Journal of Non-Newtonian Fluid Mechanics最新文献

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.

We explore the use of an Elastic Perfectly Plastic (EPP) constitutive equation for the modelling of yield stress fluids. Contrary to many other models, stresses in the EPP model arise from elastic deformation rather than as a viscous effect. In this paper, the EPP model is coupled to a standard viscous treatment of the post-yield flow stresses to produce Bingham-like behaviour, and the timescale associated with the yielding mechanism is linked to material parameters. We also show that when the yield stress is much smaller than the elastic modulus, EPP and Bingham models can produce very similar flow fields in channel and contraction geometries. The EPP model is found to be significantly cheaper computationally in both geometries. Additionally, in the case of channel flow where analytical solutions exist, the EPP model is associated with a much smaller error than the regularised Bingham model.

Understanding polymer dynamics under shear flow is crucial for studying their rheological behavior in diverse applications. However, conventional micro analyses provide limited insights into polymer elongation and conformation. To address this, we propose a hybrid model combining the Lattice Boltzmann method and Langevin Dynamics technique, which captures the multiscale nature of polymer dynamics. Using the coarse-grain bead-spring method, we optimize computational efficiency and model polymers as chains with specific mass and charge. Our hybrid model integrates Navier-Stokes equations with external drag force modified based on segment velocities from Brownian Dynamics simulations.

In our study, we investigated the effects of chain structure and solvent properties on polymer solutions under shear flow through numerical simulations. We observed that in high shear rate flows, a viscous solvent promotes polymer elongation, while low shear rate flows lead to chain insolubility in the base oil. Longer chains have a greater overall impact on the fluid due to increased contact points with the solvent. The size of the polymer coil over time is influenced by shear rate, chain length, and solvent viscosity. Moreover, solvent density, particle mass, and radius locally affect fluid flow. The higher viscosity fluids result in amplified hydrodynamic and random forces acting on the chains. These findings have implications for applications involving polymer additives that alter the properties of the host solvent in natural and artificial processes. Our study represents an initial step towards a comprehensive understanding of polymer dynamics, taking into account the diverse factors that influence them.

This work builds upon the previously published analysis of a lid-driven cavity filled with viscoplastic fluid. We extend the study from a two-dimensional case to a three-dimensional one, employing the moment representation of the lattice Boltzmann method to obtain numerical results. The findings expand the existing dataset, which can potentially serve as benchmark results for inertial regimes of viscoplastic flows. In this study, we investigate the Reynolds and Bingham numbers until the flow transition from stationary to a transient regime. The results reveal that, similarly to the Newtonian case, there is an effective Reynolds number for the bifurcation, approximately Re^⁎ = Re₀ (1 + Bn), where Re₀ represents the bifurcation point for a Newtonian fluid. Like the Newtonian cases, there were instances where the Taylor-Görtler-like vortices moved toward the cavity's side periodically. In other cases, more than two vortices simultaneously formed, with their number changing over time. Finally, similar to the two-dimensional case, the bifurcation initiated after the Moffat eddies in the downstream corner broke down into plugs.

We succeeded in developing a multiscale simulation (MSS) method for a spinning process of a polymer melt. A previous work by Sato and Taniguchi (2017) developed a MSS method where the microscopic model and macroscopic model for the spinning process are respectively modeled by using a slip-link model and a continuous fluid mechanics model. Here we replace the microscopic model with the Kremer–Grest coarse-grained (CG) model, and investigate the state of the polymer chains at steady state in the spinning process, by changing the draw ratio Dr. Unlike the previous MSS, where the microscopic simulator is a slip-link model, in which polymer chains are simulated in virtual space and entanglements are treated by virtual links, in the present MSS, a real space molecular dynamics simulator is used as the microscopic simulator. The replacement brings the advantage that we can obtain more information on the state of polymer chains, but also brings two computational difficulties, (I) the requirement of a huge computational cost, and (II) the simulation box problem related to the periodic boundary condition in the microscopic system. To deal with (I), we considered a micro-macro coupling method different from previous MSS. To resolve problem (II), we used the UEF (uniform extensional flow) method developed by Nicholson and Rutledge (2016) and Murashima et al. (2018) for a polymer melt system. By using these two ideas, we performed MSS simulations, and established a correspondence between the macroscopic flow and the microscopic polymer conformations at any position along the spinning line. Furthermore, we investigated the influence of Dr on the stretching and orientation of polymers chains and the spatial correlation between polymer chains.