Three-layer Flow Research Articles

Thermal optimisation through multilayer convective flow of CuO- MWCNT hybrid nanofluid in a composite porous annulus

The present article deals with the analysis of the three-layer convective flow of immiscible nanofluids in a composite porous annulus. Water and kerosene are chosen as base fluids due to their immiscible property that leads to the formation of a non-physical boundary separation and thus forming a multi-layer flow. In this model, the hybrid nanofluid is formed by suspending copper oxide (CuO) and multi walled carbon nanotubes (MWCNTs) in water which is sandwiched between layers of nanofluid formed by suspending CuO in kerosene leading to two boundary separations that give rise to the interface regions. Such a flow finds applications in the field of solar reactors, electronic cooling, etc. The model based on the above assumptions is in the form of a system of ordinary differential equations that are solved using the differential transformation method. The solutions are found to be in agreement with the existing literature and the results of this study are interpreted graphically. It is to be noted that the interfacial region in the multilayer nanofluid flow helps in maintaining the system at an optimum temperature which helps to cool down the systems. Further, the increase in the Eckert number increases the heat conduction of the nanofluid and pressure enhances the flow speed of the nanofluid.

Linear Non-Modal Growth of Planar Perturbations in a Layered Couette Flow

Layered flows that are commonly observed in stratified turbulence are susceptible to the Taylor–Caulfield Instability. While the modal stability properties of layered shear flows have been examined, the non-modal growth of perturbations has not been investigated. In this work, the tools of Generalized Stability Theory are utilized to study linear transient growth within a finite time interval of two-dimensional perturbations in an inviscid, three-layer constant shear flow under the Boussinesq approximation. It is found that, for low optimization times, small-scale perturbations utilize the Orr mechanism and achieve growth equal to that in the case of an unstratified flow. For larger optimization times, transient growth is much larger compared to growth for an unstratified flow as the Kelvin–Orr waves comprising the continuous spectrum of the dynamical operator and the gravity edge-waves comprising the discrete spectrum interact synergistically. Maximum growth is obtained for perturbations with scales within the region of instability, but significant growth is maintained for modally stable perturbations as well. For perturbations with scales within the unstable region, the unstable normal modes are excited at high amplitude by their bi-orthogonals. For perturbations with modally stable scales, the Orr mechanism is utilized to excite at high amplitude neutral propagating waves resembling the neutral Taylor–Caulfield modes.

Mathematical modeling of three-layer flows with evaporation based on exact solutions

The stationary flow in the “liquid-liquid-gas” system in a horizontal channel with solid impermeable upper and lower walls is investigated. Mathematical modeling in each of the layers of the system is based on exact solutions of a special type of Navier-Stokes equations in the Boussinesq approximation. The processes of vapor evaporation or condensation at the liquid-gas interface are modeled using the boundary conditions of the problem. In the upper layer the thermal diffusion effect and the effect of diffusional thermal conductivity are taken into account. Examples of three-layer flows for the “silicone oil - water - air” system are given. The influence of the thermal regime at the boundaries of the system and the thickness of the upper layer on the longitudinal velocity and temperature distribution is considered.

Instability of a liquid sheet with viscosity contrast in inertial microfluidics

Flows at moderate Reynolds numbers in inertial microfluidics enable high throughput and inertial focusing of particles and cells with relevance in biomedical applications. In the present work, we consider a viscosity-stratified three-layer flow in the inertial regime. We investigate the interfacial instability of a liquid sheet surrounded by a density-matched but more viscous fluid in a channel flow. We use linear stability analysis based on the Orr–Sommerfeld equation and direct numerical simulations with the lattice Boltzmann method (LBM) to perform an extensive parameter study. Our aim is to contribute to a controlled droplet production in inertial microfluidics. In the first part, on the linear stability analysis we show that the growth rate of the fastest growing mode xi ^{*} increases with the Reynolds number text {Re} and that its wavelength lambda ^{*} is always smaller than the channel width w for sufficiently small interfacial tension Gamma . For thin sheets we find the scaling relation xi ^{*} propto mt^{2.5}_{s}, where m is viscosity ratio and t_{s} the sheet thickness. In contrast, for thicker sheets xi ^{*} decreases with increasing t_s or m due to the nearby channel walls. Examining the eigenvalue spectra, we identify Yih modes at the interface. In the second part on the LBM simulations, the thin liquid sheet develops two distinct dynamic states: waves traveling along the interface and breakup into droplets with bullet shape. For smaller flow rates and larger sheet thicknesses, we also observe ligament formation and the sheet eventually evolves irregularly. Our work gives some indication how droplet formation can be controlled with a suitable parameter set {lambda ,t_{s},m,Gamma ,text {Re}}.Graphical

Rapid Sample Preparation Using Slug Flow-Laminar Flow: Passive In Situ Microextraction/Stripping Coupling.

