caa a22 4500 465814433 CHVBK 20180323112123.0 cr unu---uuuuu 170327e19900301xx s 000 0 eng 10.1007/BF01332380 doi (NATIONALLICENCE)springer-10.1007/BF01332380 Fractal-time stochastic processes and dynamic functions of polymeric systems [Elektronische Daten] [J. Stastna, D. De Kee, M. Powley, P. Schümmer, B. Otten] Dynamic material functions of polymeric systems are calculated via a defect-diffusion model. The random motion of defects is modelled by a fractaltime stochastic process. It is shown that the dynamic functions of polymeric solutions can be approximated by the defect-diffusion process of the mixed type. The relaxation modulus of Kohlrausch type is obtained for a fractal-time defect-diffusion process, and it is shown that this modulus is capable of portraying the dynamic behavior of typical viscoelastic solutions. The Fourier transforms of the Kohlrausch function are calculated to obtainη′ andη″. A three-parameter model forη′ andη″ is compared with the previous calculations. Experimental measurements for five polymer solutions are compared with model predictions. Steinkopff, 1990 D efect-diffusion nationallicence f ractal time nationallicence r elaxation modulus nationallicence c omplex v iscosity nationallicence D : rate of deformation tensor nationallicence G(t) : mechanical relaxation modulus nationallicence H : relaxation spectrum nationallicence I ( t ) : flux of defects nationallicence P n (s) : probability of finding a walker ats aftern-steps nationallicence P : generating function ofP n (s) nationallicence s(t) : fraction of surviving defects nationallicence Γ, (γ) : gamma function (incomplete) nationallicence η 0 : zero shear viscosity nationallicence η * (ω) : complex viscosity nationallicence ω : frequency nationallicence 〈 t 〉 n : n-th moment nationallicence F [] : Fourier transform nationallicence f * (u) : Laplace transform off(t) nationallicence η′, η″ : components ofη * nationallicence G f, ηf* : fractional model nationallicence G 3, η3* : three parameter model nationallicence $$\bar z$$ : complex conjugate ofz nationallicence $$\mathop D\limits^ \circ $$ : material time derivative ofD nationallicence Stastna J. Dépt. de génie chimique, Université de Sherbrooke, J1K 2R1, Sherbrooke, Québec, Canada aut De Kee D. Dépt. de génie chimique, Université de Sherbrooke, J1K 2R1, Sherbrooke, Québec, Canada aut Powley M. Dépt. de génie chimique, Université de Sherbrooke, J1K 2R1, Sherbrooke, Québec, Canada aut Schümmer P. Institut für Verfahrenstechnik, R.W.T.H., Aachen, FRG aut Otten B. Institut für Verfahrenstechnik, R.W.T.H., Aachen, FRG aut Rheologica Acta Steinkopff-Verlag 29/2(1990-03-01), 137-144 0035-4511 29:2<137 1990 29 397 https://doi.org/10.1007/BF01332380 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01332380 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Stastna J. Dépt. de génie chimique, Université de Sherbrooke, J1K 2R1, Sherbrooke, Québec, Canada aut NATIONALLICENCE 700 1- De Kee D. Dépt. de génie chimique, Université de Sherbrooke, J1K 2R1, Sherbrooke, Québec, Canada aut NATIONALLICENCE 700 1- Powley M. Dépt. de génie chimique, Université de Sherbrooke, J1K 2R1, Sherbrooke, Québec, Canada aut NATIONALLICENCE 700 1- Schümmer P. Institut für Verfahrenstechnik, R.W.T.H., Aachen, FRG aut NATIONALLICENCE 700 1- Otten B. Institut für Verfahrenstechnik, R.W.T.H., Aachen, FRG aut NATIONALLICENCE 773 0- Rheologica Acta Steinkopff-Verlag 29/2(1990-03-01), 137-144 0035-4511 29:2<137 1990 29 397 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer