Multilayer Flows Research Articles

New results on the motion of interfaces of multi-layer radial Hele-Shaw flows

We study the dynamical system arising from the linear stability analysis of multi-layer radial Hele-Shaw flows with time-dependent injection rates. An analysis of the system provides conditions under which the disturbances on all interfaces either monotonically decrease or monotonically increase. Additionally, we show that in any multi-layer radial Hele-Shaw flow, if all of the interfaces are circular initially except for one perturbed interface then there exists a time-dependent injection rate such that the circular interfaces remain circular as they propagate and the disturbance on the perturbed interface decays. The motion of the interfaces is also investigated numerically by integrating the dynamical system for the case of constant and time-independent injection rates. This reveals some very interesting dynamics of interfaces in multi-layer flows. It is found that: (i) A disturbance of one interface can be transferred to the other interface(s); (ii) The disturbances on the interfaces can develop either in phase or out of phase from any arbitrary initial disturbance; and (iii) The dynamics of the flow can change dramatically with the addition of more interfaces. With time-dependent injection rate, there are more possibilities. In particular it is shown that an appropriate injection rate can result in a stable configuration, which consists of all perfectly circular interfaces except for one that is perturbed with a monochromatic wave of infinitesimal amplitude. The prescribed injection rate results in the perturbation decaying even if the configuration (i.e., the setup consisting of all but one circular interface and one perturbed circular interface) itself is unstable to disturbances on any one or more of the circular interfaces. However, it may not be without a challenge to realize such a flow in practice.

Stability analysis of viscous multi-layer shear flows with interfacial slip

Abstract One of the most fundamental interfacial instabilities in ideal, immiscible, incompressible multifluid flows is the celebrated Kelvin–Helmholtz (KH) instability. It predicts short-wave instabilities that, in the absence of other mollifying physical mechanisms (e.g. surface tension, viscosity), render the nonlinear problem ill-posed and lead to finite-time singularities. The crucial driving mechanism is the jump in tangential velocity across the liquid–liquid interface, i.e. interfacial slip, that can occur since viscosity is absent. The purpose of the present work is to analyse analogous instabilities for viscous flows at small or moderate Reynolds numbers as opposed to the infinite Reynolds numbers that underpin KH instabilities. The problem is physically motivated by both experiments and simulations. The fundamental model considered consists of two superposed viscous, incompressible, immiscible fluid layers sheared in a plane Couette flow configuration, with slip present at the deforming liquid–liquid interface. The origin of slip in viscous flows has been observed in experiments and molecular dynamics simulations, and can be modelled by employing a Navier-slip boundary condition at the liquid–liquid interface. The emerging novel instabilities are studied in detail here. The linear stability of the system is addressed asymptotically for long- and short-waves, and for arbitrary wavenumbers using a combination of analytical and numerical calculations. Slip is found to be capable of destabilising perturbations of all wavelengths. In regimes where the flow is stable to perturbations of all wavelengths in the absence of slip, its presence can induce a Turing-type instability by destabilization of a small band of finite wavenumber perturbations. In the case where the underlying layer is asymptotically thin, the results are found to agree with the linear properties of a weakly non-linear asymptotic model that is also derived here. The weakly nonlinear model extends previous work by the authors that had a thin overlying layer that produces a different evolution equation.

Multilayered Energy Management Framework for Extreme Fast Charging Stations Considering Demand Charges, Battery Degradation, and Forecast Uncertainties

To achieve a cost-effective and expeditious charging experience for extreme fast charging station (XFCS) owners and electric vehicle (EV) users, the optimal operation of XFCS is crucial. It is however challenging to simultaneously manage the profit from energy arbitrage, the cost of demand charges, and the degradation of a battery energy storage system (BESS) under uncertainties. This paper, therefore, proposes a multi-layered multi-time scale energy flow management framework for an XFCS by considering long- and short-term forecast uncertainties, monthly demand charges reduction, and BESS life degradation. In the proposed approach, an upper scheduling layer (USL) ensures the overall operation economy and yields optimal scheduling of the energy resources on a rolling horizon basis, thereby considering the long-term forecast errors. A lower dispatch layer (LDL) takes the short-term forecast errors into account during the real-time operation of the XFCS. Per the latest research, monthly demand charges can be as high as 90% of the total monthly bills for EV fast charging stations; to this end, this paper takes the first attempt at the reduction of demand charges cost by considering the trade-off between the energy cost and monthly demand charges. Contrasting literature, this work allocates an energy reserve in the BESS stored energy to deal with the impact of short-term forecast errors on the optimized real-time operation of the XFCS. Moreover, degradation modeling considers the trade-off between short-term benefits and long-term BESS life degradation. Lastly, case studies and a comparative analysis prove the efficacy of the proposed framework.

Near-infrared-based quality control of plastic pre-concentrates in lightweight-packaging waste sorting plants

Today's post-consumer plastic recycling is limited by labor-intensive manual quality control (MQC) procedures, resulting in largely unknown pre-concentrate purities. Sensor-based quality control (SBQC) could enable an automated inline quality monitoring and thus contribute to a more transparent and enhanced plastic recycling. Therefore, we investigated the technical feasibility of near-infrared-based SBQC for plastic pre-concentrates in a lightweight packaging waste sorting plant. The developed SBQC method outperformed MQC methods by reducing measurement uncertainties from between ±0.8 wt% and ±6.7 wt% (MQC) to ±0.31 wt% (SBQC) for bale-specific purities at monolayered material flow presentations. In addition, we show that SBQC may even be possible at multilayered material flow presentations, although further research is needed to address identified segregation effects. The demonstrated technical feasibility of SBQC at plant scale represents a major breakthrough as it opens new opportunities in plastic recycling, such as adaptive pricing models and intelligent process control in sorting plants.

Comparison of different pilot point parameterization strategies when measurements are unevenly distributed in space

The parameterization of spatially distributed hydraulic properties is one of the most crucial steps in groundwater modeling. A common approach is to estimate hydraulic properties at a set of pilot points and interpolate the values at each model cell. Despite the popularity of this method, several questions remain about the optimum number and distribution of pilot points, which are determining factors for the efficiency of the method. This study proposes a strategy for optimal pilot point parameterization that minimizes the number of parameters while maximizing the assimilation of an observed dataset unevenly distributed in space. The performance of different pilot point distributions has been compared with a synthetic groundwater model, considering regular grids of pilot points with different spacings and adaptive grids with different refinement criteria. This work considered both prior and iterative refinements, with a parameter estimation step between successive refinements. The parameter estimation was conducted with the Gauss–Levenberg–Marquardt algorithm, and the strategies were ranked according to the number of model calls to reach the target objective function. The strategy leading to the best fit with the measurement dataset at the minimum computational burden is an adaptive grid of pilot points with prior refinement based on measurement density. This strategy was successfully implemented on a regional, multilayered groundwater flow model in the south-western geological basin of France.

Rock core VOC profiles diagnostic of aquitard occurrence and integrity in a multi-layered sedimentary rock aquifer flow system

Aquitard assessment poses a challenge for practitioners and researchers managing dense non-aqueous phase liquid (DNAPL) contaminants in sedimentary rock aquifer systems. Within these systems, DNAPL migration and bulk hydraulic properties are controlled by fracture networks which are difficult to characterize at relevant scales with conventional methods. A previous study at a DNAPL contaminated site used contrasts in high-resolution vertical gradients to delineate four aquitards and two surfaces with poor vertical connectivity within a thick (>200 m) sedimentary rock aquifer system primarily composed of layered sandstones. In this study, we corroborate that method by using the existing DNAPL contamination as a tracer to identify and characterize the aquitards in the sequence and assess aquitard integrity. Closely spaced samples of rock from four continuous cores were collected and analyzed for volatile organic compounds (VOCs). The cores were collected along a transect perpendicular to groundwater flow and 75 m downgradient of the DNAPL source zone. Dissolved phase contaminant concentrations were collected using high-resolution multilevel systems placed along the plume centerline, downgradient from the source. The rock core and groundwater VOC concentration profiles suggest a primary aquitard limits vertical migration of both DNAPL and the associated dissolved phase contaminants, despite relatively large, downward gradients across its lower boundary. A calibrated, three-dimensional numerical groundwater flow model indicates an anisotropy factor of 1,000 for this aquitard. The Kv values for all four aquitards are only slightly lower than the values for the aquifers. However, the aquitard Kv values are 1–3 orders of magnitude less than their Kh values, and the aquitard Kh values are often similar to or even greater than the Kh values for the aquifers. Therefore, large anisotropy, rather than exceptionally low Kv values, distinguish the aquitards from the aquifers in this system. Fracture network characterization of nearby outcrops showed the anisotropy of the aquitards can be attributed to laterally extensive, bedding parallel partings coupled with short, frequently terminating, and poorly connected vertical fractures. In addition, the rock VOC profiles combined with fracture network data show that fracture termination surfaces can be powerful inhibitors of downward DNAPL migration providing additional evidence for the importance of these features in sedimentary rock flow systems. Ultimately, this study reveals the important influence of anisotropic aquitards on DNAPL migration, accumulation, and persistence, as well as associated plume migration. Furthermore, it demonstrates that subtle contrasts critical to aquitard integrity may be easily missed with long screened wells and other conventional, low resolution site characterization methods.

A numerical model to simulate the vertical velocity distribution in an open channel with double-layered rigid vegetation

Abstract Vegetation flow is more and more widely studied by scholars at home and abroad because it is an important condition affecting river water quality. However, most of the studies were carried out based on the data of indoor experimental flumes, because the vegetation conditions in nature are more complex. The analytical solution of the flow velocity based on indoor conditions often has some problems when applied to practical projects. Therefore, we propose a numerical method based on the lattice Boltzmann method to simulate the vertical velocity distribution in an open channel with double-layered rigid vegetation. This method has high simulation accuracy in different vegetation conditions. At the same time, because the lattice Boltzmann method is more conducive to simulating complex boundary conditions, it is easier to combine with a multi-layered rigid vegetation flow and a flexible vegetation flow in nature after improvement, providing a basis for the application of indoor theoretical results to the outdoor.

Gold and crude oil: A time-varying causality across various market conditions

This paper examines the relationship between the returns and volatility of gold and crude oil markets using a novel procedure capturing both the quantile and time-varying Granger causality in mean and in variance, which is necessary to understand the complexity and multi-layered causal flow between these two strategic commodities. Using daily data from March 2nd, 2005, to February 7th, 2022, covering the global financial crisis and COVID-19 pandemic, the results are summarized as follows. Firstly, there is a bidirectional causal relationship in mean between gold and oil returns, regardless of the market conditions. Secondly, causality in variance varies across quantiles and mainly flows from gold to Brent during moderate to high volatility states of the volatility conditional distribution. Thirdly, the rolling-window causality-in-quantiles approach provides solid evidence that the return and volatility predictability between gold and oil markets is both time and quantile dependent, with evidence that the causal flows from Brent to gold are relatively stronger and span longer episodes than those running from gold to crude oil. The overall findings imply the unsuitability of applying a static quantile causality approach between these two strategic commodities, particularly over a long sample period, since the interactions between gold and crude oil markets tend to fracture suddenly under crisis periods. Accordingly, our main findings have important implications for portfolio diversification and hedging decisions.

Analytical study of unsteady two-layer combined electroosmotic and pressure-driven flow through a cylindrical microchannel with slip-dependent zeta potential

For investigating dynamics of two-fluid co-flows at an arbitrary time, the unsteady two-layer pressure-driven electroosmotic flow in a cylindrical microchannel is studied. To propose a model of universal significance, the interfacial slip and slip-dependent zeta potential are incorporated. The momentum equations are analytically solved and the physical picture how the unsteady two-layer flow evolves into the steady state is provided by evaluating the transient velocities. The two-layer velocities or flow rates are computed at different slip coefficients, electrokinetic widths, viscosity ratios, density ratios, radius ratios and zeta potential ratios, thereby the resulting interactive influences are assessed. When considering slip-dependent zeta potential, the change in two-layer velocity with other parameters is more pronounced. The increasing rate of flow rate with slip coefficient augments with electrokinetic width and outer zeta potential, which decreases with radius ratio. This work establishes mechanisms for the enhancement of transporting efficiency in microdevices associated with multi-layer flows.

Thermal and concentration analysis of two immiscible fluids flowing due to ciliary beating

This article explores the flow properties with mass and heat transfer of multilayered flow of two immiscible fluids (Phan-Thien-Tanner and Jeffrey fluid models) flowing due to ciliary beating in a channel, which is beneficial in different applications related to bioengineering, biomedical sciences, and medical equipment. Ciliated epithelium in airways is covered with airway surface liquid, which is mainly composed of two different layers. The first one is the mucus layer (Phan-Thien-Tanner fluid), which is a non-Newtonian, viscoelastic fluid, and the second layer is the periciliary liquid layer, which is considered the Jeffery fluid model. The fluid is considered to be incompressible, and layers of fluid do not mix with each other. The fluid flow with mass and heat transfer is first modeled as a wave and then transformed into a fixed frame. Exact solutions for stresses, velocity, temperature, and concentration profiles are obtained by simple integration. The behavior of emerging factors is shown graphically (plotted in MATHEMATICA 13.0) in the results section. The key findings from the graphical results show that the middle layer of fluid has the greatest magnitude for velocity and temperature, while the outer layer has the greatest concentration profile. This analysis may be helpful in keeping the airways clear from inhaled pollutants like viruses and bacteria.

Outlining the impact of structural properties of a multilayered porous channel with oscillating velocities and fields

In this study, we analyze the multilayered viscous potential flow, in which the effects of primary and combined resonances on the interfacial stability due to oscillating velocities and a periodic field are carried out. Fluids are assumed to be immiscible and incompressible with different electrical and dynamic properties and move through a porous nature. Viscosity occurs at the surface through the surface dynamic condition, where it is assumed to be weak in the fluid bulk and can be ignored. Given the boundary and surface conditions, the linear solutions of the motion and field equations led to simultaneous differential equations with complex periodic coefficients, which are a generalization of Mathieu’s equations. The special case of uniform velocity and the constant field is discussed where a quadruple algebraic equation has complex coefficients is obtained. The method of multiple time scales is applied to obtain analytical approximate solutions and perform the stability criteria for both the non-resonant and resonant states. The impacts of flow velocities and associated electric field properties, as well as the permeability of porous media and fluid sheet geometry, were taken into consideration. Through numerical discretization by varying the values of the quantities of the model, essential conclusions can be made that support an understanding of the stabilization process. For the primary resonance, it is found that there is an important role in increasing the thickness of the layers to the stability of the fluid sheet, while the porosity of the layers has a dual role phenomenon depending on the thickness of the upper layer. In the case of combined resonance, it was mentioned that increasing the dielectric constant between the lower layer and middle one tends to assist the system to instability, but it is worth noting that it supports it slowly, on the other hand, the electric horizontal field helps the system to be more stable.

Longitudinal velocity profile of flows in open channel with double-layered rigid vegetation

Aquatic vegetation of different heights is widely scattered in natural rivers and is conducive to their environmental function while affecting the flow hydrodynamic conditions. A semi-analytical velocity model is constructed and used to study the longitudinal velocity profile in open channel flow through double-layered rigid vegetation. The double-layered vegetation flow is separated into three zones according to the velocity profile: 1) nearly uniform distributed velocity zone 1A in the lower region of the short vegetation layer, 2) a mixing layer zone B, 3) uniform distributed velocity zone 2A in the upper region of the tall vegetation layer. Two force equilibrium equations about the gravity-driving and vegetation drag are solved to obtain the uniform velocity distribution equations in zone 1A and 2A. The velocity of zone 1A and B is further modeled as a linear superposition of two concepts: the uniform velocity distribution term of zone 1A and a hyperbolic tangent profile. Meanwhile, longitudinal velocity and the lateral vorticity profiles of open channel flow through double-layered rigid vegetation are studied by laboratory flume tests of different vegetation arrangements exposed to two water depths and three slopes. The experimental results show that the longitudinal velocity increases with the slope increase. The verification of the velocity model is based on the instantaneous velocity measured by Acoustic Doppler Velocimetry (ADV), which shows acceptable agreement, indicating that the model can give a reference to the longitudinal velocity of multi-layered vegetation flow in some cases. The effects of wake vortices and boundary friction on the model are further explored in the discussions. The results presented in this study could contribute to the management of aquatic vegetation configurations and the restoration of freshwater ecology.

Comment on “Progress and investigation on lattice Boltzmann modeling of multiple immiscible fluids or components with variable density and viscosity ratios”

We briefly comment on the generalized analytical solution for the multilayered Couette flow presented in the paper “Progress and investigation on lattice Boltzmann modeling of multiple immiscible fluids or components with variable density and viscosity ratios”.

Nonlinear waves in viscous multilayer shear flows in the presence of interfacial slip

The stability of immiscible two-fluid Couette flows is considered when slip is present at the liquid–liquid interface. The phenomena are modelled by incorporating a Navier slip condition at the interface to replace that of no slip. A nonlinear asymptotic theory is developed when the flow geometry consists of a thin layer slipping over a thick fluid layer that scales with the channel height. A nonlocal, nonlinear evolution equation is derived that is valid at finite Reynolds numbers, slip lengths, viscosity and density ratios. The nonlocal term arises from the coupling between the phases and its Fourier symbol is calculated in closed form in terms of Airy functions, thus generalising past results by the inclusion of slip. The linear spectrum is calculated and it is shown that in geometries containing a thin layer, the role of slip is to introduce dispersion and reduce instability or enhance stability.

An approach based on the porous media model for multilayered flow in the presence of interfacial surfactants

An approach based on the porous media model for multilayered flow in the presence of interfacial surfactants

A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer Shallow Water Equations with Non-Flat Bottom Topography

A well-balanced Runge-Kutta discontinuous Galerkin method is presented for the numerical solution of multilayer shallow water equations with mass exchange and non-flat bottom topography. The governing equations are reformulated as a nonlinear system of conservation laws with differential source forces and reaction terms. Coupling between the flow layers is accounted for in the system using a set of exchange relations. The considered well-balanced Runge-Kutta discontinuous Galerkin method is a locally conservative finite element method whose approximate solutions are discontinuous across the inter-element boundaries. The well-balanced property is achieved using a special discretization of source terms that depends on the nature of hydrostatic solutions along with the Gauss-LobattoLegendre nodes for the quadrature used in the approximation of source terms. The method can also be viewed as a high-order version of upwind finite volume solvers and it offers attractive features for the numerical solution of conservation laws for which standard finite element methods fail. To deal with the source terms we also implement a high-order splitting operator for the time integration. The accuracy of the proposed Runge-Kutta discontinuous Galerkin method is examined for several examples of multilayer free-surface flows over both flat and non-flat beds. The performance of the method is also demonstrated by comparing the results obtained using the proposed method to those obtained using the incompressible hydrostatic Navier-Stokes equations and a well-established kinetic method. The proposed method is also applied to solve a recirculation flow problem in the Strait of Gibraltar.

The Impact of Refugees in Neutral Hong Kong and Macau, 1937–1945

AbstractThis article investigates the complex entanglement of neutrality and displacement in Hong Kong and Macau with a focus on the impact of and responses to an unprecedented influx of refugees during the Second World War. Displaced persons were of central importance in shaping the ambiguous experience of neutrality before Hong Kong's occupation by Japan in late 1941 and until the end of the war in Macau. Building on Elizabeth Sinn's conceptualization of Hong Kong as an ‘in-between place’, this article considers these two foreign-ruled territories as ‘in-between places’ where multi-layered transborder flows developed in an ‘in-between time’ of neutrality. Highlighting similarities and connections between Hong Kong and Macau, it argues that neutrality was shaped by the movement of refugees and that refugees often experienced neutrality differently depending on perceptions of race, class, and nationality. The presence of diverse communities of refugees shaped multiple dimensions of urban life, with colonial concerns for spatial order and social control co-existing with humanitarian co-operation. The discourses and practices around refugees are an important precedent to understanding post-war refugeedom in these territories.

