In his renowned lecture on Life at low Reynolds number, E.M. Purcell established that a rigid swimmer comprised of two links cannot swim in a viscous Newtonian fluid due to the reciprocal nature of its movements. Viscoelastic fluid, on the other hand, has a characteristic time scale associated with stress relaxation and can impart asymmetrical stresses on the body of a swimmer to propel it forw...

In this work we consider theoretically the problem of a Newtonian droplet moving in an otherwise quiescent infinite viscoelastic fluid under influence externally applied temperature gradient. The outer is modelled by Oldroyd-B equation, and solved for small Weissenberg Capillary numbers terms double perturbation expansion. We assume microgravity conditions neglect convective transport energy ...

Using kinetic equation in the relaxation approximation (RTA), we investigate a flow generated by an infinite plate oscillating with frequency ω. Geometrical simplicity of the problem allows a solution in the entire range of dimensionless frequency variation 0 ≤ ωτ ≤ ∞, where τ is a properly defined relaxation time. A transition from viscoelastic behavior of Newtonian fluid (ωτ → 0) to purely el...

The displacement of a more viscous fluid by less renders the fluid-fluid interface unstable and leads to intricate patterns called fingers. Since fluids experience shear during displacement, it should be possible influence emergence instability dynamics through control rheological parameters, such as elasticity or relaxation time in case viscoelastic fluid. In this article, we record analyze in...

The dynamics of a fluid in a vertical tube, subjected to an oscillatory pressure gradient, is studied experimentally for both a Newtonian and a viscoelastic shear-thinning fluid. Particle image velocimetry is used to determine the two-dimensional velocity fields in the vertical plane of the tube axis, in a range of driving amplitudes from 0.8 to 2.5 mm and of driving frequencies from 2.0 to 11....

The motion of a slender axisymmetric rod-like particle is investigated theoretically for translation through a quiescent second-order fluid and for rotation in a simple shear flow of the same material. The analysis consists of an asymptotic expansion about the limit of rheologically slow flow, coupled with an application of a generalized form of the reciprocal theorem of Lorentz to calculate th...

We propose a unified approach to the formal long-wave reduction of several fluid models for thin-layer incompressible homogeneous flows driven by a constant external force like gravity. The procedure is based on a mathematical coherence property that univoquely defines one reduced model given one rheology and one thin-layer regime. For the first time, as far as we know, various known reduced mo...