Narrow Two-dimensional Channel Research Articles

Local description of foam flow, deformation and pressure drop in narrow constricted channels

We study in extensive detail the flow of dry and wet gas-liquid foams through a narrow two-dimensional channel comprising a complex constriction. The effects of constriction profile and size of aperture, foam flowrate, liquid holdup and liquid viscosity are experimentally investigated and a sophisticated image analysis procedure is developed to extract local fields of foam flow and deformation. Foam dynamics are scrutinised and interpreted in terms of local velocity distribution, elastic strain (texture tensor), plastic deformation (T1 events) and pressure drop. Important foam transformations occur in the vicinity of the constriction. For the first time, the relationship between pressure drop, flowrate and size of constriction aperture is investigated.

Comparative Study of Heat Transfer Performance and Visualization Images of Superfluid Helium Boiling in Narrow Two-dimensional channel

In a narrow channel, boiling heat transfer in He II is much different from that in the case of an open bath. Even under saturated pressure condition, rapid temperature rise due to the onset of film boiling is not seen when the temperature reaches the lambda temperature, but only the temperature oscillation is detected. The behaviour of this state looks like the nucleate boiling, though it is known the steady nucleate boiling state is absent in He II in open bath. The high heat transfer coefficient in this quasi-nucleation boiling state above the lambda temperature suggests the range where this advantage in heat transfer appears is wider than that based on simple prediction of He II heat transfer. The appearance of metastable states of superheated He II and superheated He I should be considered in the case of a narrow channel. In this study, the visualization experiment result using a transparent heater and the transient temperature measurement data on a copper heater surface had been compared with each other. In the case of rather high heat flux, several film boiling modes were observed in a narrow two-dimensional channel. The peak of the heat transfer coefficient appeared around the lambda pressure. In the case of low heat flux, the heat transfer coefficient variation with the pressure shows sudden rise around the lambda point. The heat transfer coefficient under nearly saturated pressure condition below the lambda pressure is larger than that above the lambda pressure.

Disruption and recovery of reaction–diffusion wavefronts colliding with obstacles

We study the damage to and restoration of planar reaction–diffusion wavefronts colliding with convex obstacles in narrow two-dimensional channels using finite-difference numerical integration of the Tyson–Fife reduction of the Oregonator model of the Belousov–Zhabotinsky reaction. We characterize the obstacles’ effects on the wavefront shape by plotting wavefront delay versus time. Due to the curvature dependent wavefront velocities, the initial planar wavefront (or iso-concentration line) is restored after a relaxation period that can be characterized by a power-law. We find that recovery times are insensitive to obstacle concatenation or to the upstream obstacle shape but are sensitive to the downstream shape, with a vertical back side causing the longest disruption. Delays vary cyclically with obstacle orientations. The relaxation power-laws confirm that larger obstacles produce larger wavefront delays and longer recovery times, and for a given area larger obstacle width-to-length ratios produce longer delays. Possible applications include elucidating the effect of inhomogeneities on wavefront recovery in cardiac tissue.

On the boundary layer structure near a highly permeable porous interface

The method of matched asymptotic expansions is used to study the canonical problem of steady laminar flow through a narrow two-dimensional channel blocked by a tight-fitting finite-length highly permeable porous obstacle. We investigate the behaviour of the local flow close to the interface between the single-phase and porous regions (governed by the incompressible Navier–Stokes and Darcy flow equations, respectively). We solve for the flow in these inner regions in the limits of low and high Reynolds number, facilitating an understanding of the nature of the transition from Poiseuille to plug to Poiseuille flow in each of these limits. Significant analytical progress is made in the high Reynolds number limit, and we explore in detail the rich boundary layer structure that occurs. We derive general results for the interfacial stress and for the conditions that couple the flow in the outer regions away from the interface. We consider the three-dimensional generalization to unsteady laminar flow through and around a tight-fitting highly permeable cylindrical porous obstacle within a Hele-Shaw cell. For the high Reynolds number limit, we give the coupling conditions and interfacial stress in terms of the outer flow variables, allowing information from a nonlinear three-dimensional problem to be obtained by solving a linear two-dimensional problem. Finally, we illustrate the utility of our analysis by considering the specific example of time-dependent forced far-field flow in a Hele-Shaw cell containing a porous cylinder with a circular cross-section. We determine the internal stress within the porous obstacle, which is key for tissue engineering applications, and the interfacial stress on the boundary of the porous obstacle, which has applications to biofilm erosion. In the high Reynolds number limit, we demonstrate that the fluid inertia can result in the cylinder experiencing a time-independent net force, even when the far-field forcing is periodic with zero mean.

Giant negative mobility of Janus particles in a corrugated channel.

We numerically simulate the transport of elliptic Janus particles along narrow two-dimensional channels with reflecting walls. The self-propulsion velocity of the particle is oriented along either its major (prolate) or minor axis (oblate). In smooth channels, we observe long diffusion transients: ballistic for prolate particles and zero diffusion for oblate particles. Placed in a rough channel, prolate particles tend to drift against an applied drive by tumbling over the wall protrusions; for appropriate aspect ratios, the modulus of their negative mobility grows exceedingly large (giant negative mobility). This suggests that a small external drive suffices to efficiently direct self-propulsion of rod-like Janus particles in rough channels.

