Page 205 - IJB-9-5

International Journal of Bioprinting Using droplet jetting for bioprinting

needleless drug delivery system. The goal in needleless Table 1. Classifying different modes of drop impact based on We
drug delivery is to have targeted drug delivery with certain Mode of droplet impact Criteria
penetration depth. Leveraging on the rapid firing rate in
jet systems, small-volume drugs are delivered into deeper Stick We < 5
depth using repetitive jetting . Hydrogels, such as gelatin Rebound 5 < We < 10
[56]
and agarose, have been used in these studies to simulate Spread 5 < We < 180. d () 05. v 025 f 0 75
.
.
2
ρ
stiffness of human skin tissue. Similarly, hydrogel has been 0 σ
widely used in bioprinting as both the ink formulation Splash We > 180. d () 05. v 025 f 0 75
2
.
.
ρ
and receiving substrate. There is limited understanding 0 σ
of droplet impact by jetting at the sol–gel transition
of hydrogel, as most ballistic studies are conducted on surface property of the substrate. The maximum spreading
crosslinked hydrogel surfaces or using solid spheres, which droplet diameter, D , and the initial droplet diameter,
does not translate to the viscoelastic nature of cells and max
cell-laden hydrogel. D , are used to calculate the spreading ratio β= D max . The
0
D 0
maximum diameter is a balance between inertial forces
3.2. Droplet impacting on nonpenetrative substrate with capillary and viscous forces. Various models have
Jetted droplet formation dissipates kinetic energy upon D max
fReWe), in which Laan
impacting a surface. Surface energy interaction of the suggested the relation D 0 = ( ,
[92]
jetted droplet with its substrate influences the spreading et al. suggested the interpolation of two scaling models
morphology of droplet on the nonpenetrative surface. between the capillary regime ( for small We, D max ∝ We ,
1
2
A high-speed droplet impacting on a solid substrate 1 D 0
5
undergoes three phases: (i) rapid spread along the substrate, and viscous regime ( for small Re, D max ∝ Re . Generally,
D 0
(ii) take-off from the surface to create the beginning of high-speed droplet will cause splashing . In comparison
[93]
splash, and (iii) splashing and fragmenting into satellite to the buoyancy force and stirring force caused by the
droplets. striking droplet, the surface tension force may produce the
Factors, such as droplet rheology, droplet size, and strongest flow.
impact velocity, affect the droplet impact on a substrate . Postimpact, nonpenetrative droplets pin onto the
[54]
The drop height, air resistance, and ink viscosity have an surface with its contact line described by Young’s law on
impact on the droplet’s impact velocity [54,89] . Aerodynamic surface energies. The spreading and retraction behavior of
effects are typically disregarded in the inkjet printing impact droplets on nonpenetrative viscoelastic substrate
process due to the short drop distance (1 mm) between is dependent on elasticity of substrate . The dynamic
[94]
the printing nozzle and the receiving substrate . Thus, wettability of soft viscoelastic surfaces, such as PDMS,
[90]
inertial force and capillary force, as represented by the affects the damping coefficient of sessile drop [59,94] . Similar
2
ρ vd 0 to PDMS surfaces, many natural and synthetic biomaterials
Weber number (We = p σ , where ρ is the density of the
fluid, v is its impact velocity, d is the droplet diameter, exist as soft and deformable films/fibers. Differences
p
0
and σ is the surface tension) best describe the behavior of between the rigidity and permeability of surfaces influence
droplet impact. Weber number will typically be higher for the droplet–substrate interaction.
high-velocity droplet with large diameter, which implies For substrates consisting of soft materials, Young’s
that the droplet is experiencing higher inertial force than law, which determines the surface energy and contact
the capillary force. Low-velocity droplets (We < 5) will angle, is no longer valid. Surface tension of the liquid, the
generally adhere to the substrate upon impact, whereas stiffness of the material, and the apparent contact angle of
droplets with 5 < We < 10 usually rebound from a substrate the droplet together affect how significantly the contact
that is smooth and hydrophobic. In other words, the line between the sessile droplet as well as the elastomeric
rebound is also the result of a surface characteristic, such as substrate deforms . The FEM simulation by Tirella
[95]
wettability or roughness. The mode of droplet impact upon et al. showed an inverse effect on substrate stiffness in
[96]
nonpenetrative substrate is summarized in Table 1 . absorbing the strain energy, which in turns influences
[91]
When a droplet impacts the surface with no splashing droplet remodeling.
or rebounding, the droplet will spread across the surface Prompt splash occurs when the inertial forces of the
until its maximum drop radius is reached . Thereafter, droplet overcome the capillary effect of the surface . This
[97]
[90]
the drop will either recede from its maximum radius phenomena can be simplified and predicted by a “splashing
to form a smaller drop or maintain its drop radius. The parameter” , defined as K = A. Oh . We . There are
a
b
[98]
c
differences between the cases are dependent on the many studies done for the value of A, a, and b at various
Volume 9 Issue 5 (2023) 197 https://doi.org/10.18063/ijb.758