Some biopolymer gelation process shows an inflection point (IP) in a growth curve of a rheological observable. In this note, a kinetic treatment is presented for such a second-order food reaction process
dx/dt=
K2 (1-
x)
2 where a general observable
o grows with reaction degree
x through the power-law type mixing rule
oν= (1-
x)
oνR+
xoνP. For-1<ν<1, the observable-time curve could possess IP at
o*= (1-ν)
1/ν (1+ν)
-1/νoP and
K2t*=2
-1 (1+ν) ν
-1 (1- (
oR/
oP)
ν) -1 with the maximum growth rate
do/dt|t*=2
2 (1-ν)
(1/ν) -1 (1+ν)
- (1/ν) -1ν (1- (
oR/
oP) ν)
-1oPK2. These results show that
oR dependence disappears in the product (1+
K2t*) do/dt|t*. The whole
o-t curve is linearized with the transformation (
oνP-
oνR) (
oνP-
oν)
-1=1+
K2t. The case of ν=0 is compensated with a logarithmic type (In
o) mixing rule.
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