To increase the detection accuracy of radioactive samples, sample preparation through liquid-liquid extraction (LLE) before instrumental analysis is a crucial step. LLE preparation involves multiple steps including the tedious separation steps of co-extraction and stripping, which may cause sample loss, radioactive contamination, and radioactive leaks. In this study, a novel hybrid slug flow-laminar flow (SFLF) microchip in passive mode was designed to couple extraction and stripping in situ to realize a one-step sample preparation. The difficulty in maintaining stable water-organic-water interfaces was mitigated by using a partition wall and three resistance isolation areas. The mass transfer performance of the SFLF microchip was investigated and compared with that of the supported liquid membrane and three-layer laminar flow microextraction/stripping systems. Furthermore, the applicability of the SFLF system in preparing radioactive samples was validated through the selective separation of Ce and Pr from Cs and Sr. The novel SFLF microextraction/stripping system has a stable flow pattern, high mass transfer efficiency, and superior operating flexibility.

Shear-augmented solute dispersion during drug delivery for three-layer flow through microvessel under stress jump and momentum slip-Darcy model

Shear-augmented solute dispersion during drug delivery for three-layer flow through microvessel under stress jump and momentum slip-Darcy model

A local eddy viscosity parameterization for wind-driven estuarine exchange flow. Part I: Stratification dependence

A new parameterization for the estuarine turbulent eddy viscosity coefficient is developed considering the influence of wind forcing and feedback between stratification and shear. The emerging tidally averaged eddy viscosity profile AvT is parameterized as parabolic under well-mixed conditions, and is composed of a skewed-Gaussian-like form for the upper layer, and a parabolic form for the bottom layer under stratified conditions. The precise shape of the profiles depends parametrically on the bottom boundary layer thickness, the bulk Richardson number, and the Wedderburn number. The parameterized AvT profiles show excellent agreement with profiles obtained from numerical models. To explore the importance of vertically varying AvT with regard to exchange processes, an analytical model is designed. This one-dimensional model is based on a balance between frictional forces and pressure gradient. The resulting exchange flow is analyzed over the relevant parameter space that is associated with horizontal and vertical stratification through the bulk Richardson number, and the bi-directional wind stress via the Wedderburn number. Down-estuary wind enhances the up-estuary flow near the bottom and down-estuary flow near the surface driving an exchange flow pattern typically associated with gravitational circulation. Up-estuary wind results in either a two-layer inverted circulation opposing the gravitational circulation, or a three-layer flow that is up-estuarine at the surface with classical two-layer circulation underneath. Three-layer flow emerges with a weak wind. With increasing runoff velocity, three-layer flow transitions to a single layer flow under weak stratification conditions.

Shear augmented microvascular solute transport with a two-phase model: Application in nanoparticle assisted drug delivery

Solutal dispersion phenomena are associated with the nanoparticle-based drug delivery in the cardiovascular system to cure cardiovascular disorder. In the present problem, we explored the solutal transport for an unsteady blood flow through a microvessel with wall absorption. The rheology of blood is characterized by a two-fluid model similar to three-layer flow, namely, the core region, the intermediate region, and the peripheral region. The nature of the blood is considered as Casson fluid near the axis of the microvessel and Newtonian fluid close to the wall of the microvessel (at the intermediate and peripheral region). The peripheral region and the wall of the microvessel are permeable, and the permeability of the microvessel wall is defined by the Darcy–Brinkman model. The permeability of the inner surface of the microvessel is subjected to a slip condition at the surface. The stress-jump condition acts at the interface of the intermediate and peripheral region. The impact of the absorption parameter, velocity slip, yield stress, stress jump constant, nanoparticle volume fraction, and permeability on the velocity, exchange coefficient, convection coefficient, dispersion coefficient, and mean concentration is shown. It observed that the mean concentration boosts by the yield stress, nanoparticle volume fraction, and absorption parameters. The stress jump constant and permeability boost the convection coefficient, while the dispersion coefficient is restricted by the yield stress and absorption parameter.

