Deformation and break-up of viscoelastic droplets Using Lattice Boltzmann Models

We investigate the break-up of Newtonian/viscoelastic droplets in a viscoelastic/Newtonian matrix under the hydrodynamic conditions of a confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and Finite Difference (FD) schemes. LBM are used to model two immiscible fluids with variable viscosity ratio (i.e. the ratio of the droplet to matrix viscosity); FD schemes are used to model viscoelasticity, and the kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). We study both strongly and weakly confined cases to highlight the role of matrix and droplet viscoelasticity in changing the droplet dynamics after the startup of a shear flow. Simulations provide easy access to quantities such as droplet deformation and orientation and will be used to quantitatively predict the critical Capillary number at which the droplet breaks, the latter being strongly correlated to the formation of multiple neckings at break-up. This study complements our previous investigation on the role of droplet viscoelasticity (A. Gupta \& M. Sbragaglia, {\it Phys. Rev. E} {\bf 90}, 023305 (2014)), and is here further extended to the case of matrix viscoelasticity.Comment: 8 pages, 5 figures, IUTAM Symposium on Multiphase flows with phase change: challenges and opportunities, Hyderabad, India 201

Deformation and break-up of viscoelastic droplets in confined shear flow

The deformation and break-up of Newtonian/viscoelastic droplets are studied in confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and finite difference schemes, the former used to model two immiscible fluids with variable viscous ratio, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). We quantify the droplet response by changing the polymer relaxation time $\tau_P$, the maximum extensibility $L$ of the polymers, and the degree of confinement, i.e. the ratio of the droplet diameter to gap spacing. In unconfined shear flow, the effects of droplet viscoelasticity on the critical Capillary number \mbox{Ca}_{\mbox{\tiny{cr}}} for break-up are moderate in all cases studied. However, in confined conditions a different behaviour is observed: the critical Capillary number of a viscoelastic droplet increases or decreases, depending on the maximum elongation of the polymers, the latter affecting the extensional viscosity of the polymeric solution. Force balance is monitored in the numerical simulations to validate the physical picture.Comment: 34 Pages, 13 Figures. This Work applies the Numerical Methodology described in arXiv:1406.2686 to the Problem of Droplet Break-up in confined microchannel

Hybrid Lattice Boltzmann/Finite Difference simulations of viscoelastic multicomponent flows in confined geometries

We propose numerical simulations of viscoelastic fluids based on a hybrid algorithm combining Lattice-Boltzmann models (LBM) and Finite Differences (FD) schemes, the former used to model the macroscopic hydrodynamic equations, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). The numerical model is first benchmarked by characterizing the rheological behaviour of dilute homogeneous solutions in various configurations, including steady shear, elongational flows, transient shear and oscillatory flows. As an upgrade of complexity, we study the model in presence of non-ideal multicomponent interfaces, where immiscibility is introduced in the LBM description using the "Shan-Chen" model. The problem of a confined viscoelastic (Newtonian) droplet in a Newtonian (viscoelastic) matrix under simple shear is investigated and numerical results are compared with the predictions of various theoretical models. The proposed numerical simulations explore problems where the capabilities of LBM were never quantified before.Comment: 32 Pages, 11 Figure

Large amplitude oscillatory shear flow of gluten dough: A model power-law gel

In a previous paper [T. S. K. Ng and G. H. McKinley, J. Rheol.52(2), 417–449 (2008)], we demonstrated that gluten gels can best be understood as a polymericnetwork with a power-law frequency response that reflects the fractal structure of the gluten network. Large deformation tests in both transient shear and extension show that in the absence of rigid starch fillers these networks are also time-strain factorizable up to very large strain amplitudes (γ∗>5). In the present work, we further explore the nonlinear rheological behavior of these critical gels by considering the material response obtained in large amplitude oscillatory shear over a wide range of strains and frequencies. We use a Lissajous representation to compare the measured material response with the predictions of a network theory that is consistent with the proposed molecular structure of gluten gels. In the linear viscoelastic regime, the Lissajous figures are elliptical as expected and can be quantitatively described by the same power-law relaxation parameters determined independently from earlier experiments. In the nonlinear regime, the Lissajous curves show two prominent additional features. First is a gradual softening of the network indicated by the rotation of the major axis of the stress ellipse. This feature is accounted for in the model by the inclusion of a simple nonlinear network destruction term that reflects the reduction in network connectivity as the polymer chains are increasingly stretched. Second, a distinct upturn in the viscoelastic stress is discernable at large strains. We show that this phenomenon can be modeled by considering the effects of finitely extensible segments in the elasticnetwork. We use this model to quantitatively predict the material response in other large amplitude transient flows such as the start-up of steady shear and transient uniaxial extension up until the onset of strongly nonlinear unsteady phenomena such as edge fracture in shear and sample rupture during extension.Kraft Foods Compan

Internally and externally driven flows of complex fluids: viscoelastic active matter, flows in porous media and contact line dynamics

