Channel Of Finite Width Research Articles

In biased and soft-walled channels: Insights into transport phenomena and damped modulation.

The motion of a particle along a channel of finite width is known to be affected by either the presence of energy barriers or changes in the bias forces along the channel direction. By using the lateral equilibrium hypothesis, we have successfully derived the effective diffusion coefficient for soft-walled channels, and the diffusion is found to be influenced by the curvature profile of the potential. A typical phenomenon of diffusion enhancement is observed under the appropriate parameter conditions. We first discovered an anomalous phenomenon of quasi-periodic enhancement of oscillations, which cannot be captured by the one-dimensional effective potential, under the combination of sub-Ohmic damping with two-dimensional restricted channels. We innovatively develop the effective potential and the formation mechanism of velocity variance under super-Ohmic and ballistic damping, and meanwhile, ergodicity is of concern. The theoretical framework of a ballistic system can be reinterpreted through the folding acceleration theory. This comprehensive analysis significantly enhances our understanding of diffusion processes in constrained geometries.

Transmission-type photonic doping for high-efficiency epsilon-near-zero supercoupling

Supercoupling effect is an exotic and counterintuitive physical phenomenon of epsilon-near-zero (ENZ) media, in which the light can be “squeezed” and tunneled through flexible channels substantially narrower than its wavelength. Theoretically, ENZ channels with infinitely small widths perform ideal supercoupling with full energy transmission and zero-phase advance. As a feasible solution to demonstrate ENZ supercoupling through a finite-width channel, photonic doping can assist the light in squeezing, but the resonant dopant introduces inevitable losses. Here, we propose an approach of transmission-type photonic doping to achieve proximate ideal ENZ supercoupling. In contrast to the conventional resonance-type photonic doping, our proposed transmission-type doping replaces high-quality-factor two-dimensional resonant doping modes with low-quality-factor one-dimensional modes, such that obviously high transmission efficiency and zero-phase advance in ENZ supercoupling is achieved and observed in experiments. Benefiting from the high-efficiency ENZ supercoupling, waveguides with near-total energy transmission can be engineered with arbitrary dimensions and shapes, serving as flexible power conduits in the paradigm of waveguide integrated circuits for future millimeter-wave and terahertz integrated circuit innovations.

Hall viscosity and hydrodynamic inverse Nernst effect in graphene

Motivated by Hall viscosity measurements in graphene sheets, we study hydrodynamic transport of electrons in a channel of finite width in external electric and magnetic fields. We consider electric charge densities varying from close to the Dirac point up to the Fermi-liquid regime. We find two competing contributions to the hydrodynamic Hall and inverse Nernst signals that originate from the Hall viscous and Lorentz forces. This competition leads to a nonlinear dependence of the full signals on the magnetic field and even a cancellation at different critical field values for both signals. In particular, the hydrodynamic inverse Nernst signal in the Fermi-liquid regime is dominated by the Hall viscous contribution. We further show that a finite channel width leads to a suppression of the Lorenz ratio, while the magnetic field enhances this ratio. All of these effects are predicted in parameter regimes accessible in experiments.

Enhanced diffusion in soft-walled channels with a periodically varying curvature.

The motion of particles along channels of finite width is known to be hindered by either the presence of energy barriers along the channel direction or by variations in the width of the channel in the transverse direction (rugged channel). Remarkably, when both features are present, they can interact to produce a counterintuitive result: adding energy barriers to a rugged channel can enhance the rate of diffusion along it. This is the result of competing energetic and entropic effects. Under the approximation of particles instantaneously in equilibrium in the transverse direction, one can tailor the energy barriers to the ruggedness to recover free diffusion. However, such fine-tuning and potentially restrictive approximations are not necessary to observe an enhanced rate of diffusion as we demonstrate by adding a range of (non-fine-tuned) energy barriers to a channel of sinusoidally varying curvature. Furthermore, this was observed to hold for systems with a finite characteristic timescale for motion in the transverse direction, thus, suggesting that the phenomenon lends itself to be exploited for practical applications.

