Page 99 - IJB-9-2

International Journal of Bioprinting Holistic charge-based MEW scaffold model

E E E E Seven more dimensionless parameters are introduced

�
p Jet FiberA p p p by non-dimensionalizing Equation IV:
E p Q

α = Q , β = q 0 x , = d X y , = d Y ,
q
2
+ )S
.
 (  05 1 f  + L 2 f f

2
= kq dl ln − Z L S
0 2 2 f (V)
 X +(05 1 f  + Z 2 z = d f , η = d f , ξ = d f
+ )S
.


2
 (  05. ++ ) 1 S f  + L 2 In this way, Equation IV can be rearranged as follows:

kqQdl ln 2
0
0
+ )
2L
 X +(05 1 S  +(Z + ) 2
.
 f  E K − 14
f x yz α βη ξ ) = p = ∑∑  [ ] i
( , , , , ,,, K
2
2
+ )S
.
 (  05 1 f  + L 2 k q dl k = 0 =i 1

0
−kQqdl ln
0 2
 X +(05 1 f  +(Z − ) L2 2   ln   (0.5+ )   2 + k ξ (0.5 )η 2  
+ )S
.


2
i
+

+kQQdl lln  (  . 05 1)S f  + L 2 (III)      (0.5+ k )  + x  2 + ξ ( + z  [ ]) 2   
0
0
2
+
 X +( . 05 1)S  + Z 2   (0.5+ )  2 + k ξ (0.5 )η 2 
 f   
 + ln 2 2 
    (0.5+ k )  − x  + ξ ( + z  [ ])  i 
Q and Q denote the positive charge density in the  
0
incoming jet segment and deposited fiber, respectively.    (0.5+ )   2 + k ξ (0.5 ) η 2 
 + ln 
By the similar logic, when all the fibers in the topmost   (0.5+ k )  + y 2 + ξ [ ]) 2 
i
two layers are considered, the total electric potential energy    ( + z  
can be calculated as follows:     (0.5+ )   2 + k ξ (0.5 ) η 2 
+ ln  (VI)
K − 14   y (0.5+ )  − 2 + k ξ i 2 
0 ∑∑
E p = k dl  [ ] i    ( +z  [ ])   
k = 0 = i 1
  (0.5+ ) kS  2 + L 2  Where f is the normalized electric potential energy
ln   f   function.
 2 [ ]) 2  th
   + (0.5+ ) kS f  X  + ( + Z  i   i [] and  i [] denote the i element in set
 2   = [αβ α − , β − , , ] 0 , respectively.
  (0.5+ ) kS  + L 2  − , , ] 1 and  = [0,
 ln  f  + From Equation VI, the normalized electric potential
  −  X 2 + [ ]) 2 
i
  (0.5+ ) kS f  ( + Z   energy f is a function of x, y, z, α, β, ξ, η, and K. These
  parameters can be divided into four categories: position
  (0.5+ ) kS  2 + L 2  parameters (x, y, and z), charge parameters (α and β),
+ ln  f  
  (0.5+ ) kS  + Y 2 + ( + Z  [ ]) 2  polarization parameter (η), and design parameters
i
  f   (ξ and K). The net charge polarity of the incoming jet
 2 2  segment before deposition is positive due to the charge
   (0.5+ ) kS f   + L  emission and dissociation process [28] , which is reflected
 + ln 2 2  (IV)
i
   (0.5+ ) kS f  − Y  + ( + Z  [ ])  by α > 1. Moreover, 2L is smaller than d , which is
f


reflected by η < 1. Finally, S is larger than d , which is
reflected by ξ > 1. f f
th
 i [] and  i [] denote the i element in set
3.2. General characterization of the energy surface
2 
 =  QQ , −Qq, −qQ q,  and  = [02 20, − LL , ] , Considering the multiparametric nature of the model, it
,

0
0
respectively. (, ,)XY Z denotes coordinates of the is not feasible to graphically illustrate the dependence of
incoming jet segment. 2L denotes the distance between f on all eight dimensionless parameters. Therefore, in this
centroids of positive and negative charges or polarization model, x and y are chosen to be the independent variables
distance in short. 2K denotes the number of fibers in each to graphically illustrate the energy variation in form of
printing direction. the energy surface (Figure 3B–D and 3G–I). It should be
Volume 9 Issue 2 (2022) 91 https://doi.org/10.18063/ijb.v9i2.656