Journal of Non-Newtonian Fluid Mechanics最新文献

We present predictions for the flow of elastoviscoplastic (EVP) fluids in the 4 to 1 planar contraction geometry. The Saramito-Herschel-Bulkley fluid model is solved via the finite-volume method with the OpenFOAM software. Both the constitutive model and the solution method require using transient simulations. In this benchmark geometry, whereas viscoelastic fluids may exhibit two vortices, referred to as lip and corner vortices, we find that EVP materials are unyielded in the concave corners. They are also unyielded along the mid-plane of both channels, but not around the contraction area where all stress components are larger. The unyielded areas using this EVP model are qualitatively similar to those using the standard viscoplastic models, when the Bingham or the Weissenberg numbers are lower than critical values, and then, a steady state is reached. When these two dimensionless numbers increase while they remain below the respective critical values, which are interdependent, (a) the unyielded regions expand and shift in the flow direction, and (b) the maximum velocity increases at the entrance of the contraction. Increasing material elasticity collaborates with increasing the yield stress, which expands the unyielded areas, because it deforms the material more prior to yielding compared to stiffer materials. Above the critical Weissenberg number, transient variations appear for longer times in all variables, including the yield surface, instead of a monotonic approach to the steady state. They may lead to oscillations which are damped or of constant amplitude or approach a flow with rather smooth path lines but complex stress field without a plane of symmetry, under creeping conditions. These patterns arise near the entrance of the narrow channel, where the curvature of the path lines is highest and its coupling with the increased elasticity triggers a purely elastic instability. Similarly, a critical value of the yield stress exists above which such phenomena are predicted.

Parallel and Orthogonal Superposition experiments may be employed to probe a material’s non-linear rheological properties through the rate-dependent parallel and orthogonal superposition moduli, $G_{\parallel }^{\ast }(\omega ,\dot{\gamma })$ and $G_{\perp }^{\ast }(\omega ,\dot{\gamma })$, respectively. In a recent series of publications, we have considered the problem of interconversion between parallel and orthogonal superposition moduli as a means of probing flow induced anisotropy. However, as noted by Yamomoto (1971) superposition flows may be used to assess the ability of a particular constitutive model to describe the flow of complex fluids. Herein, we derive expressions for the superposition moduli of the Gordon–Schowalter (or Johnson–Segalman) fluid. This model contains, as special cases, the corotational Maxwell model, the upper (and lower) convected Maxwell models, the corotational Jeffreys model, and the Oldroyd-B model. We also consider the conditions under which the superposition moduli may take negative values before studying a specific, non shear banding, worm like micellular system of cetylpyridinium chloride and sodium salicylate. We find that, using a weakly non-linear analysis (in which the model parameters are rate independent) the Gordon–Schowalter/Johnson–Segalman (GS/JS) model is unable to describe the superposition moduli. However, by permitting strong non-linearity (allowing the GS/JS parameters to become shear rate dependent), the superposition moduli, at all rates studied, are described well by the model. Based on this strongly non-linear analysis, the shear rate dependency of the GS/JS ‘slip parameter’, $a$, suggests that the onset of shear thinning in the specific worm-like micellular system studied herein is driven by a combination of microstructural modification and a transition from rotation dominated (as in the corotational Jeffreys model) to shear dominated (as in the Oldroyd-B model) deformation of the microstructural elements.

The mechanical behavior of spherical capsules and red blood cells in shear and confined pressure-driven flow of polymeric fluids was studied computationally. In particular, we study the effect of suspending fluid elasticity on the steady mechanical behavior of spherical capsules and red blood cells suspended in an Oldroyd-B fluid, in dilute shear and confined pressure-driven flow, as a model system for dilute suspensions of capsules in polymeric fluids. We investigate the effects of suspending fluid elasticity at fixed capillary number on the capsule deformation, membrane tensions, and effective viscosity for a range of capsule capillary numbers. For both spherical capsules and red blood cells, capsule deformation was found to decrease with increasing fluid elasticity in shear flow, and increase in confined pressure-driven flow. The average membrane tension for spherical capsules was found to follow the same trends: decreasing in shear and increasing in pressure-driven flow; however, the average membrane tension for red blood cells had a less pronounced trend with fluid elasticity, which we attribute to the reduced volume of the red blood cell. On the other hand, the effective viscosity of the suspension was found to be non-monotonic with an increase in suspending fluid elasticity for both flows and particle types. The underlying mechanisms for these trends were investigated by comparing these capsule simulations to results from rigid spherical particles. These results indicate that the mechanical behavior of these dilute capsule suspensions can be qualitatively understood by examining the disturbance flow created by the introduction of rigid spherical particles, and the subsequent stress induced in the polymeric fluid to these disturbances.

The extrusion of polymer melts is known to be susceptible to ‘melt fracture’ instabilities, which can deform the extrudate, or cause it to break entirely. Motivated by this, we consider the impact that the recently discovered polymer diffusive instability (PDI) can have on polymer melts and other concentrated polymeric fluids using the Oldroyd-B model with the effects of polymer stress diffusion included. Analytic progress can be made in the concentrated limit (when the solvent-to-total-viscosity ratio $\beta \to 0$), illustrating the boundary layer structure of PDI, and allowing the prediction of its eigenvalues for both plane Couette and channel flow. We draw connections between PDI and the polymer melt ‘sharkskin’ instability, both of which are short wavelength instabilities localised to the extrudate surface. Inertia is shown to have a destabilising effect, reducing the smallest Weissenberg number ($W$) where PDI exists in a concentrated fluid from $W\sim 8$ in inertialess flows, to $W\sim 2$ when inertia is significant.

Water-lubricated transportation of viscous oil is an important application of core annular flow (CAF), which significantly reduces friction pressure drop and saves pump power. However, the core oil floats up due to the density difference of oil and water, causing instability and even destruction of CAF, which restricts the application and development of the drag reduction technology. The viscoelastic fluid in the annular can inhibit the tendency of the core oil to float up and enhance the stability of the CAF. Nevertheless, theoretical studies related to the viscoelastic fluid CAF are currently missing. To make up for the lack of theoretical research, the solutions of laminar concentric viscous oil-viscoelastic fluid CAF in horizontal and inclined pipes are obtained in this work, and the annular fluid is regarded as viscoelastic fluid conforming to the FENE-P model. Based on the Navier–Stokes equation and FENE-P model, a non-dimensional CAF model is established, and the Newton–Raphson method is used to solve the model. The rheological behavior of annular fluid and the effects of viscoelastic fluid rheology and viscosity ratio on various CAF flow characteristics, including holdup, pressure gradient, slip ratio, and Ledinegg instability, are investigated. The results indicate that the shear-thinning effect of viscoelastic fluid has a significant effect on water holdup and expands the multi-solution region. Different from Newtonian fluid, when the annulus fluid is viscoelastic, the slip ratio can be less than 2. The most significant property is that the shear-thinning effect can transform the hydraulic characteristic curve in the multi-valued region into a single-valued curve, which helps to eliminate Ledinegg instability.

In this work, Poiseuille flows of viscoplastic fluids in typically thin channels equipped with a superhydrophobic groovy wall are numerically studied. The orientation of the groove relative to the applied pressure gradient can vary, and this orientation is measured via the groove orientation angle ($\theta$). In particular, longitudinal ($\theta =0$), oblique ($0<\theta <90^{\circ }$), and transverse ($\theta =90^{\circ }$) flow configurations are considered. The Bingham constitutive equation is employed to model the viscoplastic rheology, within the framework of the Papanastasiou regularization method. Assuming that air (gas) fills the groove completely and that the formed liquid/air interface remains flat while pinned at the groove edges, the viscoplastic fluid slippage is modeled on the liquid/air interface using the Navier slip law. Due to the anisotropic slip dynamics for the oblique flow configuration, a secondary flow is generated normal to the direction of the pressure gradient, offering unique flow features. Our work systematically analyzes the effects of the flow parameters, i.e., the groove orientation angle ($\theta$), the Bingham ($B$) and slip ($b$) numbers, the groove periodicity length ($\ell$), and the slip area fraction ($\phi$) on the flow variables of interest, i.e., the main and secondary velocity fields, the unyielded center plug zone, the effective slip length tensor ($\chi$), the secondary flow index ($I_S$), the slip angle difference ($\theta -s$), and the pressure drop ($\Delta P$). It is demonstrated that $\chi$’s shear component, $I_S$, and $\theta -s$ are maximum at intermediate $\theta$, the value of which generally decreases with $B$. In addition, the center plug is unbroken for the longitudinal flow while it breaks with an increase in $\theta$ for sufficiently large $b$.