Wave loads by an oscillating water column in presence of bottom-mounted obstacle in the channel of finite width

In the present study, we solved the problem of diffraction in water waves with consists of a pair of vertical cylinders in a channel having finite width. It consists of a partially submerged floating hollow cylinder place above a fixed coaxial bottom-mounted obstacle. With the help of matched eigenfunction expansion, channel multipole and variables separation methods, the analytical expression of potentials are obtained. Using these analytical expressions of diffracted velocity potentials, we can derive the expressions of exciting forces exerted by the cylinders. The influence of various parameters viz draft of the hollow cylinder, radius of the cylinders, the gap between the cylinders and the width of the channel walls on the exciting forces have been investigated. The results have been validated by comparing our results with available results. All the observations are validated through suitable graphs.

Analytical Solution of Surge Hydrodynamic Coefficients by an Offshore-structure Model in a Channel of Finite Width

Analytical Solution of Surge Hydrodynamic Coefficients by an Offshore-structure Model in a Channel of Finite Width

Strongly coupled electron fluids in the Poiseuille regime

In the context of describing electrons in solids as a fluid in the hydrodynamic regime, we consider a flow of electrons in a channel of finite width, i.e.~a Poiseuille flow. The electrons are accelerated by a constant electric field. We develop the appropriate relativistic hydrodynamic formalism in 2+1 dimensions and show that the fluid has a finite dc conductivity due to boundary-induced momentum relaxation, even in the absence of impurities. We use methods involving the AdS/CFT correspondence to examine the system in the strong-coupling regime. We calculate and study velocity profiles across the channel, from which we obtain the differential resistance $dV/dI$. We find that $dV/dI$ decreases with increasing current $I$ as expected for a Poiseuille flow, also at strong coupling and in the relativistic velocity regime. Moreover, we vary the coupling strength by varying $\eta/s$, the ratio of shear viscosity over entropy density. We find that $dV/dI$ decreases when the coupling is increased. We also find that strongly coupled fluids are more likely to become ultra-relativistic and turbulent. These conclusions are insensitive to the presence of impurities. In particular, we predict that in channels which are clearly in the hydrodynamic regime already at small currents, the DC channel resistance strongly depends on $\eta/s$.

Trapped-wave modes of bodies in channels

Trapped waves can exist in the presence of bodies in open water, and also in channels of finite width. Various examples are found for bodies that support trapped waves in channels, including floating and submerged bodies and bottom-mounted cylinders. Different types of trapping are considered where the body is fixed or free to move in response to the oscillatory pressure. In some cases both types are supported by the same body. In most cases for fixed bodies the fluid motion is antisymmetric about the centreline of the channel, but special body shapes exist where the trapped mode is asymmetric. For free bodies the trapping modes and body motions are symmetric about the centreline if the body is floating or antisymmetric if it is submerged.

Experiments on mixing in wakes in shallow water

We report on a series of laboratory experiments in which we investigate the mixing in a wake produced downstream of an obstacle in a uniform flow. The fluid is confined within a channel of finite width, and the water depth is small compared with the channel width. The mixing appears to be dominated by dispersion caused by the circulation of the eddies that are shed alternately from each side of the obstacle. However, due to bottom friction, these eddies gradually dissipate downstream. In turn, the intensity of the cross-stream mixing of the tracer decays in the downstream direction, limiting the cross-stream extent of the tracer. We present a time-averaged picture of the experiments which illustrates the deviation of the time-averaged flow in the wake relative to the uniform flow upstream. We then develop a time-averaged model for the flow, using mixing length theory to account for the cross-channel momentum transfer as an eddy viscosity $\unicode[STIX]{x1D706}_{1}ud$, where $2ud$ is the cross-channel integral of the perturbation in the along-channel speed associated with the wake. We also include a frictional stress to account for the bottom friction. The model predicts a similar pattern of variation of the along-channel velocity in both the along- and cross-channel directions to our experimental data. By matching the cross-channel data with the model, we find that the constant $\unicode[STIX]{x1D706}_{1}$ has value 0.2. We also analyse our experimental data to develop a time-dependent picture of the mixing of a stream of dye released into the wake. Using the model for the evolution of the flow, we develop a model for the time-averaged mixing, again based on mixing length theory. The model predicts a similar spatial distribution for the tracer in both the cross-stream and along-stream directions to that seen in our experimental data. By quantitative comparison of the model with the data, we find that the best fit of the empirical eddy diffusivity, $\unicode[STIX]{x1D706}_{2}ud$, with the data occurs with $\unicode[STIX]{x1D706}_{2}=0.22$. We discuss implications of our results for modelling cross-stream mixing in shallow turbulent flow.

