The steady thin film flow on a vertical belt of a non-Newtonian Johnson–Segalman fluid for lifting and drainage problems are investigated in this paper. The analytical solutions of the non-linear problems are obtained by Adomian Decomposition Method (ADM) and Homotopy Perturbation Method (HPM). Expressions for the velocity profile, average velocity, volume flux, the belt speed of the lifting an...

Starting from stationary bifurcations in Couette-Dean flow, we compute nontrivial stationary solutions in inertialess viscoelastic circular Couette flow. These solutions are strongly localized vortex pairs, exist at arbitrarily large wavelengths, and show hysteresis in the Weissenberg number, similar to experimentally observed "diwhirl" patterns. Based on the computed velocity and stress fields...

We investigate the dynamics of the two-dimensional periodic Kolmogorov flow of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct numerical simulations. Above a critical Weissenberg number the flow displays a transition from stationary to randomly fluctuating states, via periodic ones. The increasing complexity of the flow in both time and space at progressively higher v...

The conformational dynamics of individual, flexible polymers in steady shear flow were directly observed by the use of video fluorescence microscopy. The probability distribution for the molecular extension was determined as a function of shear rate, gamma;, for two different polymer relaxation times, tau. In contrast to the behavior in pure elongational flow, the average polymer extension in s...

A recently-developed microfluidic device, the optimized shape cross-slot extensional rheometer, or OSCER [S.J. Haward, M.S.N. Oliveira, M.A. Alves and G.H. McKinley, Phys. Rev. Lett. 109, 128301 (2012)], is used to investigate the stability of viscoelastic polymer solutions in an idealized planar stagnation point flow. Aqueous polymer solutions, consisting of poly(ethylene oxide) and of hyaluro...

We present direct numerical simulations of turbulent channel flow with passive Lagrangian polymers. To understand the polymer behavior we investigate the behavior of infinitesimal line elements and calculate the probability distribution function (PDF) of finite-time Lyapunov exponents and from them the corresponding Cramer's function for the channel flow. We study the statistics of polymer elon...

We report numerical evidence of elastic turbulence phenomenology in a two-dimensional periodic Kolmogorov flow. By direct numerical simulations of the Oldroyd-B viscoelastic model at very small Reynolds numbers, we find that above the elastic instability threshold the flow develops an elastic turbulent regime. We observe that both the turbulent drag and the Lyapunov exponent increase with the W...