Multilayer Flow Research Articles

직사각형 단면을 갖는 미세채널에서 완전 발달된 다층유동에 관한 해석

An analytical solution for a vertically stratified viscous flow in a microchannel with a rectangular cross-section is constructed, assuming fully developed laminar flow where the interfaces between the fluid layers are flat. Although the solution is for n-layer flow, restricted results to symmetrical three-layer flow are presented to investigate the effects of the viscosity and thickness ratios of the fluid layers and the aspect ratio of the microchannel on the flow field. Relations between the flow rate and thickness ratios of the fluid layers with varying viscosity distributions are found, considering the cross -sectional velocity profiles which vary noticeably with the three parameters and differ significantly from the velocity profiles of the flow between infinite parallel plates. Interfacial instability induced by the viscosity stratification in the microchannel is discussed referring to previous studies on the instability analysis for plane multilayer flow. Exact solution derived in the present study can be used for examining a diffusion process and three -dimensional stability analysis. More works are needed to formulate the equations including the effects of interfacial` tension between immiscible liquids and surface wettability which are important in microscale transport phenomena.

Interface development and encapsulation in simultaneous coinjection molding. I. Two‐dimensional modeling and formulation

AbstractIn the coinjection‐molding process two polymers are injected into a mold sequentially or simultaneously. During the process one polymer melt forms the skin and the other forms the core, resulting in an encapsulated sandwich structure. In an attempt to develop a process model and simulation of simultaneous coinjection molding, along with the interface treatment a theoretical approach, physical model, and numerical algorithm were formulated based on the Hele–Shaw approximation. A detailed picture of the dynamics and kinematics of the interface evolution, providing a description of the multilayer flow and interface development during the multicomponent injection‐molding process, information typically lacking in the available literature, is systematically presented. Based on the developed numerical simulation code, the moldability of various material combinations can be evaluated, which is required for process optimization. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 2300–2309, 2003

Interface development and encapsulation in simultaneous coinjection molding of disk. II. Two‐dimensional simulation and experiment

AbstractTwo‐dimensional simulation and experimental studies of flow‐rate‐controlled coinjection molding were carried out. Skin polymer was injected first, and then both skin and core polymers were injected simultaneously into a center‐gated disk cavity through a two‐channel nozzle to obtain an encapsulated sandwich structure. The physical modeling and simulation developed, reported in Part I of this series, were based on the Hele–Shaw approximation and the kinematics of the interface to describe the multilayer flow, and the interface development was used to predict the skin/core distribution in the moldings. The effects of rheological properties and processing conditions on the material distribution, penetration behavior, and breakthrough phenomena were investigated. The predicted and measured results were found to be in a good agreement. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 2310–2318, 2003

Estimation of multi-layer pebble flow in pebble divertor

Pebble divertor concept is proposed for high-power density steady state fusion reactor. In this system, the dropping pebbles receive the divertor plasma and the pebbles are circulated to be cooled down. In this report, the total storage amount of pebble in the circulation system is estimated. That total amount depends on the pebble cooling time, which is the duration that the temperature of the pebbles after irradiation is recovered to the initial temperature before irradiation. The pebble cooling time is changed by how the pebbles are cooled. In this study, the pebbles are considered to be laid in the pebble cooling bed for the radiation sink and to be cooled at a concerned temperature. From the calculation, the desired pebble flow rate has been found to be 30 kg/s/m in toroidal direction at the slit width of 2.5 cm. The pebble cooling time becomes shorter when the pebble cooling bed is thinner or the initial temperature of pebbles before the irradiation is higher so that the storage amount of the pebble in the circulation system will be suppressed to small value.

Chemicofunctional membrane for integrated chemical processes on a microchip.

Here we report a design and synthesis of a chemically functional polymer membrane by an interfacial polycondensation reaction and multilayer flow inside a microchannel. Single and parallel dual-membrane structures are successfully prepared by using organic/aqueous two-layer flow and organic/aqueous/organic three-layer flow inside the microchannel followed by an interfacial polycondensation reaction. By using the inner-channel membrane, permeation of ammonia species through the inner-channel membrane is successfully achieved. Furthermore, horseradish peroxidase is immobilized on one side of the membrane surface to integrate the chemical transform function onto the inner-channel membrane. Here substrate permeation through the membrane and subsequent chemical transformation at the membrane surface are realized. The polymer membrane prepared inside the microchannel has an important role in ensuring stable contact of different phases such as gas/liquid or liquid/ liquid and the permeation of chemical species through the membrane. Furthermore, membrane surface modification chemistry allows chemical transformation of permeated chemical species. These methods are expected to lead to development of complicated and sophisticated chemical systems involving membrane permeation and chemical reactions.

