We consider a general model for a non-Newtonian fluid of second grade which is capable of describing shear thinning and shear thickening effects. The model incorporates parameters m and n which are varied to account for which effect, shear thinning or thickening, is desired in the tangential and normal shear rate directions, although here we restrict attention to the shear thickening case. By constructing a generalized energy-like equation and manipulating this we show that the solution may exhibit finite-time blow up if the initial data are regular enough for the solution to exist for a sufficiently long time. The nature of the blow up, or nonexistence, behavior depends critically on the normal stress coefficients α1 and α2, and on the parameters m and n.

Explosive instabilities for a generalized second grade fluid

CIARLETTA, Michele;STRAUGHAN, BRIAN;TIBULLO, VINCENZO
2015-01-01

Abstract

We consider a general model for a non-Newtonian fluid of second grade which is capable of describing shear thinning and shear thickening effects. The model incorporates parameters m and n which are varied to account for which effect, shear thinning or thickening, is desired in the tangential and normal shear rate directions, although here we restrict attention to the shear thickening case. By constructing a generalized energy-like equation and manipulating this we show that the solution may exhibit finite-time blow up if the initial data are regular enough for the solution to exist for a sufficiently long time. The nature of the blow up, or nonexistence, behavior depends critically on the normal stress coefficients α1 and α2, and on the parameters m and n.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4656741
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 0
social impact