Interaction of surface gravity wave motion with elastic bottom in three-dimensions

A general three-dimensional hydroelastic model is developed to study the effect of elastic bottom on surface gravity wave motion in three-dimensions under the action of uniform compressive force based on linearized theory of water wave in finite water depth. The elastic bottom bed is modeled as a thin plate theory. The progressive wave characteristics in different wave modes are analyzed in both the cases of deep and shallow water waves. Further, the linearized long wave equation under shallow water approximation in a direct manner is derived and compared the results obtained based on the small amplitude wave theory. Three-dimensional Green's function associated with surface gravity wave motion with elastic bed is derived using the fundamental source potentials. Fourier-type expansion formula and corresponding orthogonal mode-coupling relations are derived in finite depth and finite/semi-infinite width in three-dimensions. Utilizing the expansion formula, two classical problems (i) forced motion and (ii) wave reflection by a rigid wall in a channel of finite width and finite/semi-infinite length are illustrated which will play significant role in the analysis of wave-structure interaction problems arising in ocean engineering.The effects of elastic bottom on surface gravity waves are analyzed by presenting several numerical results on reflection wave amplitudes in different cases. Further, the behavior of free motions and oscillations in a basin of finite width and finite/semi-infinite length with elastic bed under the action of uniform compressive force are discussed.

Natural convection flows of a Bingham fluid in a long vertical channel

We analyze the 1D flow of a Bingham fluid between two differentially heated vertical plates, in the presence of a stabilizing vertical temperature gradient, imposed at the walls. The solution is parameterized by the Bingham number, B, and the stratification parameter Γ, and is surprisingly complex. When B⩾Bcr=1/16 the fluid is unyielded everywhere and heat transfer is via pure conduction. We refer to this as a 1-plug solution. For B≲Bcr, a perturbation solution shows that yielding starts at the walls and the centerline of the channel, breaking into two asymmetric counter-current streams and with a single plug in each stream (a 2-plug solution). We characterize the solution regimes in the Γ–B plane in terms of the number of plugs that are found. We identify the main characteristics of these solutions and provide data suitable for numerical benchmarking. For increasing Γ and decreasing B, we show that in principle, an arbitrarily large number of plugs can be found in the finite width channel. Primarily we solve for the 1-plug (conductive), 2-plug and 3-plug solutions, which are found to dominate the Γ–B parameter space.

Hydrodynamic instability of the coflow filtration combustion: Numerical simulation

