Page 235 - IJB-10-5

International Journal of Bioprinting Effect of ingredient flow speed

flow speed V is defined as a ratio between the total length the assumption that the printing process parameters are
IFS
required based on the material’s rheological properties L truly independent variables and work similarly to typical
and the length required based on the design of the model E 3D food printers. However, this is not the case as the
(Equation [V]). An increase or decrease in L would lead to printing process parameter does not operate in a way that
a linear change in the ingredient flow speed, which affects conforms to this logic. Thus, the factorial design to find
the amount of material extruded subsequently. Based out the interaction between the controllable variables (V
IFS
on this understanding, the ingredient flow speed is also and V ) is not suitable, as the two variables might not be
PS
equal to the ratio of the total required volume V and the truly independent of each other. In addition, the actual
Req
volume of the design model V . printing speed is largely different from the set printing
E
speed (Table 2), and the control over printing speed is not
L V Re q precise and limited.
V IFS = = V
E V E 4.3. Integration of constitutive equations into the
fluid flow model
Equation (V) can be rearranged to Equation (VI), Based on our understanding of the Foodini process
where V is the subject: parameters and fluid flow model, the constitutive Foodini
Req
Equation (VI) is integrated into the governing Equation
V = V . V VI (IV) of the fluid flow model to derive a novel equation that
Req
E
IFS
models the food extrusion process using Foodini control
parameters, as well as the rheological properties of the
Following conservation of mass, the volume extruded food ink.
by the plunger is equivalent to the amount of food ink
exiting the nozzle. The total volume required (Equation
[VII]) is tantamount to the volume of the printed straight Q = V = V . V X
E
IFS
Req
line, which was modeled using the general equation
π
2
V = d h , where d represents the diameter and h
Req
4
represents the height. Equation (VII) is derived by XI
replacing d with the diameter of the printed line d and h
f
with the length of printed line l , which is equal to the
line
printing speed V multiplied by the time taken to extrude.
PS
V
Subsequently, replacing L with the following L = Req
π 2 gives Equation (XII). π R 2
V Req = 4 d ⋅ f ⋅ V ⋅ t VII
PS
Equation (VIII) is derived by replacing V with
Equation (VI). Req XII
π 2
V IFS ⋅ V = 4 d ⋅ f ⋅ V ⋅ t VIII
E
PS
To understand the relationship between ΔP and the
ingredient flow speed V , the ingredient flow speed
IFS
IX is taken out and combined, which is expressed in the
equation below.
From Equation (IX), it can be observed that there
is a complex relationship between the independent (d)
f
and dependent parameters (V and V ). In addition,
IFS
PS
the equation states that an increase in ingredient flow XIII
speed and a decrease in printing speed will result in a
reduction in the width of the straight line. This is under

Volume 10 Issue 5 (2024) 227 doi: 10.36922/ijb.2787