dynamics and nozzle design

Engineering mechanics is the science behind the design of all kind of products and structures people encounter in daily life. It is the science that makes it possible to let airplanes fly safely, reliably, with low noise and more and more cost effectively and to bring vehicles in space such as the International Space Station and Mars Rovers. It is the science that is behind an ages lasting process leading mankind to the building of longer and longer bridges, earthquake safe buildings, larger and larger ships, larger and faster airplanes, larger and larger wind turbines for generating electric power, household automation, engines with an ever increasing power over weight ratio, omnipresent communication means and so on. Engineering mechanics embraces structural mechanics, fluid dynamics, rheology, electrical engineering, measurement and control theory, materials science, etc. and is an integral part of the curriculum of educational programs for the mechanical engineer, civil engineer and architect, aerospace engineer, maritime engineer, precision mechanics engineer, manufacturing engineer.

A nice example where all these engineering mechanics aspects come together is the inkjet printhead. It is a daily life example of precision engineering that makes it possible to print documents, photos, biosensors, displays and even 3-D products. It is all about a synthesis between software, low cost and highly reliable manufacturing, micro-fluid dynamics, heat and mass transfer, ink design, acoustics, structural mechanics, electronics and electrical engineering and control theory.

From a fluid dynamics point of view a printhead is manifold of micro-fluidic devices without valves and other mechanical means to direct the flow. It is about an ink reservoir connected to a channel layout that ends at a large number of nozzles, each nozzle is individually addressable making delivery of a droplet on demand possible. The printhead is mounted on a carriage; together with a paper feed mechanism a printer is able to place droplets of ink with great spatial accuracy onto the substrate (usually paper). 

As the dimensions are very small and the fluid viscosity is between water (0.001 Pa s) and let’s say ethylene glycol (0.02 Pa s) the flow is certainly laminar. By actuating the fluid column of one pump out of the manifold e.g. by a generating a bubble by intense local heating or a piezo actuator, pressure waves inside the pump are generated that at the nozzle are converted into fluid velocity and ultimately into a high-speed droplet or a stream of droplets. Such droplets travel towards the substrate. After landing droplets spread and form a dot on paper or another substrate material. It is always about making images, an image can be text or a photo, but also the layouts of conducting tracks on a printed circuit board, patterns of dots of solder paste, dots of capture probes on biosensor surfaces for DNA, cell or protein probing, color filters of LCD screens or patterns of light emitting diodes for making emissive displays. It is all about many, many dots, spatially correctly deposited.

Acoustics determine whether the actuation is effective or not. Actuation at too low a rate does not generate pressure waves and does not produce droplets. It is like a recorder, the air column inside the recorder must be set into motion by a kick of airflow generated by the player, after that the sustaining breath maintains the motion, an effect referred to as resonance. Resonance is connected to frequency; this frequency is defined as the ratio of speed of sound over length. A short air column makes a high pitched tone, a long air column a low pitched tone. A small musical instrument has a high pitched register; a large instrument can produce low frequency tones. By over-blowing higher modes (over tones) are set into motion, enlarging the span of tones a musical instrument can possibly generate. The same holds true for string instruments, a piano tone is generated by a hammer set into motion by hitting the appropriate key. Too low a hammer speed does not result in an audible tone, hitting the key harder generates a tone, hitting the key even harder ends up to louder and louder tones.

The basic understanding of a musical instrument is also applicable to understand the action of a single pump out of the manifold of different pumps integrated into a multi-nozzle printhead. Its key tone has a very high frequency (up to hundreds of kHz); in order to start pressure waves travelling back and forth through the pump extremely steep pulses are needed.

Another interesting feature is the refilling mechanism. A printhead does not contain any valve; to replenish the volume of a droplet that has left the nozzle surface tension is the driving mechanism for refilling. This effect works up to a certain frequency; for higher frequencies asymmetric dynamic effects become dominant and cause a net flow towards the nozzle. Asymmetry occurs due to the fact that the fluid displacement in the nozzle is of the order of magnitude of the nozzle length, so the inertial forces in the nozzle depend on the extent of filling of the nozzle. Another phenomenon causing asymmetry has to do with the inflow and outflow from the pump to the nozzle. In a similar situation a cigarette smoker can make a jet of smoke during blowing out, but is unable to suck the jet back in.

You can hear more from Prof Dijksman about the fluid mechanics behind printhead operation at the IMI Europe Inkjet Engineering Conference, 14 March 2017 in Lausanne, Switzerland. Frits will also be presenting an entire 1.5 day course on the topic at the IMI Europe Inkjet Summer School on 12-13 June in Ghent, Belgium.