Of concern in the paper is a study of steady incompressible viscoelastic and electrically conducting fluid flow and heat transfer in a parallel plate channel with stretching walls in the presence of a magnetic field applied externally. The flow is considered to be governed by Walter's liquid B fluid. The problem is solved by developing a suitable numerical method. The results are found to be in good agrement with those of earlier investigations reported in existing scientific literatures. The study reveals that a back flow occurs near the central line of the channel due to the stretching walls and further that this flow reversal can be stopped by applying a strong external magnetic field. The study also shows that with the increase in the strength of the magnetic field, the fluid velocity decreases but the temperature increases. Thus the study bears potential applications in the study of the haemodynamic flow of blood in the cardiovascular system when subjected to an external magnetic field.
Comment on Conjugate heat transfer of mixed convection for viscoelastic fluid past a stretching sheet, by Kai-Long Hsiao and Guan-Bang Chen, Mathematical Problems in Engineering, Volume 2007, article 17058, 21 pages
Viscoelastic flows are pervasive in a host of natural and industrial processes, where the emergence of nonlinear and time-dependent dynamics regulate flow resistance, energy consumption, and particulate dispersal. Polymeric stress induced by the advection and stretching of suspended polymers feeds back on the underlying fluid flow, which ultimately dictates the dynamics, instability, and transport properties of viscoelastic fluids. However, direct experimental quantification of the stress field is challenging, and a fundamental understanding of how Lagrangian flow structure regulates the distr…
In this work, we study the role of viscoelastic instability in the mechanical dispersion of fluid flow through porous media at high Peclet numbers. Using microfluidic experiments and numerical simulations, we show that viscoelastic instability in flow through a hexagonally ordered (staggered) medium strongly enhances dispersion transverse to the mean flow direction with increasing Weissenberg number (Wi). In contrast, preferential flow paths can quench the elastic instability in disordered media, which has two important consequences for transport: First, the lack of chaotic velocity fluctuatio…
The effects of fluid elasticity on the swimming behavior of the nematode \emph{Caenorhabditis elegans} are experimentally investigated by tracking the nematode's motion and measuring the corresponding velocity fields. We find that fluid elasticity hinders self-propulsion. Compared to Newtonian solutions, fluid elasticity leads to 35% slower propulsion speed. Furthermore, self-propulsion decreases as elastic stresses grow in magnitude in the fluid. This decrease in self-propulsion in viscoelastic fluids is related to the stretching of flexible molecules near hyperbolic points in the flow.
This study presents a numerical investigation of how fluid viscoelasticity influences the flow dynamics past a transversely forced oscillating cylinder in the laminar vortex shedding regime at a fixed Reynolds number of 100. In particular, we examine how fluid viscoelasticity influences the boundary between the lock-in and no lock-in zones and the associated wake topology compared to that seen in a simple Newtonian fluid. All in all, we find that the fluid viscoelasticity facilitates the synchronization of the vortex street with the cylinder motion at lower oscillation frequencies than that re…
The flow of viscoelastic fluids in porous media is encountered in many practical applications, such as in the enhanced oil recovery process or in the groundwater remediation. Once the flow rate exceeds a critical value in such flows, an elastic instability with fluctuating flow field is observed, which ultimately transits to a more chaotic and turbulence-like flow structure as the flow rate further increases. In a recent study, it has been experimentally shown that this chaotic flow behaviour of viscoelastic fluids can be suppressed by increasing the geometric disorder in a model porous media …
Simulations of undulatory swimming in viscoelastic fluids with large amplitude gaits show concentration of polymer elastic stress at the tips of the swimmers.We use a series of related theoretical investigations to probe the origin of these concentrated stresses. First the polymer stress is computed analytically at a given oscillating extensional stagnation point in a viscoelastic fluid. The analysis identifies a Deborah number (De) dependent Weissenberg number (Wi) transition below which the stress is linear in Wi, and above which the stress grows exponentially in Wi. Next, stress and velocit…