Construction of Exact Solution Describing Three-layer Flows with Evaporation in a Horizontal Channel

The paper considers the flow in a three-layer system "liquid–liquid–gas" in a horizontal chan- nel with solid impermeable walls.The evaporation process at the thermocapillary interface of the liquid and gas is taken into account. The Soret and Dufour effects are taken into account in the upper layer filled with a gas-vapor mixture. The system of Navier-Stokes equations in the Boussinesq approximation is used as a mathematical model. A temperature regime is set on the channel walls. Liquid evaporation is modeled using the conditions at the liquid-gas interface. Exact solution of a special type describing the flow in a three-layer system is constructed. The velocity profiles are presented on the example of the "silicone oil–water–air" system for various values of gas flow rate, longitudinal temperature gradients at the system boundaries, thicknesses of liquid and gas-vapor layers

Multi-UAV surveillance implementation under hierarchical dynamic task scheduling architecture

In this paper, we consider a multi-UAV surveillance scenario where a team of unmanned aerial vehicles (UAVs) synchronously covers an area for monitoring the ground conditions. In this scenario, we adopt the leader-follower control mode and propose a modified Lyapunov guidance vector field (LGVF) approach for improving the precision of surveillance trajectory tracking. Then, in order to adopt to poor communication conditions, we propose a prediction-based synchronization method for keeping the formation consistently. Moreover, in order to adapt the multi-UAV system to dynamic and uncertain environment, this paper proposes a hierarchical dynamic task scheduling architecture. In this architecture, we firstly classify all the algorithms that perform tasks according to their functions, and then modularize the algorithms based on plugin technology. Afterwards, integrating the behavior model and plugin technique, this paper designs a three-layer control flow, which can efficiently achieve dynamic task scheduling. In order to verify the effectiveness of our architecture, we consider a multi-UAV traffic monitoring scenario and design several cases to demonstrate the online adjustment from three levels, respectively.

Hyperbolic model of internal solitary waves in a three-layer stratified fluid

We derive a new hyperbolic model describing the propagation of internal waves in a stratified shallow water with a non-hydrostatic pressure distribution. The construction of the hyperbolic model is based on the use of additional instantaneous variables. This allows one to reduce the dispersive multi-layer Green–Naghdi model to a first-order system of evolution equations. The main attention is paid to the study of three-layer flows over an uneven bottom in the Boussinesq approximation with the additional assumption of hydrostatic pressure in the intermediate layer. The hyperbolicity conditions of the obtained equations of three-layer flows are formulated, and solutions in the class of travelling waves are studied. Based on the proposed hyperbolic and dispersive models, numerical calculations of the generation and propagation of internal solitary waves are carried out and their comparison with experimental data is given. Within the framework of the proposed three-layer hyperbolic model, a numerical study of the propagation and interaction of symmetric and non-symmetric soliton-like waves is performed.

Weakly nonlinear analysis of the Saffman-Taylor problem in a radially spreading fluid annulus

Viscous fingering formation in a three-layer radial Hele-Shaw flow is studied. The inclusion of a third layer of fluid adds a new outer interface that couples with the inner one. It is found that the initial distance between these two interfaces has a great impact on the final morphologies of the patterns.

Electro-kinetically modulated peristaltic transport of multilayered power-law fluid in an axisymmetric tube

The objective of this paper is to investigate three-layered flow of power-law fluid driven by peristaltic activity and electro-osmotic phenomenon. The flow problem is modeled by invoking long wavelength and low Reynolds number constraints. Closed-form expressions of stream function are obtained for each region. The interfaces between core and intermediate and intermediate and peripheral regions are computed by solving a system of nonlinear equations numerically and displayed graphically. Pressure rise, mechanical efficiency and trapping phenomena are also evaluated by varying the involved parameters. The results show that peristaltic pumping may alter by applying external electric fields. The present study generalizes many of the available studies on multi-phase peristaltic transport. This theoretical analysis may be applicable to electro-kinetic multilayered blood transport in microvascular system. It may also be helpful for designing and developing of biochips and other electro-osmotic biological micro-electromechanical devices.

