Mandeep Saini

Numerical simulations of inkjet printing

Abstract:

Inkjet printing presents a range of fascinating and challenging fluid dynamics problems, as highlighted in [1]. In this talk, we focus on two such problems: 1. the breakup of liquid jets into droplets, and 2. the development of a mass- and momentum-conserving numerical method for simulating Marangoni flows. Both studies use the Basilisk solver. 

In the first problem, we examine how the polymer additives in the jetting fluid influence jet breakup and droplet formation. In particular, we investigate the effect of polymer additives in suppressing the formation of satellite drops. Our results show that the addition of small concentrations of polymers can lead to the suppression of satellite droplets. However, if the polymer concentration increases beyond a certain limit, the jet breakup is impeded altogether. To predict the transitions between these regimes, we develop simplified models based on slender-jet theory. The second problem concerns the development of a numerical method that conserves mass and momentum while accurately simulating Marangoni flows—phenomena that arise during droplet evaporation in inkjet printing. We extend the integral formulation approach of [2] into a Volume of Fluid (VOF) framework for interface capturing. Three schemes are proposed, differing in how they compute interface geometry—curvature, tangent vectors, and surface fractions—from the VOF field. These include: a. Coupled Level Set Volume of Fluid (CLSVOF) method using a signed-distance function coupled with VOF, b. a Height Function (HF) method relying on height functions derived from VOF, and a Height Function to Distance (HF2D) method using a signed-distance function reconstructed from the height functions. Each scheme is rigorously validated with benchmark problems.

[1] Lohse, Detlef. "Fundamental fluid dynamics challenges in inkjet printing." Annual review of fluid mechanics 54.1 (2022): 349-382.
[2] Abu-Al-Saud, Moataz O., Stéphane Popinet, and Hamdi A. Tchelepi. "A conservative and well-balanced surface tension model." Journal of Computational Physics 371 (2018): 896-913.