The stability of the front to infinitely small distor� tions was analyzed under the assumption that the reac� tor channel width is infinitely large in comparison with the combustion zone thickness (5). It was concluded that the plane filtration combustion wave may be unstable. The experimental investigation of the filtra� tion combustion wave stability confirmed (6) that the propagation of a plane filtration combustion front may be unstable and may be accompanied by the formation of structures similar to Saffman-Taylor fingers, which were observed as a highviscosity liquid was displaced by a lowviscosity liquid (7). In this work, for the first time, we made mathemat� ical modeling of twodimensional unsteady filtration combustion during the forced oxidant filtration in the combustion wave direction. The purposes of the study was to determine the conditions for the occurrence of filtration combustion with a stable plane front in chan� nels of finite width and investigate the filtration com� bustion wave propagation modes in the range of insta� bility of the plane reaction front. The physical formulation of the problem is the fol� lowing. A gas mixture with oxidant concentration a0 is fed to a reactor filled with a porous mixture containing a fuel component. The gas flow rate at the inlet (x = 0) is maintained constant (G0). Reaction initiation with a hightemperature source leads to reaction front prop� agation in the х direction at rate u. As the fuel is burned out, the structure of the porous medium changes, because of which the porosity, thermal diffusivity, and permeability of the combustion products may differ from the respective characteristics of the initial reac� tion mixture. The problem is considered in the plane geometry under the assumption that the reactor is shaped as a thin slitlike channel. If the reaction front propagation velocities are low, which is characteristic of filtration combustion waves, the difference between the temperatures of the parti� cles and the gas can be ignored and the porous medium can be considered locally uniform in temper� ature and concentration. Under this assumption, the dimensionless system of equations describing filtra� tion combustion has the form (1, 2)

Flow of a Bingham-like fluid in a finite channel of varying width: A two-scale approach

In this paper we consider the flow of a Bingham-like fluid driven by a known pressure gradient in a channel of finite width and length. We model the continuum as a linear viscous fluid when the stress is above a certain threshold and as a linear elastic solid when the stress is below such a threshold. We consider a channel of varying width. Moreover, the ratio, denoted by ε, between the channel width and length is small. This allows for a two-scale approach. Indeed, we seek a solution performing an asymptotic expansion in powers of ε of the main variables. Under specific assumptions on the model characteristic parameters, we prove some analytical results for the zero order approximation. In particular, we show that, when the deformations of the inner elastic core are non-negligible, its width may vary along the longitudinal coordinate. On the other hand, when the core deformations are negligible, the Bingham model is retrieved along with the well known “lubrication paradox”. We also show some numerical simulations.

Wave structure interaction problems for two-layer fluids in three dimensions

The effect of compressive force on flexural gravity waves in two-layer fluids is analysed. Wave characteristics for surface and interfacial modes in the cases of deep and shallow water are studied and the effect of compression on these modes is analysed in special cases from the general problem. Generalized expansion formulae and associated orthogonal mode-coupling relations are derived for the velocity potentials to deal with wave structure interaction problems in three dimensions in both the cases of finite and infinite water depths in channels of finite and semi-infinite widths. Several characteristics of the eigenfunctions are derived in specific cases. As an application of the expansion formulae, wave scattering due to partially frozen cracks in floating ice sheet is analysed in a channel of finite width and depth in the presence of compressive force in two-layer fluids.

Impact of Transversely-Oriented Wall Corrugation on Hydraulic Resistance of a Channel Flow

The impact of the transversely-oriented sinusoidal wall corrugation on the hydraulic drag is investigated numerically for the flow through the channel of finite width and with flat sidewalls. The numerical method, based on the domain transformation and Chebyshev-Galerkin discretization, is used to investigate the flow resistance of the laminar, parallel and pressure-driven flow. The obtained results are compared to the reference case, i.e., to the flow through the channel with rectangular cross section of the same aspect ratio. Simple explanation of the gain in the volumetric flow rate observed in the flow through spanwise-periodic channel with long-wave transversely-oriented wall corrugation is provided. In the further analysis, pressure drop in the flows with larger Reynolds numbers are studied numerically by means of the finite-volume commercial package Fluent. Preliminary experimental results confirm the predicted tendency.

