Page 380 - IJB-10-3

International Journal of Bioprinting Multi-physical field control inkjet bioprinting

lumped parameter method, we evaluated the Biot number relationship between air temperature and microdroplet
using Equation VIII: 44 temperature is shown in Figure 6G.
hV A(/ ) 3.2.3. GelMA microdroplet assembly
B = λ < . 01 M (VIII) process optimization
i
The assembly of microdroplets is a complex process that
where , h, V, A, λ, and M are the Biot number, convection depends on several critical factors such as the forces of
transfer rate, superficial volume, superficial area, thermal inertia, viscosity, and wettability. During this process,
conductivity, and geometric parameter, respectively. We energy is transformed in various ways, including kinetic
used 192 V for the inkjet test and the relationship between energy, surface tension potential energy, gravitational
microdroplet diameter and velocity distribution obtained potential energy, elastic potential energy resulting
in the previous section. In this test, a 150 µm diameter from solidification, and dissipated work from viscosity.
nozzle was used. The microdroplet diameter was 192 μm, These complex interactions are accounted for in the
and the falling velocity was 0.23 m/s. The Bi was 0.016, comprehensive energy balance equation in Equation XI: 46
which is less than 0.033. d  ∆ Et +∆() E () E () E () dL t∆ f () = 0 (XI)
t +∆
t +∆
t  +
Newton’s cooling law describes the behavior of objects dt  k p1 p2 p3  dt
that are hotter than their surroundings and gradually
cool down by releasing heat. This law is also applicable where ΔE is the kinetic energy of the microdroplet;
k
to the process of cooling microdroplets in a temperature- ΔE , ΔE , and ΔE are the gravitational potential energy,
p1
p2
p3
controlled chamber. The heat balance of GelMA elastic potential energy, and surface tension potential
microdroplets can be explained by Equations IX and X, energy of the microdroplet, respectively; and ΔL is the
f
which follow Newton’s cooling law: viscous dissipation. The integral form of the equation in
45
Equation XII is:
θ d
ρcV =− hA θ (IX) (XII)
=
t
t
t
τ d ∆Et() +∆E () +∆E () +∆E () +∆Lt() 0
p3
k
p1
p2
f

−
θ = TT a = exp  − hA τ = exp  − hA ⋅  l At different temperatures, GelMA microdroplets
θ 0 T 0 −T a   ρcV     ρcV v   (X) were in different states of gelation that corresponded
to different physical characteristics, and thus, the
where T, T , T , ρ, c, τ, l, v, A, and V are the actual energy transformation in the assembly process was also
0
a
temperature of the microdroplet, the initial temperature different. To achieve a good assembly effect, according
of the GelMA microdroplet, the actual temperature to the GelMA gel point measured previously at 16°C, we
of the air, the microdroplet density, the microdroplet- expected to control the temperature of the microdroplet
specific heat capacity, the falling time of the microdroplet, at approximately 16°C when the microdroplet assembled.
the distance between the nozzle and the baseplate, the The ideal microdroplet assembly temperature was
GelMA microdroplet falling speed, superficial area, and obtained using the control relationships pressure field and
volume, respectively. temperature field obtained previously. To obtain a suitable
We substituted the physical parameters of GelMA microdroplet temperature for assembly, we performed a
and the relevant temperature into the above equation. GelMA printing experiment. We adopted a nozzle with
The calculation showed that when the air temperature a diameter of 150 μm, an actuation waveform of 192 V,
increased from 2.1°C to 9.7°C, the microdroplet and a pulse width parameter of 1 ms for the inkjet test,
temperature ranged from 15.3°C to 20.0°C. To verify the and we set the printhead temperature to 37°C. Referring
correctness of the calculation, the thermal imager was used to the data in Figure 6G, we gradually reduced the air
to observe the highest temperature of the microdroplet temperature inside the temperature-controlled chamber
falling to the rectangular area of the baseplate, which and observed the assembly phase of GelMA microdroplets
was the instantaneous temperature of the microdroplet with a high-speed camera.
contacting the baseplate. As shown in Figure 6F, when As shown in Figure 6H, there were three phases in the
the air temperature was 2.1°C, the calculated GelMA process of microdroplet assembly. The first was the liquid
microdroplet temperature was 15.3°C, and the measured phase, as shown in Figure 6H(Ⅰ). When the air temperature
microdroplet temperature was 14.7°C. The margin of error was above 4.9°C, the GelMA microdroplet temperature
was only 2.8%, which indicated that the system could was over 17°C. The microdroplet was in the liquid phase
accurately control the microdroplet temperature. The when it fell to the floor and could not assemble into
Volume 10 Issue 3 (2024) 372 doi: 10.36922/ijb.2120