Kinetics of Observable with Power-law Mixing Rule in the Second-Order Reaction Process

Abstract

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(l-x)2 where a general observable o grows with reaction degree × through the power-law type mixing rule O = (1-x)OR + xOp. For -1 < formula ommitted(< v <1, the observable-time curve could possess IP at 0*=(1-v)1/i;(l+v)~1/vor and K2t*=2~1(l+u) v_1(l-(0R/0P)1')-1 with the maximum growth rate do/dt\t*=22v)(1A0_1(1 + v)(1-(or/orY) OPK2.) These results show that 0r dependence disappears in the product formula ommitted((l+K2t*)do/dt\f*). The whole 0-t curve is linearized with the transformation formula ommitted((or-or) {oR-ov)~1=\+K2t.) The case of v =0 is compensated with a logarithmic type (Ino) mixing rule. © 2007, Japan Society for Food Engineering. All rights reserved.