Analytical study of micropolar fluid flow through porous layered microvessels with heat transfer approach

The transport theory of three-layered fluid flow and heat transfer aspects in porous layered tubes is considered in the present work to study the flow of microlevel fluids through porous layered microvessels. The transportation of energy through porous media and the applications associated with heat transfer in physiological aspects are analyzed. Blood is considered as three-layered liquid model in which the core and peripheral regions of the tube are occupied by micropolar and Newtonian fluids, respectively. A thin glycocalyx layer near the wall is considered that represents the porous region due to the deposition of carbohydrates, fibrous tissues or macromolecules inside the interior surface of the tube wall. Analytical expressions for the various flow quantities like velocity, temperature profile, flow rate, flow impedance and additional quantities like hematocrit and Fahraeus effect are obtained and the impacts of various parameters like heat transfer and porous layer parameters are analyzed pictorially for two different formulations (no-spin and no-couple stress conditions). A noteworthy observation is that the impact of no-couple stress condition is relatively more significant in flow quantities, hematocrit and Fahraeus effect than the no-spin condition at the interface. The motivational work of the blood flow through porous blood vessels by selecting the micropolar fluid for the microlevel effects of the molecules may leave a significant impact in the treatment of the various diseases in medical sciences.

CIRCULACIÓN OCEÁNICA DEL GOLFO DE URABÁ USANDO CAMPOS DE VIENTO DE ALTA RESOLUCIÓN TEMPORAL

Los procesos físicos que tienen mayor influencia en la dinámica oceánica al interior del golfo de Urabá son las descargas fluviales, los viento y las diferencias de densidad. La influencia del río Atrato en la circulación se ve afectada por la dinámica de los vientos que se rigen por la variación latitudinal de la Zona de Convergencia Intertropical, que genera dos épocas climáticas: época seca (diciembre a marzo) y época lluviosa (mayo a noviembre). La circulación oceánica del golfo de Urabá (GU) tiene impactos en sus ecosistemas marino-costeros, en la calidad de las aguas, e incluso en las actividades económicas de la zona. Con el propósito de avanzar en el conocimiento hidrodinámico del golfo de Urabá (GU), en este trabajo se analizó la modulación que producen los vientos sobre las corrientes en esta zona para la escala intra e interanual. Se utilizó el modelo numérico de circulación oceánica regional CROCO, bajo un forzamiento atmosférico de tiempo variable durante el periodo 2010-2015. Se encontró que, teniendo en cuenta solo el forzamiento del viento, el golfo puede dividirse dinámicamente en tres zonas (norte, centro y sur). Los resultados sugieren que la modulación del viento a la circulación del golfo de Urabá, confina las aguas dulces en el sur cuando su dirección (norte-sur) es contraria al flujo del río Atrato. En este escenario se encontraron las menores magnitudes de la corriente superficial, principalmente para la zona centro y sur, con valores promedio de 0.1 m/s. En este caso, el mar Caribe tiene una mayor influencia sobre la circulación en su parte profunda. Cuando el esfuerzo del viento está en la misma dirección del flujo del río Atrato (sur-norte), las corrientes superficiales siguen esa dirección, con aguas saliendo del golfo por su costado este (escenario común). Se encontró, además, que la descarga fluvial de los ríos al interior del golfo tiene influencia en gran parte de su área aproximadamente hasta los 3 m de profundidad. Entre los 4 m y 8 m se encuentra la haloclína, formada por la transición de aguas dulces a saladas. En esta profundidad se forma un corte de velocidades, que permite la formación de remolinos en las aguas profundas del golfo. Finalmente, a partir de los 10 m es notoria la influencia de algunos sistemas de corrientes del mar Caribe en la circulación del golfo. Cabe resaltar que en bahía Colombia se encontró un flujo de tres capas con un corte de velocidades casi permanente, dando lugar a una mayor circulación de las masas de agua en JAS y un mayor intercambio de flujo en la zona central del GU. Por último, los resultados sugieren que en el periodo de tiempo analizado las fases del ENSO no modulan la variación atmosférica y oceánica al interior del golfo de Urabá, debido a que en esta zona dominan los fenómenos locales. En trabajos futuros se recomienda emplear bases de datos de viento con una resolución espacial fina y tener en cuenta el aporte de otros afluentes importantes como el río León.