Nominally two-dimensional waves in inclined film flow in channels of finite width

Traveling waves in inclined film flow in channels of finite width are never truly two-dimensional (2D) because of a long-range effect of sidewalls. The present study documents the characteristics of the first waves that are observed beyond the primary instability (termed nominally 2D) by taking measurements in a 3000 mm long inclined facility with adjustable width up to 450 mm using a fluorescence imaging technique. It is observed that nominally 2D waves are very persistent structures with their crests attaining a parabolic shape, which is symmetric with respect to the channel centerplane irrespective of the 3D content of the inlet forcing. The apex curvature of the parabola varies inversely with channel width and Reynolds number. The wave height is maximum at the centerplane and decreases to zero at the sidewalls, irrespective of the wetting properties of the system. The linear phase velocity of nominally 2D waves is always lower than predicted by the theory for small amplitude, 2D waves, and significantly in narrow channels and/or small inclinations. The above characteristics are shown to explain discrepancies between theory and observations, in particular the recently reported deviation of the onset of the primary instability from the classical prediction [M. Vlachogiannis et al., Phys. Fluids 22, 012106 (2010)].

Laminar mixed convection on a horizontal plate of finite length in a channel of finite width

The steady two-dimensional laminar mixed-convection flow past a horizontal plate of finite length is analysed for large Peclet numbers, small Prandtl numbers and weak buoyancy effects. The plate is placed in a channel of finite width, with the plane walls of the channel being parallel to the plate. The temperature of the plate is assumed to be constant. The hydrostatic pressure difference across the wake behind the plate is compensated by a perturbation of the inviscid channel flow. This outer flow perturbation affects the temperature distribution in the thermal boundary layer at the plate and the heat transfer rate, respectively. Solutions in closed form are given. The forces acting on the plate due to the potential flow perturbation are also determined.

Plasma Ion Evolution in the Wake of a High-Intensity Ultrashort Laser Pulse

Experimental investigations of the late-time ion structures formed in the wake of an ultrashort, intense laser pulse propagating in a tenuous plasma have been performed using the proton imaging technique. The pattern found in the wake of the laser pulse shows unexpectedly regular modulations inside a long, finite width channel. On the basis of extensive particle in cell simulations of the plasma evolution in the wake of the pulse, we interpret this pattern as due to ion modulations developed during a two-stream instability excited by the return electric current generated by the wakefield.

High-Frequency Asymptotics of Edge Waves on a Beach of Nonconstant Slope

The paper is devoted to the construction of asymptotic expansions for frequencies of water waves trapped by a beach of nonconstant slope as the longshore wave number tends to infinity. The existence of such trapping modes in this asymptotic regime was proved recently in [A.-S. Bonnet-Ben Dhia and P. Joly, SIAM J. Appl. Math., 53 (1993), pp. 1507--1550]. For a beach of constant slope the formulas obtained reduce to the classical result of Ursell. Some generalizations to other geometries (waves trapped by afloating semisubmerged cylinder and by shores of a channel of finite width) are indicated. The main analytical tool used for the construction of the asymptotics is an explicit solution of a mixed boundary value problem for the Helmholtz equation in an angle with nonhomogeneous boundary conditions.

Crystalline Saffman–Taylor Fingers

We study the existence and structure of steady-state fingers in two-dimensional solidification, when the surface energy has a crystalline anisotropy so that the energy-minimizing Wulff shape and hence the solid–liquid interface are polygons, and in the one-sided quasi-static limit so that the diffusion field satisfies Laplace’s equation in the liquid. In a channel of finite width, this problem is the crystalline analog of the classic Saffman–Taylor smooth finger in Hele–Shaw flow. By a combination of analysis and numerical Schwarz–Christoffel mapping methods, we show that, as for solutions of the smooth problem, for each choice of Wulff shape there is a critical maximum value of the magnitude of surface tension above which no convex steady-state solutions exist. We then exhibit convergence of convex crystalline solutions to convex smooth solutions as the Wulff shape approaches a circle. We also consider the open dendrite geometry and show that there are no steady-state solutions having a finite number of sides for any crystalline surface energy. This is in striking contrast to the smooth case and an indication that the time-dependent behavior may be more complicated for crystalline surface energies.