We consider three varied soft matter topics from a continuum fluid mechanics perspective, namely: viscoelastic active matter, viscoelastic flows in porous media, and contact line dynamics. Active matter. For the purposes of this thesis, the term active matter describes a collection of active particles which absorb energy from their local environment or from an internal fuel tank and dissipate it to the surrounding fluid. We explore the stability and dynamics of active matter in a biological context in the presence of a polymeric background fluid. Using a novel coarse-grained model, we generalise earlier linear stability analyses (without polymer) and demonstrate that the bulk orientationally ordered phase remains intrinsically unstable to spontaneous flow instabilities. This instability remains even as one takes an ’elastomeric limit’ in which the polymer relaxation time τC → ∞. The 1D nonlinear dynamics in this limit are oscillatory on a timescale set by the rate of active forcing. Then, by considering the rheological response of our model under shear, we explore the mechanism behind the above generic flow instability, which we show exists not only for orientationally ordered phases but also for disordered states deep in the isotropic phase. Our linear stability analysis in 1D for sheared suspensions predicts that initially homogeneous states represented by negatively sloping regions of the constitutive curve are unstable to shear-banding flow instabilities. In some cases, the shear-bands themselves are unstable which leads to a secondary instability that produces rheochaotic flow states. Consistent with recent experiments on active cellular extracts (without applied shear) which show apparently chaotic flow states, we find that the dynamics of active matter are significantly more complex in 2D. Focusing on the turbulent phase that occurs when the activity ζ (or energy input) is large, we show that the characteristic lengthscale of structure in the fluid l∗ scales as l∗ ∝ 1/ √ζ. While this lengthscale decreases with ζ, it also increases with the polymer relaxation time. This can produce a novel ‘drag reduction’ effect in confined geometries where the system forms more coherent flow states, characterised by net material transport. In the elastomeric limit spontaneous flows may still occur, though these appear to be transient in nature. Examples of exotic states that arise when the polymer is strongly coupled to the active particles are also given. Flows in porous media. The second topic treats viscoelastic flows in porous media, which we approximate numerically using geometries consisting of periodic arrays of cylinders. Experimentally, the normalised drag χ (i.e., the ratio of the pressure drop to the flow rate) is observed to undergo a large increase as the Weissenberg number We (which describes the ratio of the polymer relaxation time to the characteristic velocity-gradient timescale) is increased. An analysis of steady flow in the Newtonian limit identifies regions dominated by shear and extension; these are mapped to the rheological behaviour of several popular models for polymer viscoelasticity in simple viscometric protocols, allowing us to study and influence the upturn in the drag. We also attempt to reproduce a recent study in the literature which reported fluctuations for cylinders confined to a channel at high We. At low numerical resolution, we observe fluctuations which increase in magnitude with the same scaling observed in that study. However, these disappear at very high resolutions, suggesting that numerical convergence was not properly obtained by the earlier authors. Contact line dynamics. We finish by investigating the dynamics of the contact line, i.e., the point at which a fluid-fluid interface meets a solid surface, under an externally applied shear flow. The contact line moves relative to the wall, apparently contradicting the conventional no-slip boundary conditions employed in continuum fluid dynamics. A mechanism where material is transported within a ‘slip region’ via diffusive processes resolves this paradox, though the question of how the size of this region (i.e., slip length ξ) scales with fluid properties such as the viscosity η and the width of the interface between phases l, remains disputed within the literature. We reconcile two apparently contradictory scalings, which are shown to describe different limits: (a) a diffuse interface limit where ξ/l is small and (b) a sharp interface limit for large ξ/l. We demonstrate that the physics of the latter (which more closely resembles real fluids in macroscopic experimental geometries) can be captured using simulations in the former regime (which are numerically more accessible)

Predicting large experimental excess pressure drops for Boger fluids in contraction–expansion flow

More recent finite element/volume studies on pressure-drops in contraction flows have introduced a variety of constitutive models to compare and contrast the competing influences of extensional viscosity, normal stress and shear-thinning. In this study, the ability of an extensional White–Metzner construction with FENE-CR model is explored to reflect enhanced excess pressure drops (epd) in axisymmetric 4:1:4 contraction-expansion flows. Solvent-fraction is taken as =0.9, to mimic viscoelastic constant shear-viscosity Boger fluids. The experimental pressure-drop data of Rothstein & McKinley [1] has been quantitatively captured (in the initial pronounced rise with elasticity, and limiting plateau-patterns), via two modes of numerical prediction: (i) flow-rate Q-increase, and (ii) relaxation-time 1-increase. Here, the former Q-increase mode, in line with experimental procedures, has proved the more effective, generating significantly larger enhanced-epd. This is accompanied with dramatically enhanced trends with De-incrementation in vortex-activity, and significantly larger extrema in N1, shear-stress and related extensional and shear velocity-gradient components. In contrast, the 1-increase counterpart trends remain somewhat invariant to elasticity rise. Moreover, under Q-increase and with elasticity rise, a pattern of flow transition has been identified through three flow-phases in epd-data; (i) steady solutions for low-to-moderate elasticity levels, (ii) oscillatory solutions in the moderate elasticity regime (coinciding with Rothstein & McKinley [1] data), and (iii) finally solution divergence. New to this hybrid algorithmic formulation are - techniques in time discretisation, discrete treatment of pressure terms, compatible stress/velocity-gradient representation; handling ABS-correction in the constitutive equation, which provides consistent material-property prediction; and introducing purely-extensional velocity-gradient component specification at the shear-free centre flow-line through the velocity gradient (VGR) correction