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The Ohnesorge number (Oh) is a key dimensionless parameter used to evaluate the jetting behavior
of fluids. It encapsulates the balance between viscous, inertial, and surface tension forces, and is
defined as Oh = μ / √(ρσd), where μ is the dynamic viscosity, ρ the fluid density, σ the surface
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tension, and d the characteristic length scale (typically the nozzle or jet diameter) . In this work,
the Ohnesorge number ranged from 0.021 for the lowest-viscosity ink (2.8 cP) to 1.31 for the
highest-viscosity ink (165 cP). In accordance with our results, for Newtonian fluids, a range of
0.01 < Oh < ~1.5 has been shown to produce stable, satellite-free droplets in laser-assisted flow-
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focusing systems . The Weber number (We) was also calculated to characterize the ratio of
inertial to surface tension forces, defined as We = (ρv²d) / σ, where v is the jet velocity. The Weber
number is useful for assessing droplet behavior upon impact, such as splashing or penetration into
soft substrates (e.g., tissue) 49,50 . Across all tested viscosities and laser energies using the mobile
LIST printer, the Weber number ranged from 20 to 320 - placing it well within the drop spreading
regime and avoiding conditions associated with splashing or substrate penetration when targeting
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soft tissue .
Compared to our previous LIST implementation using a fixed printing head with free-space
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optics , the present mobile fiber-based setup shows a consistently higher printing threshold
energy—by a factor of 1.5—across all tested viscosities (2.8 cP to 140 cP) with the same model
ink. Two factors likely contribute to this difference. The primary factor is that, in the mobile fiber-
based setup, the bubble is generated at the top part of the capillary, which is farther from the
opening compared to the free-space optics system, where the bubble forms in the middle of the
capillary. The second factor is the focusing lens used in the fixed setup, which produced a smaller
spot size compared to the 105 μm fiber output, thereby yielding a higher power density at the focus
for the same deposited energy. Nevertheless, both systems achieved printing over a similar
viscosity range.
One limitation of the present study is that printing experiments were conducted using a step-by-
step movement of the robotic arm rather than continuous motion along predefined paths. This was
necessary due to the need for continuous z-coordinate updates using input from the OCT-based
position tracking system. However, this operational mode introduced vibrations, which
significantly contributed to drop placement errors. For instance, when the update frequency of the
XYZ coordinates was reduced from 5 Hz to 2 Hz, the droplet placement error decreased from 220
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