For my PhD, I have to look in fluid dynamics especially the inkjet printing using a Drop-On-Demand Printhead.
In most of the paper, they talked about the inflight droplet volume which is related to its diameter. I cannot find an equation linking the droplet diameter and the nozzle diameter.
Dear Benjamin,
If the nozzle diameter dn is small enough (typically smaller than 1 mm for most liquids), the droplet diameter is generally ruled by the capillary length, irrespective of the nozzle diameter, lc = (sigma/(rho g))^(1/2), with sigma: liquid-air surface tension and rho the liquid density, on condition that lc is larger than the nozzle diameter. This is the drop detachment condition under gravity and surface tension forces. Therefore, to have droplets smaller than lc, one often has to insert a piezoelectric within the nozzle (as you mentioned in your question), in order to exert a force that will push the droplet through.
If the piezo exerts a pressure that leads to an effective acceleration larger than gravity, you will be able to produce smaller droplets, which size will scale approximately as d = (sigma/(rho (g+acc)))^(1/2) (this also depends on your acoustic wave form and nozzle tip geometry), with acc the acceleration associated to the pressure wave. If the pressure amplitude is Dp, the force will be Dp*pi*dn^2/4, and the acceleration can be estimated by dividing by the drop weight : acc = Dp*pi*dn^2/4/(1/2*rho pi*d^3))
You get an implicit relationship for d, that can be solved in any basic solvers.
Of course, what is hard to determine here, is Dp, as this is really dependent on how the piezo is mechanically/acoustically coupled to the nozzle, and that you generally only control the voltage.
For more practical info, you can have a look here : A low‑cost, precise piezoelectric droplet‑on‑demand generator. Exp Fluids (2015) 56:83 DOI 10.1007/s00348-015-1950-6.
Hope this helps.
Philippe
Maybe this paper can help you:
https://pubs.rsc.org/en/content/articlelanding/2019/ee/c8ee02657b/unauth#!divAbstract
It is on bubbles on surfaces, but as droplets and bubbles can be treated similarly, this could maybe give you a ball park.
- Badges
- Science topic
- Similar topics
- Engineering
- Thermal Engineering
- Thermofluid
- Fluid Mechanics
- Fluid Dynamics