In this work, a new solver, FPSolve, is developed to study fiber orientation kinetics using the Fokker–Planck (FP) equation. The solver employs the finite-volume method. The FP equation is discretized on unstructured cubed-sphere grids using the centered differencing scheme (CDS) or a blend of the CDS and the upwind differencing scheme. Time integration is performed using a second-order two-stage explicit Runge–Kutta scheme. Different shape factors and rotational diffusion coefficients are implemented to study suspensions in dilute to semiconcentrated regimes. The verification of the solver is performed for the fiber orientation in simple shear flow up to a Peclet number of $10^5$. Grid independence analysis is presented to show the second-order accuracy of FPSolve. It is demonstrated that the solver does not need stabilization by upwinding. Simulations for semiconcentrated suspensions are performed using the model of Ferec et al. (2014). Time-accurate solutions of the FP equation with explicit time stepping for this model are presented for the first time.

The effects of harmonically co-oscillating the inner and outer cylinders about zero mean rotation in a Taylor–Couette flow are examined numerically using Floquet theory, for the case where the fluid confined between the cylinders obeys the upper convected Maxwell model. Although stability diagrams and mode competition involved in the system were clearly elucidated recently by Hayani Choujaa et al. (2021) in weakly elastic fluids, attention is focused, in this paper, on the dynamic of the system at higher elasticity with emphasis on the nature of the primary bifurcation. In this framework, we are dealing with pure inertio-elastic parametric resonant instabilities where the elastic and inertial mechanisms are considered of the same order of magnitude. It turns out, on the one hand, that the fluid elasticity gives rise, at the onset of instability, to the appearance of a family of new harmonic modes having different axial wavelengths and breaking the spatio-temporal symmetry of the base flow: invariance in the axial direction generating the $O\left(2\right)$ symmetry group and a half-period-reflection symmetry in the azimuthal direction generating a spatio-temporal $Z_2$ symmetry group. On the other hand, new quasi-periodic flow emerging in the high frequency limit and other interesting bifurcation phenomena including bi and tricritical states are also among the features induced by the fluid elasticity. Lastly, and in comparison with the Newtonian configuration of this system, the fluid elasticity leads to a total suppression of the non-reversing flow besides emergence of instabilities with lower wavelengths. Such a comparison provides insights into the dynamics of elastic hoop stresses in altering the flow reversal in modulated Taylor–Couette flow.

Accidental release of pressurized hydrocarbon fuels and lubricants are a major fire hazard due to the formation of small droplet mists that can readily evaporate and ignite. Mist control through increasing droplet size and suppressing droplets has been previously demonstrated with high molecular weight polymer additives, but traditional long polymer additives do not survive the pumping that would usually precede accidental release. This constraint inspired associative polymer additives that can transiently form the high molecular weights needed for mist control, while reversibly breaking during pumping. A prior study demonstrated the efficacy of such a system in fuel: long telechelic polycyclooctadiene (PCOD) with pairwise associating acid and base end-groups. Here, we address an obstacle to applying this same polymeric system in a polyalphaolefin (PAO) solvent—its poorer solvent quality for PCOD than fuel. We measured the effects of the end-associative PCOD compared to a non-associative control on the rheological properties of solutions in both PAO (a common lubricant and heat transfer fluid) and decahydronapthalene (decalin, a solvent with PCOD solubility similar to fuel) in shear and extension, and connect those rheological modifications to observed changes in PAO spray under simulated accidental release conditions. The PCOD additives demonstrated substantial mist control in PAO, both in terms of reduced spray angle and droplet suppression. Despite the worse solubility in PAO and thus smaller effective coil size, these associative PCOD additives are effective at the low concentrations (¡0.1 wt %) necessary for practical use as a safety measure.