Strongly nonlinear effects on internal solitary waves in three-layer flows

We consider a strongly nonlinear long wave model for large amplitude internal waves in a three-layer flow between two rigid boundaries. The model extends the two-layer Miyata–Choi–Camassa (MCC) model (Miyata, Proceedings of the IUTAM Symposium on Nonlinear Water Waves, eds. H. Horikawa & H. Maruo, 1988, pp. 399–406; Choi & Camassa, J. Fluid Mech., vol. 396, 1999, pp. 1–36) and is able to describe the propagation of long internal waves of both the first and second baroclinic modes. Solitary-wave solutions of the model are shown to be governed by a Hamiltonian system with two degrees of freedom. Emphasis is given to the solitary waves of the second baroclinic mode (mode 2) and their strongly nonlinear characteristics that fail to be captured by weakly nonlinear models. In certain asymptotic limits relevant to oceanic applications and previous laboratory experiments, it is shown that large amplitude mode-2 waves with single-hump profiles can be described by the solitary-wave solutions of the MCC model, originally developed for mode-1 waves in a two-layer system. In other cases, however, e.g. when the density stratification is weak and the density transition layer is thin, the richness of the dynamical system with two degrees of freedom becomes apparent and new classes of mode-2 solitary-wave solutions of large amplitudes, characterized by multi-humped wave profiles, can be found. In contrast with the classical solitary-wave solutions described by the MCC equation, such multi-humped solutions cannot exist for a continuum set of wave speeds for a given layer configuration. Our analytical predictions based on asymptotic theory are then corroborated by a numerical study of the original Hamiltonian system.

Asymptotic Study of Instability in a Three-Layer Stokes Flow with an Inhomogeneous Layer Thickness. Modeling of the Folding Process

Zero-Reynolds-number instability in a three-layer Stokes flow of viscous fluid with an inhomogeneous layer thickness in a two-dimensional region with a free boundary is investigated. The method of multiple scales is applied for constructing an asymptotic expansion of the solution of the boundary-value problem for the Stokes equations. The stability of the system of first-approximation equations is analyzed using the Fourier method, and it is concluded that the most significant increase in the zero-Reynolds-number instability occurs in a region of waves whose lengths are comparable with the thickness of the middle layer. In contrast to the case of a constant layer thickness, the instability parameters are variables. The mechanism of formation of geological folds is studied.

Evolution of the Horizontal Mixing Layer In Shallow Water

Horizontal shear motion of a homogeneous fluid in an open channel is considered in the approximation of the shallow water theory. The main attention is paid to studying the mixing process induced by the development of the Kelvin–Helmholtz instability and by the action of bottom friction. Based on a three-layer flow pattern, an averaged one-dimensional model of formation and evolution of the horizontal mixing layer is derived with allowance for friction. Steady solutions of the equations of motion are constructed, and the problem of the mixing layer structure is solved. The bottom friction produces a stabilizing effect and reduces the growth of the mixing layer. Verification of the proposed one-dimensional model is performed through comparisons with available experimental data and with the numerical solution of the two-dimensional equations of the shallow water theory.

Experimental study of two-phase oil – Polymer flow in horizontal flow path

Two-phase flow inside the oil and gas wells and flow path lines is a usual occurrence in petroleum and petrochemical studies. Due to its complexity, flow transfer parameters such as hold up and pressure drop and their dependency on the flow regime maps are not well understood yet. This study is aimed at analyzing holdup for oil- water system and evaluation of this parameter by means of Image processing under different available flow regime conditions. In addition, different oil-polymer systems have been studied to evaluate the impact of polymer concentration on transport criteria. The experimental setup used for this study is consisted of a 12 m long Plexiglas pipe with an inner diameter of 30 mm. The results revealed that the only polymer solutions with polymer concentration below than 333 ppm behave as Newtonian fluids. The results showed that low concentration of polymer solution acts as drag reducing agent and reduces the amount of pressure gradient in comparison with oil – water system. Furthermore, the change in flow pattern map between oil-low concentration polymer solution and oil-high concentration polymer solution systems have been analyzed. The results showed that high concentration polymer solution not only leads to higher degrees of pressure drop but also impacts the flow pattern map and more specifically the Three-Layer flow regime cannot be observed in such flow systems. Therefore, a generalized model has been developed to define the flow regime map and the transition criteria between different flow regimes as well as pressure drop and hold up for oil – polymer systems.

Indicators for contaminant transport in a three-layer wetland with wind

Abstract The effect of global climate change is increasing and it can influence agriculture in many ways, especially in that it makes great threaten on agricultural water resources. Since agricultural water supply is a key issue for agricultural production, indicators for contaminant transport in wetlands should be considered in order to solve agricultural water pollution and promote water protection. In this paper, we analyze the environmental dispersion in a typical three-layer wetland flows with the effect of wind taken into account. The analytical solution for velocity distribution is rigorously derived and the dependence of characteristic parameters on averaged dimensionless velocity is recorded. The asymptotic analysis theory of Gill is employed to measure dispersivity for natural wetland flows with a commonly high Peclet number. Both velocity and environmental dispersion are significantly influenced by wind, in terms of its direction and the magnitude of force. The effects of hydraulics and ecological degradation are considered to obtain the analytical solution for the mean concentration and maximal critical length of the region influenced by the process of contaminant transport.