The rimming flow of a viscoelastic thin film inside a rotating horizontal cylinder is studied theoretically. Attention is given to the onset of non-Newtonian free-surface instability in creeping flow. This non-inertial instability has been observed in experiments, but current theoretical models of Newtonian fluids can neither describe its origin nor explain its onset. This study examines two models of non Newtonian fluids to see if the experimentally observed instability can be predicted analytically. The non-Newtonian viscosity and elastic properties of the fluid are described by the Generali…
We studied experimentally the breakup of liquid bridges made of aqueous solutions of Poly(acrylic acid) between two separating solid surfaces with freely moving contact lines. For polymer concentrations higher than a certain threshold ($\sim$ 30 ppm), the contact line on the surface with the highest receding contact angle fully retracts before the liquid bridge capillary breakup takes place at its neck. This means that all the liquid remains attached to the opposing surface when the surfaces are separated. This behavior occurs regardless of the range of liquid volume and stretching speed studi…
We analyze transient dynamics during shear start-up in viscoelastic flows between two parallel plates, with a specific focus on the signatures for the onset of transient shear banding using the Johnson-Segalman, non-stretching Rolie-Poly and Giesekus models. We explore the dynamics of shear start-up in monotonic regions of the constitutive curves using two different methodologies: (i) the oft-used `frozen-time' linear stability (eigenvalue) analysis, wherein we examine whether infinitesimal perturbations imposed on instantaneous stress components (treated as quasi steady states) exhibit expone…
We give the first correction to the suspension viscosity due to fluid elasticity for a dilute suspension of spheres in a viscoelastic medium. Our perturbation theory is valid to $O(ϕ\mathrm{Wi}^2)$ in the Weissenberg number $\mathrm{Wi}=\dotγλ$, where $\dotγ$ is the typical magnitude of the suspension velocity gradient, and $λ$ is the relaxation time of the viscoelastic fluid. For shear flow we find that the suspension shear-thickens due to elastic stretching in strain hot spots near the particle, despite the fact that the stress inside the particles decreases relative to the Newtonian case. W…
The research is aimed at creating a method for rheological testing of viscoelastic fluids, the droplets of which, when stretched, form thinning filaments, i.e. exhibit the property of spinning. The typical example of such fluid is oral fluid (or mixed saliva). Among other things, the rheological features of the oral fluid actively affect the mechanisms of transmission of infection by airborne droplets. In this work, the oral fluid was studied both from the point of view of a participant in the transmission of infection and as a model for studying the rheology of viscoelastic fluids. The method…
We experimentally investigate the flow of a viscoelastic fluid in a parallel shear geometry at low Reynolds number. As the flow becomes unstable via a nonlinear subcritical instability, velocimetry measurements show non-periodic fluctuations over a broad range of frequencies and wavelengths, consistent with the main features of elastic turbulence. Using the same experimental setup, we compare these features to those in the flow around cylinders, which is upstream to the parallel shear region; we find significant differences in power spectra scaling, intermittency statistics, and flow structure…
Viscoelastic fluids are a subclass of complex fluids used in widespread applications ranging from biological to large-scale industrial settings. These fluids are often associated with various complex flow phenomena due to the presence of non-linear elastic stresses, originating due to the stretching and relaxation phenomena of microstructure (such as polymer molecules in the case of a viscoelastic polymer solution) in a deformed flow field. One such phenomenon is elastic instability (EI) which emerges due to the interaction between elastic stresses and streamline curvature present in a flow sy…
Nonmodal amplification of stochastic disturbances in elasticity-dominated channel flows of Oldroyd-B fluids is analyzed in this work. For streamwise-constant flows with high elasticity numbers $μ$ and finite Weissenberg numbers $We$, we show that the linearized dynamics can be decomposed into slow and fast subsystems, and establish analytically that the steady-state variances of velocity and polymer stress fluctuations scale as $O (We^2)$ and $O (We^4)$, respectively. This demonstrates that large velocity variance can be sustained even in weakly inertial stochastically driven channel flows of …
