We present a brief survey of recent results concerning the existence of global-in-time weak solutions in a bounded Lipschitz domain in R, d ∈ {2, 3}, to a class of kinetic models for dilute polymeric liquids with noninteracting polymer chains. The mathematical model is a coupled Navier–Stokes–Fokker–Planck system. The velocity and the pressure of the fluid satisfy a Navier–Stokes-like system of...

Abstract We report a unique tuneable analogue trend in particle focusing the laminar and weak viscoelastic regime of elasto-inertial flows. observe experimentally that particles circular cross-section microchannels can be tuned to any bandwidths lie between “Segre-Silberberg annulus” centre microcapillary. use direct numerical simulations investigate this phenomenon understand how minute amount...

The recently discovered centre-mode instability of rectilinear viscoelastic shear flow (Garg et al. , Phys. Rev. Lett. vol. 121, 2018, 024502) has offered an explanation for the origin elasto-inertial turbulence that occurs at lower Weissenberg numbers ( $Wi$ ). In support this, we show using weakly nonlinear analysis subcriticality found in Page 125, 2020, 154501) is generic across neutral cur...

It has been well-known for over six decades that the addition of minute amounts of long polymer chains to organic solvents, or water, can lead to significant turbulent drag reduction. This discovery has had many practical applications such as in pipeline fluid transport, oil well operations, vehicle design and submersible vehicle projectiles, and more recently arteriosclerosis treatment. Howeve...

We revisit the rapid stretching of a liquid filament under the action of a constant imposed tensile force, a problem which was first considered by Matta & Tytus [JNNFM vol. 35, pp 215-229, 1990]. A liquid bridge formed from a viscous Newtonian fluid or from a dilute polymer solution is first established between two cylindrical disks. The upper disk is held fixed and may be connected to a force ...

The FENE-P model of a fluid is particularly suitable for describing the rheology of dilute polymer solutions (Newtonian solvents containing small amounts of dissolved polymer) as a result of its ability to capture nonlinear effects arising from the finite extensibility of the polymer chains. In extensional flows, these polymer solutions exhibit dramatically different behavior from the correspon...