Journal of Non-Newtonian Fluid Mechanics最新文献

Few simulations currently explore the dynamics of microswimmers swimming through viscoelastic environments. In this study, we employ a direct-forcing fictitious domain method to investigate the collective behavior of spherical squirmers within viscoelastic fluids at low Reynolds numbers. Our findings reveal clear differences between pusher and puller swimmers: puller swimmers exhibit a tendency to aggregate into clusters, particularly noticeable in suspensions with high concentrations, which increases the average speed of the swimmers. Through an analysis of the cluster-size distribution function, we observe the larger-scale clusters of puller swimmers with increasing concentration. Moreover, the presence of fluid elasticity significantly reduces both the average swimming speed of squirmers and the fluid’s kinetic energy.

Droplet-based microfluidic devices can be powered or manipulated by applying an external electric field, and the ability to precisely control the flow in such devices is essential for various engineering and biomedical applications. In this numerical study, we investigate the deformation dynamics of a viscoelastic droplet in a ratchet microchannel under the influence of an AC electric field. We employ the leaky-dielectric electrohydrodynamic model for both the immiscible fluid phases coupled with the Oldroyd-B model for the droplet fluid. The effect of geometrical parameters such as the type of ratchet and the wavenumber of the ratchets along with the flow parameters such as the electrocapillary number, Weissenberg number and the capillary number significantly affect the droplet shape dynamics and the polymer chain extension. For the parameters considered in this work, the electric force tends to stretch the droplet in the streamwise direction and enhances the droplet deformation and polymer extension. Several interesting effects arise as a result of the coupling of the periodic hydrodynamic forcing of the ratchet walls and the electric field. Specifically, an exponential rise in the polymer chain extension for higher ratchet wavenumbers is observed, along with the cross-stream migration of the droplet for higher electrocapillary numbers when it reaches the outlet of the ratchet constriction.

To capture specific characteristics of non-Newtonian fluids, during the past years fractional constitutive models have become increasingly popular. These models are able to capture, in a simple and compact way, the complex behaviour of viscoelastic materials, such as the change in power-law relaxation pattern during the relaxation process of some materials. Using the Lagrangian Smoothed-Particle Hydrodynamics (SPH) method we can easily track particle history; this allows us to solve integral constitutive models in a novel way, without relying on complex tasks.

Hence, we develop here a SPH integral viscoelastic method which is first validated for simple Maxwell or Oldroyd-B models under Small Amplitude Oscillatory Shear (SAOS) and start-up channel flows. By exploiting the structure of the integral method, a multi-mode Maxwell model is then implemented. Finally, the method is extended to include fractional constitutive models, validating the approach by comparing results with theory.

The imbalance of normal stress around a particle induces its transverse migration in pressure-driven viscoelastic flow, offering possibilities for particle manipulation in microfluidic devices. Theoretical predictions align with experimental evidence of particles migrating towards the center-line of the flow. However, these arguments have been challenged by both experimental and numerical investigations, revealing the potential for a reversal in the direction of migration for viscoelastic shear-thinning fluids. Yet, a significant property of viscoelastic liquids that remains largely unexplored is the ratio of solvent viscosity to the sum of solvent and polymer viscosities, denoted as $\beta$. We computed the lift coefficients of a freely flowing cylinder in a bi-dimensional Poiseuille flow with Oldroyd-B constitutive equations. A transition from a negative (center-line migration) to a positive (wall migration) lift coefficient was demonstrated with increasing $\beta$ values. Analogous to inertial lift, the changes in the sign of the lift coefficient were strongly correlated with abrupt (albeit small) variations in the rotation velocity of the particle. We established a scaling law for the lift coefficient that is proportional, as expected, to the Weissenberg number, but also to the difference in rotation velocity between the viscoelastic and Newtonian cases. If the particle rotates more rapidly than in the Newtonian case, it migrates towards the wall; conversely, if the particle rotates more slowly than in the Newtonian case, it migrates towards the center-line of the channel. Finally, experiments in microfluidic slits confirmed migration towards the wall for viscoelastic fluids with high viscosity ratio.

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.