Three-dimensional linear instability in pressure-driven two-layer channel flow of a Newtonian and a Herschel-Bulkley fluid

The three-dimensional linear stability characteristics of pressure-driven two-layer channel flow are considered, wherein a Newtonian fluid layer overlies a layer of a Herschel-Bulkley fluid. We focus on the parameter ranges for which Squire's theorem for the two-layer Newtonian problem does not exist. The modified Orr-Sommerfeld and Squire equations in each layer are derived and solved using an efficient spectral collocation method. Our results demonstrate the presence of three-dimensional instabilities for situations where the square root of the viscosity ratio is larger than the thickness ratio of the two layers; these "interfacial" mode instabilities are also present when density stratification is destabilizing. These results may be of particular interest to researchers studying the transient growth and nonlinear stability of two-fluid non-Newtonian flows. We also show that the "shear" modes, which are present at sufficiently large Reynolds numbers, are most unstable to two-dimensional disturbances

Numerical simulations of miscible channel flow with chemical reactions

We study the pressure-driven miscible displacement of one fluid by another in a horizontal channel in the presence of an exothermic chemical reaction. We solve the continuity, Navier-Stokes, and energy conservation equations coupled to convective-discussion equations of the reactant and product. The viscosity is assumed to depend on the volume fraction of the reactant and product as well as the temperature. The effects of relevant parameters such as the Reynolds number, Schmidt number, Damköhler number and viscosity ratio of the reactant and product are studied. Our results indicate that increasing the intensity of the chemical reaction by increasing the Damköhler number and decreasing the dimensionless activation energy increases the displacement rate. We have also found that increasing Reynolds number leads to more pronounced instabilities and roll-up phenomena, which in turn promote rapid displacement of the resident fluid inside the channel. Variation of the relative significance of the heat of reaction and the Schmidt numbers of the reactants and products, however, has a negligible influence on the displacement rates for the parameter ranges considered in the present work

Dynamics of surfactant-laden evaporating droplets

We consider the flow dynamics of a thin evaporating droplet in\ud the presence of an insoluble surfactant and small particles in the bulk. Evolution\ud equations for the film height, the interfacial surfactant and bulk particle concentra-\ud tion are derived using a lubrication model coupled by a constitutive relation for the\ud dependence of the viscosity on local particle concentration. An important ingredient\ud of our model is that it takes into account the fact that the surfactant adsorbed at\ud the surface hinders the evaporation. Time-dependent simulations are performed to\ud determine how the presence of surfactants affects the evaporation and flow dynamics\ud with and without the presence of particles in the bulk. We discuss the various mech-\ud anisms that affect the shape of the droplet as it evaporates as well as the resulting\ud pattern of particle deposition

Data-driven modeling for drop size distributions

The prediction of the drop size distribution (DSD) resulting from liquid atomization is key to the optimization of multiphase flows from gas-turbine propulsion through agriculture to healthcare. Obtaining high-fidelity data of liquid atomization, either experimentally or numerically, is expensive, which makes the exploration of the design space difficult. First, to tackle these challenges, we propose a framework to predict the DSD of a liquid spray based on data as a function of the spray angle, the Reynolds number, and the Weber number. Second, to guide the design of liquid atomizers, the model accurately predicts the volume of fluid contained in drops of specific sizes while providing uncertainty estimation. To do so, we propose a Gaussian process regression (GPR) model, which infers the DSD and its uncertainty form the knowledge of its integrals and of its first moment, i.e., the mean drop diameter. Third, we deploy multiple GPR models to estimate these quantities at arbitrary points of the design space from data obtained from a large number of numerical simulations of a flat fan spray. The kernel used for reconstructing the DSD incorporates prior physical knowledge, which enables the prediction of sharply peaked and heavy-tailed distributions. Fourth, we compare our method with a benchmark approach, which estimates the DSD by interpolating the frequency polygon of the binned drops with a GPR. We show that our integral approach is significantly more accurate, especially in the tail of the distribution (i.e., large, rare drops), and it reduces the bias of the density estimator by up to 10 times. Finally, we discuss physical aspects of the model's predictions and interpret them against experimental results from the literature. This work opens opportunities for modeling drop size distribution in multiphase flows from data

The stability of slowly evaporating thin liquid films of binary mixtures

We consider the evaporation of a thin liquid layer which consists of a binary mixture of volatile liquids. The mixture is on top of a heated substrate and in contact with the gas phase that consists of the same vapour as the binary mixture. The effect of thermocapillarity, solutocapillarity and the van der Waals interactions are considered. We derive the long-wave evolution equations for the free interface and the volume fraction that govern the two-dimensional stability of the layer subject to the above coupled mechanisms and perform a linear stability analysis. Our results demonstrate two modes of instabilities, a monotonic instability mode and an oscillatory instability mode. We supplement our results from stability analysis with transient simulations to examine the dynamics in the nonlinear regime and analyse how these instabilities evolve with time. More precisely we discuss how the effect of relative volatility along with the competition between thermal and solutal Marangoni effect defines the mode of instability that develops during the evaporation of the liquid layer due to preferential evaporation of one of the components.Comment: 19 page

Effect of the good solvent nature in flash nano-precipitation via population balance modelling and computational fluid dynamics coupling approach

The effect of the good solvent nature on polymer nano-particles (NP) formation in flash nano-precipitation is here investigated through a combined population balance model-computational fluid dynamics approach (PBM-CFD). Four good solvents are considered: acetone, acetonitrile, tetrahydrofuran and tert-butanol and the different resulting mean NP size is predicted in terms of mean radius of gyration via the Flory law of real polymers. Good solvents effects are here modelled in terms of solute–solvent interactions, using the Flory–Huggins theory and the Hansen solubility parameters. In this way, kinetics and thermodynamics are intertwined in a unique modelling tool. Our results show that the proposed methodology is able to predict the role played by the different good solvents, analysing single factors at the time. More specifically, the dynamics of mixing is decoupled from the dynamics of aggregation achieving a deeper insight into the fundamental fluid properties which affect the final NP size, pointing out the main mechanisms involved and showing a good agreement with experimental data

Spreading and retraction dynamics of sessile evaporating droplets comprising volatile binary mixtures

Abstract </jats:p

Dynamics of long gas bubbles rising in a vertical tube in a cocurrent liquid flow

© 2019 American Physical Society. When a confined long gas bubble rises in a vertical tube in a cocurrent liquid flow, its translational velocity is the result of both buoyancy and mean motion of the liquid. A thin film of liquid is formed on the tube wall and its thickness is determined by the interplay of viscous, inertial, capillary and buoyancy effects, as defined by the values of the Bond number (Bo≡ρgR2/σ with ρ being the liquid density, g the gravitational acceleration, R the tube radius, and σ the surface tension), capillary number (Cab≡μUb/σ with Ub being the bubble velocity and μ the liquid dynamic viscosity), and Reynolds number (Reb≡2ρUbR/μ). We perform experiments and numerical simulations to investigate systematically the effect of buoyancy (Bo=0-5) on the shape and velocity of the bubble and on the thickness of the liquid film for Cab=10-3-10-1 and Reb=10-2-103. A theoretical model, based on an extension of Bretherton's lubrication theory, is developed and utilized for parametric analyses; its predictions compare well with the experimental and numerical data. This study shows that buoyancy effects on bubbles rising in a cocurrent liquid flow make the liquid film thicker and the bubble rise faster, when compared to the negligible gravity case. In particular, gravitational forces impact considerably the bubble dynamics already when B