Stability of extensional flows and extending viscoelastic fluid sheets

The theory of nearly-extensional flow is developed to study the stability of extensional flow. For such flows a simple constitutive equation is derived for slightly disturbed extensional flow when a ‘short memory’ assumption is admissible.Following Minoshima and White and utilizing the constitutive equation obtained, a stability analysis for non-Newtonian fluid sheets is presented. The theoretical analysis presented is specific for an integral consitutive equation. The influence of the fluid elasticity on the stability behaviour is investigated. It is shown that the fluid sheet stability depends upon λk, where λ is the relaxation time and K is the elongation rate.