The instability mechanism of single and multilayer Newtonian and viscoelastic flows down an inclined plane

The instability mechanism of single and multilayer flow of Newtonian and viscoelastic fluids down an inclined plane has been examined based on a rigorous energy analysis as well as careful examination of the eigenfunctions. These analyses demonstrate that the free surface instability in single and multilayer flows in the limit of longwave disturbances (i.e., the most dangerous disturbances) arise due to the perturbation shear stresses at the free surface. Specifically, for viscoelastic flows, the elastic forces are destabilizing and the main driving force for the instability is the coupling between the base flow and the perturbation velocity and stresses and their gradient at the free surface. For Newtonian flows at finite Re, the driving force for the interfacial instability in the limit of longwaves depends on the placement of the less viscous fluid. If the less viscous fluid is adjacent to the solid surface then the main driving force for the instability is interfacial friction, otherwise the bulk contribution of Reynolds stresses drives the instability. For viscoelastic fluids in the limit of vanishingly small Re, the driving force for the instability is the coupling of the base flow and perturbation velocity and stresses and their gradients across the interface. In the limit of shortwaves the interfacial stability mechanism of flow down inclined plane is the same as plane Poiseuille flows (Ganpule and Khomami 1998, 1999a, b).

Super-stable parallel flows of multiple visco-plastic fluids

We consider the stability of a multi-layer plane Poiseuille flow of two Bingham fluids. It is shown that this two-fluid flow is frequently more stable than the equivalent flow of either fluid alone. This phenomenon of super-stability results only when the yield stress of the fluid next to the channel wall is larger than that of the fluid in the centre of the channel, which need not have a yield stress. Our result is in direct contrast to the stability of analogous flows of purely viscous generalised Newtonian fluids, for which short wavelength interfacial instabilities can be found at relatively low Reynolds numbers. The results imply the existence of parameter regimes where visco-plastic lubrication is possible, permitting transport of an inelastic generalised Newtonian fluid in the centre of a channel, lubricated at the walls by a visco-plastic fluid, travelling in a stable laminar flow at higher flow rates than would be possible for the single fluid alone.

Integrated multilayer flow system on a microchip.

We utilized microchip technology and found that the multilayer flow of liquids can be formed in microchannels. Liquid/liquid interfaces were formed parallel to the side wall of the microchannels, because the surface tension and friction force are stronger than the force of gravity. A water/ethylacetate/water interface was formed in a 70-microm-wide and 30-microm-deep channel. The interface was observed to be quite stable and to be maintained for a distance of more than 18 cm. As an example of a multilayer flow application, we demonstrated the liquid/liquid extraction of Co-dimethylaminophenol complex in a microchannel. The solvent-extraction process of the complex into m-xylene in the multilayer flow was found to reach equilibrium in 4 s, while it took 60 s in a simple two-phase extraction.

ON THE CHANGE OF SALT WATER INTRUSION IN THE ESTUARY CAUSED BY SEA LEVEL RISE

The characteristic of salt-water intrusion will change by sea level rise. This phenomenon could result in salt damage. So, it is important to clarify characteristics of salt-water movement to predict the intrusion. In this paper, it is attempted to represent all the mixing conditions of salt-water intrusion in the estuary by one model, which is based on a multi-layer flow of the one dimension. Toverify the applicability of the model, numerical calculation is performed by using the data from Egawa and Murasaki Rivers. Results indicate that the model would be applicable to all the mixing conditions of salt-water intrusion in the estuary. And the salt water intrusion affected by sea level rise is simulated.

共押出成形プロセスの数値シミュレーション

Numerical simulations of the coextrusion process used in producing multi-layer plastics products have been carried out. The isothermal multi-layer axisymmetric coextrusion flow was analyzed with a streamline finite element method. Extrudate swell from an annular die was predicted and the position of the multi-layer fluid interface was also determined. The K-BKZ integral type viscoelastic constitutive equation was employed to provide good descriptions of rheological properties for polymer melts. A double nodes technique at the interfaces was used to capture pressure discontinuity and to ensure continuity of total stress and velocity. Numerical case studies were performed to examine the behaviors of two or three layers extruded from a straight type annular die. Numerical results show that even at the same flow rate, variations of the layer configurations produce changes in the extrudate swell. For Newtonian fluids, the less viscous outer layer material reduces the extrudate swell relative to the mono-layer configuration. On the other hand, for viscoelastic fluids, the more elastic outer layer material enhances the extrudate swell even if the outer layer is less viscous than the inner layer. These are in general agreement with the numerical results found in the literatures. The numerical predictions for the extrudate swell of a practical problem were quantitatively examined with experimental data.

