Continuous inkjet printing is an established technology that has been around for 150 years. Simply put, it is a method of droplet generation where once the print head is running there is a continuous stream of fluid. Although this concept was first patented by Lord Kelvin in 1867, the first commercial devices appeared more than 80 years later, in 1951 by Siemens. Initially the technology was used for high speed, contact-less printing of variable information such as expiration dates, batch codes as well as names and product logos.

Continuous inkjet printing begins with a high-pressure pump that directs liquid from a reservoir to a bank of micrometer-sized nozzles, thus creating a continuous stream of droplets at frequencies determined by the oscillations of a vibrating piezoelectric crystal. For printing applications specifically, ink droplets are being deflected from the continuous stream due to the presence of an external electric field. This generates patterns on the surface of a printing medium. Some of the advantages of this technique are high throughput, high droplet velocities, increased distances from printhead to substrate, and no nozzle clogging due to continuous operation. Thanks to these positive attributes, this technology has, nowadays, evolved from regular printing ink on paper to depositing a variety of materials (even living cells), to creating modern OLED (Organic Light Emitting Diode) displays.

In this blog, I will discuss the physics behind continuous inkjet printing, followed by the FLOW-3D simulation studies conducted by Ioannis H. Karampelas, CFD Engineer at Flow Science. Further advancing his work, I ascribe randomness to the droplet generation process, inspired by the application of inkjet in the OLED printing industry, and illustrate the variation in the resulting droplets.

Droplet Generation

Nozzle size selection

In order to calculate the system parameters for droplet generation, Rayleigh jet instability theory can be used. According to this theory the optimal wavelength (λ) of stimulation for jet breakup leading to the drop formation is approximately:

Nozzle size selection

Operating frequency selection

The optimal drop generation frequency can be directly calculated from the optimal wavelength:

Using the theory above and known industrial parameters, a nozzle radius of 125 μm and a frequency of 10 kHz was used while setting up the computational model in FLOW-3D.

Validation of FLOW-3D Results

FLOW-3D is well-suited for simulating droplet based processes, such as continuous inkjet printing, because of its powerful and accurate surface tension model.

In the simulation results below, we can see the input pressure pulse, oscillating at a frequency of 10 kHz. The average droplet size is around 240 μm, which is in good agreement with the theoretically estimated droplet size of approximately 250 μm.

Droplet formation input pressure pulse simulation results
Simulation results from FLOW-3D highlighting the droplet formation and the input pressure pulse

OLED Mura Problem

In theory, it is possible to generate pressure pulses with exactly the same amplitudes. But, in industrial applications, such as inkjet printing of OLEDs, every nozzle is slightly different either because of inherently imperfect manufacturing, or operational parameters. All these imperfections cause fluctuations in droplet volumes leading to variations in the volume of organic compound deposited into each sub-pixel of an OLED panel, which in turn leads to proportional variations in the deposited film thickness. Such thickness variations are one of the most important causes of non-uniformity in panel luminance in inkjet printed OLED displays (Madigan et al.). This non-uniformity in panel luminance is called “mura effect.”

One approach to resolve the mura problem is to use the law of averages. What this means is to randomly combine drops from different nozzles (intra-pixel mixing) to average out the positive and negative errors in droplet volumes, thus forcing the droplet volume error towards near zero.

In order to simulate this process of intra-pixel mixing in FLOW-3D, some randomness was added to the input pressure pulse amplitudes. The magnitude of the maximum fluctuation was set to 200 kPa, on top of the original pressure amplitude of 1.7 MPa. The animation below shows a comparison of the case with randomness versus the initial case without randomness.

As expected the droplet generation is not uniform in terms of droplet shape, droplet size, inter-droplet spacing and the flight velocity. The constant amplitude case on the right however generates evenly spaced droplets of uniform shape and size.


In this blog article, FLOW-3D was used to promote an understanding of the physics involved in continuous inkjet printing processes. Thanks to its powerful surface tension model, FLOW-3D can also be useful in a variety of advanced droplet generation and deposition applications. In the case of OLED printing for example, FLOW-3D can be effectively used to understand the variations caused in droplets during intra-pixel mixing, resulting in better quality of OLED panels.


Madigan C. F., Hauf C. R., Barkley L. D., Harjee N., Vronsky E., Slyke S. A. V., Advancements in Inkjet Printing for OLED Mass Production. Kateeva, Inc.

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