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

Fe and N self-diffusion in non-magnetic Fe:N

Fe and N self-diffusion in non-magnetic FeN has been studied using neutron reflectivity. The isotope labelled multilayers, FeN/57Fe:N and Fe:N/Fe:15N were prepared using magnetron sputtering. It was remarkable to observe that N diffusion was slower compared to Fe while the atomic size of Fe is larger compared to N. An attempt has been made to understand the diffusion of Fe and N in non-magnetic Fe:N

Entropy production in systems with unidirectional transitions

The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenberg's work and hitherto can be carried out when for each transition between two states also the reverse one is allowed. Nevertheless, several physical systems may exhibit a mixture of both unidirectional and bidirectional transitions, and how to properly define the entropy production in this case is still an open question. Here, we present a solution to such a challenging problem. The average entropy production can be consistently defined, employing a mapping that preserves the average fluxes, and its physical interpretation is provided. We describe a class of stochastic systems composed of unidirectional links forming cycles and detailed-balanced bidirectional links, showing that they behave in a pseudo-deterministic fashion. This approach is applied to a system with time-dependent stochastic resetting. Our framework is consistent with thermodynamics and leads to some intriguing observations on the relation between the arrow of time and the average entropy production for resetting events.Comment: (Accepted for publication in Physical Review Research

Entropy scaling based viscosity predictions for hydrocarbon mixtures and diesel fuels up to extreme conditions

An entropy scaling based technique using the Perturbed-Chain Statistical Associating Fluid Theory is described for predicting the viscosity of hydrocarbon mixtures and diesel fuels up to high temperatures and high pressures. The compounds found in diesel fuels or hydrocarbon mixtures are represented as a single pseudo-component. The model is not fit to viscosity data but is predictive up to high temperatures and pressures with input of only two calculated or measured mixture properties: the number averaged molecular weight and hydrogen to carbon ratio. Viscosity is predicted less accurately when the mixture contains high concentrations of iso-alkanes and cyclohexanes. However, it is shown that predictions for these mixtures are improved by fitting a third parameter to a single viscosity data point at a chosen reference state. For hydrocarbon mixtures, viscosity is predicted with average mean absolute percent deviations (MAPDs) of 12.2% using the two-parameter model and 7.3% using the three-parameter model from 293 to 353 K and up to 1000 bar. For two different diesel fuels, viscosity is predicted with an average MAPD of 21.4% using the two-parameter model and 9.4% using the three-parameter model from 323 to 423 K and up to 3500 bar

Chi_1 and Polarisation Asymmetries for Quarkonia at High Orders in Non-relativistic QCD

We study doubly polarised asymmetries of c-cbar and b-bbar mesons in hadro- and photo-production at low transverse momentum in non-relativistic QCD to high orders in the relative velocity of the pair, v. We give the complete set of expressions required for the asymmetries up to order v^9. The asymmetries in the production of eta_{c,b} states are a stable measure of the polarised gluon densities. The asymmetries for chi_{c,b}, J/psi, psi', and the various Upsilon states are stringent tests of the NRQCD scaling relations.Comment: 21 pages LaTeX including 2 figure

High-Temperature, High-Pressure Viscosities and Densities of n-Hexadecane, 2,2,4,4,6,8,8-Heptamethylnonane, and Squalane Measured Using a Universal Calibration for a Rolling-Ball Viscometer/Densimeter

The development of reference correlations for viscous fluids is predicated on the availability of accurate viscosity data, especially at high pressure, high temperature (HPHT) conditions. The rolling ball viscometer (RBV) is a facile technique for obtaining such HPHT viscosity data. A new, universal RBV calibration methodology is described and applied over a broad T-p region and for a wide range of viscosities. The new calibration equation is used to obtain viscosities for n-hexadecane (HXD), 2,2,4,4,6,8,8-heptamethylnonane (HMN), and 2,6,10,15,19,23-hexamethyltetracosane (squalane) from 298 – 530 K and pressures to 250 MPa. The available literature data base for HMN is expanded to 520 K and 175 MPa and for squalane to 525 K and 250 MPa. The combined expanded uncertainties are 0.6% and 2.5% for the densities and viscosities, respectively, each with a coverage factor, k = 2. The reliability of the viscosity data is validated by comparison of HXD and squalane viscosities to accepted reference correlations and HMN viscosities to available literature data. The necessity of this new calibration approach is confirmed by the large deviations observed between HXD, HMN, and squalane viscosities determined using the new, universal RBV calibration equation and viscosities determined using a quadratic polynomial calibration equation. HXD, HMN, and squalane densities are predicted with the Perturbed Chain Statistical Associating Fluid Theory using pure component parameters calculated with a previously reported group contribution (GC) method. HXD, HMN, and squalane viscosities are compared to Free Volume Theory (FVT) predictions using FVT parameters calculated from a literature correlation for nalkanes. Although the FVT predictions for HXD, a normal alkane, result in an average absolute percent deviation (∆AAD) of 3.8%, predictions for HMN and squalane, two branched alkanes, are four to 13 times larger. The fit of the FVT model for the branched alkanes is dramatically improved if the FVT parameters are allowed to vary with temperature