Experimental studies of interfacial instabilities in multilayer pressure-driven flow of polymeric melts

Experimental studies of interfacial instabilities in multilayer pressure-driven flow of polymeric melts

Experimental studies of interfacial instabilities in multilayer pressure-driven flow of polymeric melts

The interfacial deformation and stability of two-(A-B) as well as three-layer symmetric (A-B-A) and asymmetric (A-B-C) pressure-driven flow of viscoelastic fluids has been investigated. Flow visualization in conjunction with digital image processing has been used to observe and measure the rate of encapsulation and interfacial stability/instability of the flow. Specifically, the encapsulation behavior as well as stability/instability of the interface and the corresponding growth or decay rate of disturbances as a function of various important parameters, namely, number of layers and their arrangement, layer depth ratio, viscosity and elasticity ratio as well as disturbance frequency, have been investigated. Based on these experiments, we have shown that the encapsulation phenomena occurs irrespective of the stability/instability of the interface and in cases when both encapsulation and instability occur simultaneously their coupling leads to highly complex and three-dimensional interfacial wave patterns. Moreover, it has been shown that the simple notion that less viscous fluids encapsulate more viscous fluids is incorrect and depending on the wetting properties of the fluid as well as their first and second normal stresses the reverse could occur. Additionally, in two- and three-layer flows it has been shown that by placing a thin, less viscous layer adjacent to the wall longwave disturbances can be stabilized while short and intermediate wavelength disturbances are stabilized when the more elastic fluid is the majority component. Furthermore, in three-layer flows it has been demonstrated that in the linear instability regime no dynamic interaction between the two interfaces is possible for short and intermediate wavenumber disturbances. However, in the nonlinear stability regime dynamic interactions between interfaces have been observed in this range of disturbance wavenumbers leading to highly chaotic flows. Finally, in the parameter space of this study no subcritical bifurcations were observed while supercritical bifurcations resulting in waves with a pointed front and a gradual tail were observed.

Self-similar multi-layer exchange flow through a contraction

The multi-layer exchange equations for gravitationally driven flows between two basins with stable Boussinesq type of stratification in discrete layers, specified far upstream on either side of a connecting strait, result in a hydraulic control condition that must be satisfied at the narrowest part of the contraction, the control point. If one stagnant layer is present at the control point, the control condition that applies to all layers collectively may be separated into two such conditions that apply independently to two groups of layers going in opposite directions separated by the stagnant layer. Such bidirectional flow regimes exist if the structure of the prespecified density profiles permits each of the opposing groups to vertically reduce their thickness by the ratio 2/3 relative to their upstream thicknesses, leaving space for the stagnant layer to protrude through the contraction. Under these restrictions, the bidirectional flow is controlled by the fastest propagating wave mode and the stationary solution then relies on the superposition of two previously known unidirectional self-similar flow regimes that are completely decoupled. Techniques for their numerical computation are presented. The transition into loosely coupled and fully coupled flow is discussed. The decoupling principle also applies when several non-adjacent stagnant layers are simultaneously present at control in which case multiple groups of decoupled layers flow in alternating directions.

Two‐dimensional multilayer coextrusion flow in a flat coat‐hanger die. Part 2: Experiments and theoretical validation

AbstractIn a previous paper (1), a two‐dimensional computation model for multilayer flows in coat‐hanger dies was proposed. It was based on lubrication approximation theory and enabled us to obtain the pressure field, the streamlines, and the interface positions in the whole die. The present paper is aimed to present experimental results obtained on an industrial line for a three‐layer configuration and to compare the results to the theoretical computation. The order of magnitude of pressure drops, flow rates, and interface positions were correctly predicted by the model. Some remaining discrepancies may be explained by the isothermal assumption and the lack of encapsulation mechanism in the computation.

Model Evaluation of Adsorbate Transport in Mesoporous Media in the Multilayer Adsorption Region

A theoretical description of multilayer adsorbate film flow, consistent with the simple multilayer adsorption theory in common use, is derived on the basis of the simple pore model previously used by Flood et al. (Can. J. Chem. 1952, 30, 389). The resulting expression clearly supersedes the earlier one of Flood et al. (Can. J. Chem. 1952, 30, 389), both on theoretical grounds and from the point of view of successful interpretation of the surface flow behavior exhibited by a typical mesoporous adsorbent/permeating vapor system in the multilayer adsorption/condensation region.

Multilayer rheology: A comparison of experimental data with modeling of multilayer shear flow

AbstractThe rheological behavior of multilayer polyjeric structures has been investigated Measurements of the bulk viscoelastic properties via small‐amplitude oscilatory rheometry indicated that the shear viscosity is independent of both the numbe of layers (83 vs. 165) and the composition (30/70, 50/50, and 70/30 PC/PMMA by weight) within the limits of the data obtained. It is also apparent tha tthe shear viscosity is influenced strongly by the skin layer material. In additon, a model has been developed tha tcan be used to proedict the shear viscosity and shear stress ofa multilayer structure experiencing shear flow. The model predicts tha thte shear viscosity of a multilayer structure should be independent of the number of layers and strongly dependent on the material in the skin layer. These predictions are in agreement with experimental data.

