Journal of Non-Newtonian Fluid Mechanics最新文献

Yield-stress materials such as structurally complex formulations of paints, slurries, and waxes have been long ubiquitous in the coating industry, though the practice of coating engineering remains largely empirical as the fundamental role of viscoplasticity due to the yield stress of the coating material in most coating applications is still unclear. Here, we couple a recent harmonic mean viscosity regularization for the Bingham model with a well-established finite element/elliptic mesh generation method for free surface flows to present a detailed computational study of slot coating applications of viscoplastic materials. By neglecting inertia and focusing on the downstream section of a slot coater, we introduce suitable dimensionless parameters to discuss a comprehensive set of results that unravels a striking impact of viscoplasticity on the flow dynamics and low-flow limit. We show that viscoplastic effects have major implications to the velocity field and recirculation pattern in the coating bead as well as to the development length and free surface in the film formation region. Most importantly, we find that viscoplastic effects markedly widen the operating window of the process, delaying the onset of the low-flow limit and thereby suggesting that structurally complex yield-stress materials may be used to coat thinner films and/or at higher speeds than predicted by the standards far established for simple Newtonian liquids.

The evaluation of nanoparticle dispersion within viscoelastic fluids upon impact on hydrophobic and hydrophilic surfaces is conducted using the Euler-Lagrangian technique. The volume-of-fluid approach is employed in conjunction with the Lagrangian method to model the transport of nanoparticles in a three-phase system (particles-air-viscoelastic fluid). The assessment of nanoparticle dispersion was conducted over a range of Péclet numbers and contact angles ($\theta =30°$ and $120°$) in three-dimensional (3D) space using the mean square displacement method. The findings suggest that the dispersion of nanoparticles is mainly influenced by normal stress. During droplet impact, nanoparticles exhibit non-Fickian superdiffusive behaviour due to the viscoelastic fluid’s non-Gaussian distribution of velocity and stresses (normal and shear) fields. The wettability of the fluid with solid surfaces substantially affected the dispersion of nanoparticles in the viscoelastic fluid.

The shear and elongational rheology of graft polymers with poly(norbornene) backbone and one poly((±)-lactide) side chain of length N_sc = 72 per two backbone repeat units (grafting density z = 0.5) was investigated recently by Zografos et al. [Macromolecules 56, 2406–2417 (2023)]. Above the star-to-bottlebrush transition at backbone degrees of polymerization of N_bb>70, increasing strain hardening was observed with increasing N_bb, which was attributed to side-chain interdigitation resulting in enhanced friction in bottlebrush polymers. Here we show that the elongational rheology of the copolymers with entangled side chains and an unentangled backbone can be explained by the Hierarchical Multi-mode Molecular Stress Function (HMMSF) model, which takes into account hierarchical relaxation and dynamic dilution of the backbone by the side chains, leading to constrained Rouse relaxation. In nonlinear viscoelastic flows with larger Weissenberg numbers, the effect of dynamic dilution is increasingly reduced leading to stretch of the backbone chain caused by side chain constraints and resulting in strain hardening. If the backbone is sufficiently long, hyperstretching is observed at larger strain rates, i.e. the stress growth is greater than expected from affine stretch.

In the present work, under-resolved direct numerical simulation (UDNS) is used to study the turbulent flow of Herschel–Bulkley fluids in a concentric annular region with the rotation effect of the inner cylinder. The current numerical method is verified against the first- and second-order statistics of the velocity field with the large-eddy simulation (LES) data available in the literature for the Reynolds number of 8,900. The influence of the flow behavior index ($n=$ 0.65, 0.70, and 0.75), the Bingham number ($Bn=$ 0.10, 0.25, and 0.40), and the Rotation number ($N=$ 0, 0.15 and 0.30) on the flow characteristics are explored. The instantaneous flow quantities, including contours of the axial velocity and viscosity and vortical structures, and mean flow features, such as the first- and second-order turbulence statistics, mean viscosity profiles, pressure gradient, and skin friction coefficients, are investigated. The results show that weaker Reynolds stress tensor components are generated as the $n$ value is reduced and the Bingham number increases. Moreover, raising the rotation rate increases the magnitudes of turbulent statistics and makes the velocity fluctuations more asymmetrical.

This study explores the growth and static stability of bubble clouds in yield-stress fluids using an experimental approach. Carbopol gels with varying concentrations and initial gas contents as well as Laponite gels are used as model yield stress fluids in our experiments. A vacuum system is exploited to generate the bubbles and control their growth in the gels. The focus of this study is on determining the maximum gas concentration which could be held trapped in the system and the critical yield number, i.e. the ratio of the yield stress to the buoyancy stress at the onset of motion. Our findings demonstrate the effect of the bubbles proximity as well as the gel structure and rheology on both the maximum gas concentration and critical yield number. Our results confirm that for higher gas fractions, the critical yield number is larger. Also, they show that the size and degree of elongation of the bubbles at the onset of motion are controlled by their proximity as well as the gel rheology. Moreover, our results reveal two different scenarios for the bubble release depending on the uniformity of the structure of the gel. In the case of low concentration Carbopol gels, characterized by uniform structures, quasi mono-dispersed bubble suspensions are formed. At a pretty high gas concentration, this might lead to a bubble cloud burst upon static instability onset. Conversely, in the case of high concentration Carbopol gels or Laponite gels, the polydisperse bubble suspensions emerge and the bubble release occurs gradually rather than suddenly. It can be associated with the heterogeneous structure of these gels stemming from their significant shear history dependence.

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.