Validation of the low dissipation computational algorithm CABARET-MFSH for multilayer hydrostatic flows with a free surface on the lock-release experiments

The article presents the results of validation in lock-release experiments of a new low-dissipative multilayer hydrostatic model CABARET-MFSH. This model describes the dynamics of fluid with variable density and free surface. The computational algorithm of the new model is based on the method of hyperbolic decomposition, which presents of a multilayer structure in the form of separate layers interacting throughout interfaces. An explicit CABARET scheme is used to solve the system of hyperbolic equations in each layer. The scheme has a second order of approximation and is time reversible. Consequently, the scheme is initially non-dissipative. Besides, mass and momentum exchange between layers and filtering of flux variables are used to regularize the multilayer hydrostatic model, which introduces additional numerical dissipation into the scheme. The parameters of the filtering procedure are determined empirically from the condition of the stability of the algorithm and the minimal of the scheme viscosity. A 2D spatial version of our model is used for modeling lock-release experiments described in this article due to the uniformity of the current in the transverse direction. The results of numerical calculations are in satisfactory agreement with experimental data.

Understanding viscoelastic flow instabilities: Oldroyd-B and beyond

The Oldroyd-B model has been used extensively to predict a host of instabilities in shearing flows of viscoelastic fluids, often realized experimentally using polymer solutions. The present review, written on the occasion of the birth centenary of James Oldroyd, provides an overview of instabilities found across major classes of shearing flows. These comprise (i) the canonical rectilinear shearing flows including plane Couette, plane and pipe Poiseuille flows; (ii) viscometric shearing flows with curved streamlines such as those in the Taylor-Couette, cone-and-plate and parallel-plate geometries; (iii) non-viscometric shearing flows with an underlying extensional flow topology such as the flow in a cross-slot device; and (iv) multilayer shearing flows. While the underlying focus in all these cases is on results obtained using the Oldroyd-B model, we also discuss their relation to the actual instability, and as to how the shortcomings of the Oldroyd-B model may be overcome by the use of more realistic constitutive models. All the three commonly used tools of stability analysis, viz., modal linear stability, nonmodal stability, and weakly nonlinear stability analyses are discussed, with supporting evidence from experiments and numerical simulations as appropriate. Despite only accounting for a shear-rate-independent viscosity and first normal stress coefficient, the Oldroyd-B model is able to qualitatively predict the majority of instabilities in the aforementioned shearing flows. The review also highlights, where appropriate, open questions in the area of viscoelastic stability.

Investigation of the Polymer Coextrusion Process: A Review.

A review of the different coextrusion processes and the related processing problems is presented. A one-dimensional bilayer coextrusion Poiseuille flow model is first developed with Newtonian and shear-thinning rheological behaviors. A transitory computation at the convergence between the two independent polymer layers shows that stationary interface position and velocity profile are established after a short distance of the order of the die gap which justifies the validity of the 1D stationary model. This model is then applied to multilayer temperature dependent coextrusion flows which correspond to realistic industrial coextrusion conditions. Marked interface instabilities may be observed depending on the rheology of the coextruded polymers and of their flow rate ratios. Experiments point clearly out that these instabilities may be amplified along the die land. Convective stability analysis as well as direct numerical computation discriminate flow situations which amplify or damp down instabilities. These 1D models are unable to account for the complex feedblock coat-hanger die geometries. A thin layer coextrusion model is then developed, based on the Hele-Shaw lubrication approximations already used for single layer extrusion problems. It allows to predict the location of the interfaces between the different layers in the whole die, and especially at die exit. This represents a major issue in feedblock die coextrusion. These thin layer approaches are unable to address the encapsulation of one polymer by the other in these complex die geometries with important gap thicknesses. Experiments conducted in dies of square section allow identifying the dynamics of encapsulation. 3D models are required to account for this phenomenon but the management of the sticking contact at the die wall poses difficult numerical problems.