Explosive resonant interaction of baroclinic Rossby waves and stability of multilayer quasi-geostrophic flow

The amplitude equations governing the nonlinear interaction among normal modes are derived for a multilayer quasi-geostrophic channel. The set of normal modes can represent any wavy disturbance to a parallel shear flow, which may be stable or unstable. Orthogonality in the sense of pseudomomentum or pseudoenergy is used to obtain the amplitude equations in a direct fashion, and pseudoenergy and pseudomomentum conservation laws permit the properties of the interaction coefficients to be deduced. Particular attention is paid to triads exhibiting explosive resonant interaction, as they lead to nonlinear instability of the basic flow. The relationship between this mechanism and the most recently discovered nonlinear stability conditions is discussed.Situations in which the basic velocity is constant in each layer are treated in detail. A particular formulation of the stability condition is given that emphasizes the close connection between linear and nonlinear stability. It is established that this stability condition is also a necessary condition: when it is not satisfied, and when the flow is linearly stable, explosive resonant interaction of baroclinic Rossby waves acts as a destabilizing mechanism. Two- and three-layer models are specifically considered; their stability features are presented in the form of stability diagrams, and interaction coefficients are calculated in particular cases.

An exact recursion relation solution for the steady-state surface temperature of a general multilayer structure

A recursion relation technique has been used in the past to determine the surface potential from the multilayer electrical Laplace equation. This has provided for a vastly simplified evaluation of the electrical spreading resistance and four-probe resistance. The isomorphism of the multilayer Laplace equation and the multilayer steady-state heat flow equation suggests the possibility of developing a recursion relation applicable to the multilayer thermal problem. This recursive technique is developed and is shown to provide the surface temperature of the multilayer steady-state heat flow equation. For the three-layer case, the thermal recursion relation readily yields the surface results,which are identical with those presented by Kokkas and the TXYZ thermal code. This recursive technique can be used with any number of layers while incurring only a small increase in computation time for each added layer. For the case of complete, uniform top surface coverage by a heat source, the technique gives rise to the generalized one-dimensional thermal resistance result. An example of the use of the new recursive method is provided by the preliminary calculations of the surface temperature of a buried oxide (SOI, SIMOX) structure containing several thicknesses of the surface silicon layers. This new technique should prove useful in the investigation and understanding of the steady-state thermal response of modern multilayer microelectronic structures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Longitudinal solute transport in the Upper Clyde Estuary, Scotland

The paper discusses vertical profiles of salinity and longitudinal velocity observed in an 11-km study reach of the Upper Clyde Estuary in Scotland. Corresponding tide level measurements and calculated are mean velocities are also presented. The data indicate that the upper estuary was highly stratified during two survey periods and was almost well mixed during a third. This is broadly consistent with an earlier classification of the estuary as a type 2b within the scheme proposed by Hansen and Rattray (1966). When the upper estuary is stratified, the salinity data demonstrate the existence of a classical multi-layer flow structure consisting of an approximately well-mixed upper layer, an approximately well-mixed lower layer, and an interfacial layer containing a large vertical density gradient. The velocity data, obtained from one of the stratified flow periods, reveal a commensurate velocity field with water moving seawards in the upper layer and landwards in the lower layer. As a consequence of strong vertical shear, longitudinal dispersion coefficients of the order of 1000 m 2/s are estimated. Since the data only describe conditions on a limited number of occasions, they are more illustrative of possible conditions than representative of typical ones. Nevertheless, they clearly indicate that water quality models of the upper estuary need to be capable of resolving the depth variation of environmental parameters.

Nonlinear stability of multilayer quasi-geostrophic flow

New nonlinear stability theorems are derived for disturbances to steady basic flows in the context of the multilayer quasi-geostrophic equations. These theorems are analogues of Arnol’d's second stability theorem, the latter applying to the two-dimensional Euler equations. Explicit upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy in terms of the initial disturbance fields. An important feature of the present analysis is that the disturbances are allowed to have non-zero circulation. While Arnol’d's stability method relies on the energy–Casimir invariant being sign-definite, the new criteria can be applied to cases where it is sign-indefinite because of the disturbance circulations. A version of Andrews’ theorem is established for this problem, and uniform potential vorticity flow is shown to be nonlinearly stable. The special case of two-layer flow is treated in detail, with particular attention paid to the Phillips model of baroclinic instability. It is found that the short-wave portion of the marginal stability curve found in linear theory is precisely captured by the new nonlinear stability criteria.