TY - JOUR
T1 - Flow-induced gelation of living (micellar) polymers
AU - Bruinsma, Robijn
AU - Gelbart, William M.
AU - Ben-Shaul, Avinoam
PY - 1992
Y1 - 1992
N2 - We consider the effect of shear velocity gradients on the size (L) of rodlike micelles in dilute and semidilute solution. A kinetic equation is introduced for the time-dependent concentration of aggregates of length L, consisting of "bimolecular" combination processes L + L′ →(L + L′) and "unimolecular" fragmentations L→L′ + (L - L′). The former are described by a generalization (from spheres to rods) of the Smoluchowski mechanism for shear-induced coalesence of emulsions, and the latter by incorporating the tension-deformation effects due to flow. Steady-state solutions to the kinetic equation are obtained, with the corresponding mean micellar size (L̄) evaluated as a function of the Peclet number P, i.e., the dimensionless ratio of flow rate γ̇ and rotational diffusion coefficient Dr. For sufficiently dilute solutions, we find only a weak dependence of L̄ on P. In the semidilute regime, however, an apparent divergence in L̄ at P≃1 suggests a flow-induced first-order gelation phenomenon.
AB - We consider the effect of shear velocity gradients on the size (L) of rodlike micelles in dilute and semidilute solution. A kinetic equation is introduced for the time-dependent concentration of aggregates of length L, consisting of "bimolecular" combination processes L + L′ →(L + L′) and "unimolecular" fragmentations L→L′ + (L - L′). The former are described by a generalization (from spheres to rods) of the Smoluchowski mechanism for shear-induced coalesence of emulsions, and the latter by incorporating the tension-deformation effects due to flow. Steady-state solutions to the kinetic equation are obtained, with the corresponding mean micellar size (L̄) evaluated as a function of the Peclet number P, i.e., the dimensionless ratio of flow rate γ̇ and rotational diffusion coefficient Dr. For sufficiently dilute solutions, we find only a weak dependence of L̄ on P. In the semidilute regime, however, an apparent divergence in L̄ at P≃1 suggests a flow-induced first-order gelation phenomenon.
UR - http://www.scopus.com/inward/record.url?scp=36449001770&partnerID=8YFLogxK
U2 - 10.1063/1.462371
DO - 10.1063/1.462371
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AN - SCOPUS:36449001770
SN - 0021-9606
VL - 96
SP - 7710
EP - 7727
JO - The Journal of Chemical Physics
JF - The Journal of Chemical Physics
IS - 10
ER -