Effect of Superheating on Heat Transfer from a Good Thermal Conductorin a Two-dimensional Channel to He II below the λ-point Pressure

Heat transfer characteristics in He II have been investigated in relation to superheating. When a good thermal conductor in a narrow two-dimensional channel is heated above the critical heat flux of the λ-transition, superheated He I nucleates in the hottest area of the conductor covered with superheated He II. The spread of superheated He I, which has low thermal conductivity, forms an intermediate state in which superheated He I coexists with superheated He II. Superheated He I together with superheated He II is apparently stabilized since part of the heat cut off by superheated He I tends to flow in the conductor. Higher heat input turns the intermediate state into a mixed state where superheating and boiling alternate irregularly. (Translation of the article originally published in Cryogenics 49 (2009) 700-706)

Diffusion in a two-dimensional channel with curved midline and varying width: Reduction to an effective one-dimensional description

Diffusion in a narrow two-dimensional channel with a midline that need not be straight and a width that may vary is reduced to an effective one-dimensional equation of motion. This equation takes the form of the Fick-Jacobs equation with a spatially varying effective diffusivity. The effective diffusivity includes a contribution that comes from the slope of the midline as well as the usual term stemming from variations in the channel width along the length of the channel. Our derivation of our equation of motion is completely rigorous and is based on an asymptotic expansion in a small dimensionless parameter that characterizes the channel width. For a channel that has a straight midline or wall, our equation of motion reduces to Zwanzig's equation [R. Zwanzig, J. Phys. Chem. 96, 3926 (1992)]. Our derivation therefore provides a rigorous proof of the validity of the latter equation. Finally, the equation of motion is solved analytically for channels with curved midline and constant width.

Effect of superheating on heat transfer from a good thermal conductor in a two-dimensional channel to He II below the λ-point pressure

Heat transfer characteristics in He II have been investigated in relation to superheating. When a good thermal conductor in a narrow two-dimensional channel is heated above the critical heat flux of the λ-transition, superheated He I nucleates in the hottest area of the conductor covered with superheated He II. The spread of superheated He I, which has a low thermal conductivity, forms an intermediate state in which superheated He I coexists with superheated He II. Superheated He I together with superheated He II is apparently stabilized since part of the heat cut off by superheated He I tends to flow in the conductor. Higher heat input turns the intermediate state into a mixed state where superheating and boiling alternate irregularly.

Projection of two-dimensional diffusion in a narrow channel onto the longitudinal dimension

Diffusion in a narrow two-dimensional channel of width A(x), depending on the longitudinal coordinate x, is the object of our study. We show how the 2+1 dimensional diffusion equation can be projected onto a 1+1 dimensional one, governing corresponding one-dimensional density, in a steady-state approximation. Then we demonstrate the method on a nontrivial exactly solvable case for A(x)=x and discuss projection of the initial condition.

Molecular-dynamics simulation of compressible fluid flow in two-dimensional channels.

We study compressible fluid flow in narrow two-dimensional channels using a novel molecular dynamics simulation method. In the simulation area, an upstream source is maintained at constant density and temperature while a downstream reservoir is kept at vacuum. The channel is sufficiently long in the direction of the flow that the finite length has little effect on the properties of the fluid in the central region. The simulated system is represented by an efficient data structure, whose internal elements are created and manipulated dynamically in a layered fashion. Consequently the code is highly efficient and manifests completely linear performance in simulations of large systems. We obtain the steady-state velocity, temperature, and density distributions in the system. The velocity distribution across the channel is very nearly a quadratic function of the distance from the center of the channel and reveals velocity slip at the boundaries; the temperature distribution is only approximately a quartic function of this distance from the center to the channel. The density distribution across the channel is non-uniform. We attribute this non-uniformity to the relatively high Mach number, approximately 0.5, in the fluid flow. An equation for the density distribution based on simple compressibility arguments is proposed; its predictions agree well with the simulation results. Validity of the concept of local dynamic temperature and the variation of the temperature along the channel are discussed.

Size effect in the longitudinal hopping conduction of a narrow two-dimensional channel.

The variable-range-hopping conduction of a narrow two-dimensional (2D) strip is studied analytically. The gradual transition from 2D to 1D behavior of conductivity with the narrowing of the strip is traced. It is shown that, in the wide range of the width of the strip, the intermediate regime of conduction takes place. In this regime the passage of current through a typical cross section is determined by the subnetwork of the 2D infinite cluster, but the total resistance is dominated by ``cuts''---sparse high-Ohmic regions in which the subnetwork is broken. These cuts are responsible for the size effect---an exponentially strong dependence of the resistance on the width. They are also responsible for the fluctuations of the resistance of a sufficiently short strip with a change of the Fermi-level position. The amplitude of the fluctuations as a function of temperature and the parameters of the strip is evaluated.

Magnetic depopulation of electronic subbands in a narrow two-dimensional channel

The subband depopulation due to a magnetic field in a quasi-one-dimensional GaAs-AlGaAs heterostructure system is examined in the framework of an infinite box potential. The results are compared with calculations using a parabolic confinement and experimental results from Shubnikov-de Haas oscillations. The two models give good agreement with the experimental values in different regions of the channel widths.

Flows of red blood cell suspensions through narrow two-dimensional channels.

Apparent viscosity and mean channel hematocrits have been measured at various shear rates and feed hematocrits for red blood cell (RBC) suspensions flowing in two-dimensional channels. Three types of RBC were used in the suspensions : normal, partially hardened by heating at 50 degrees C and completely hardened by glutaraldehyde fixation. Channel height was varied from 20 to 200 mu and feed hematocrit from 5 to 55%. Measurements show that RBC deformability plays a dominant role in narrow channels and viscosity increases rapidly with decreasing cell deformability. Like in narrow tubes the apparent viscosity as well as the mean channel hematocrits decrease as the channel height is reduced. However the apparent viscosity in a channel remains slightly higher than the viscosity in a tube of diameter equal to the channel height. These results are consistent with the existence of a cell-depleted layer near the channel walls.