Finite Channel Width Research Articles

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.

Scattering of water waves by a wave energy device consisting of a pair of co-axial cylinders in a uniform water having finite channel width

We consider a device which consists of a floating structure over a cylindrical plate placed at a finite height from the impermeable ocean floor. This paper developes the interaction of linear water waves with such a device. The whole fluid domain is divided into a number of sub-domains and boundary value problems are formulated for each identified sub-domain. The channel multipoles, separation of variables and matched eigenfunction expansion methods allow us to solve boundary value problems for the diffracted velocity potentials in each sub-domain. We investigate the wave forces exerted on the proposed device. Consequently, the effects of the various parameters, e.g., drafts, radii, the gap between the cylinders and mainly channel width of the device on the wave forces exerted by the cylinders are presented graphically. We observe a small oscillation nature near the peak value of the exciting force for the particular value of channel width w=2.4m. The peak value of the exciting forces occurs near the wavenumber kr1=1.0 for different width of the channel walls. The obtained results are compared with some available results, and it shows a good agreement between the obtained and available results.

Poiseuille Flow of Soft Polycrystals in 2D Rough Channels.

Polycrystals are partially ordered solids where crystalline order extends over mesoscopic length scales, namely, the grain size. We study the Poisuielle flow of such materials in a rough channel. In general, similar to yield stress fluids, three distinct dynamical states, namely, flowing, stick-slip, and jammed can be observed, with a yield threshold dependent on channel width. Importantly, the interplay between the finite channel width, and the intrinsic ordering scale (the grain size) leads to a new type of spatiotemporal heterogeneity. In wide channels, although the average flow profile remains pluglike, at the underlying granular level, there is vigorous grain remodeling activity resulting from the velocity heterogeneity among the grains. As the channel width approaches typical grain size, the flowing polycrystalline state breaks up into a spatially heterogeneous mixture of flowing liquid like patches and chunks of nearly static grains. Despite these static grains, the average velocity still shows a parabolic profile, dominated by the moving liquidlike patches. However, the solid-liquid front moves at nearly constant speed in the opposite direction of the external drive.

Nonlocal voltage in a spin field effect transistor with finite channel width

Spin transport in the two-dimensional electron gas with strong spin–orbit interaction is examined by using a simple phenomenological simulation. The large spin–orbit interaction and the randomized electron trajectory due to the impurity scattering make the nonlocal voltage of a spin field effect transistor undetectable in the diffusive regime. However, the spin-precessional phase accumulates coherently in the ballistic regime and the nonlocal voltage is given by a function of spin–orbit interaction parameter. If the distance between injector and detector is comparable to the mean free path, a sinusoidal oscillation of nonlocal voltage is restored even for a wide channel.

Spin field effect transistor with a graphene channel

A spin field effect transistor (FET) is proposed by utilizing a graphene layer as the channel. Similar to the conventional spin FETs, the device involves spin injection and spin detection by ferromagnetic source and drain. Due to the negligible spin-orbit coupling in the carbon based materials, spin manipulation in the channel is achieved via electrical control of the electron exchange interaction with a ferromagnetic gate dielectric. Numerical estimates indicate the feasibility of the concept if the bias can induce a change in the exchange interaction energy of the order of meV. When nanoribbons are used for a finite channel width, those with armchair-type edges can maintain the device stability against the thermal dispersion.

Mass transfer in rectangular chromatographic channels

Rectangular channels are explored nowadays for use in chromatographic and electrophoretic separations, especially after the possibilities of micromachining have become available to separation scientist. Expressions for plate heights expected for such experiments with an infinite channel width has been given by Giddings, while Golay derived the effect of finite channel width for unretained components. However, it remains unclear how the classical equations for plate height for retained components should be modified when the effect of finite channel width is taken into account. Also, the application of electroosmotic propulsion of the mobile phase leads to a flow profile different from the Poiseuille-type profile assumed in the above treatments, and no equations seem to be available for this situation. In this work, these problems have been addressed by an approach involving numerical Fourier transforms. Expressions for the plate height contribution from mobile phase mass transfer as a function of characteristic length d c (the height of the channel, or the diameter for open cylindrical systems, OT), mean mobile phase velocity, u m , diffusion coefficient D m , retention factor, k′, and width-to-height ratio, ϕ, can always be written as: H= d c 2 u m / D m F( k′, ϕ). For cylindrical open systems, F( k′, ϕ) equals 1/96 (1+6 k′+11 k′ 2)/(1+ k′) 2, the well-known Golay equation. In the present work, this is taken as a reference point; results are cast in the form F( k′, n)=(A+B k′+C k′ 2)/(1+ k′) 2, where A, B and C replace the factors 1/96, 6/96 and 11/96 of the Golay equation. Values of A, B and C are reported for various values of ϕ. This is done for a selection from the large variety of conditions that can be imagined: Coating on one, two or four walls of the channel, non-uniform or uniform coating, pressure-driven (Poiseuille-type) or electro-osmotically-driven flow, surface charge on one, two of four walls, etc. It is found that the effect of finite channel width is large for unretained solutes (plate height for a wide channel is nearly eight times larger than that predicted when the finite channel width is ignored), whereas the plate height increase with retention is in many cases influenced only slightly.

A statistical approach to the choice of channel-width in gamma-ray spectrometry

Equations giving the percentage of extra peak-broadening caused by the finite channel-width in multichannel gamma-ray spectrometry were earlier developed by means of a statistical treatment. Empirical straight-line fits were used for the energy vs. resolution curves. In this paper this treatment is applied, but using instead a semi-empirical second-order equation for NaI(Tl) detectors. The disadvantage of the use of two equations to describe one detector is thus overcome. We present four different ways to estimate the extra peak-broadening as a function of channel-width, depending on the degree of precision required. A statistical consideration giving the precision of each estimate is included. It appears that for many cases no specific detector information is required. For these cases a generally applicable plot is given.

The effect of finite channel width on concentration polarisation in reverse osmosis under laminar flow conditions

The effect of finite channel width on concentration polarisation in reverse osmosis under laminar flow conditions

The finite channel width and the analysis of experimental data

The distortion introduced in the data accumulated in a mutichannel analyser due to the finite width of the channels is easily taken into account in the analysis, when the function describing the phenomenon is known and can be integrated analytically over the channel width. This idea was applied to the analysis of simulated Lorentzian lines, i.e., lines with a priori known parameters. The parameters derived from least-squares fits using (a) a Lorentzian function and (b) the integrated function were compared with the original values for different ratios of channel width to peak width.

The two-dimensional elliptical cap bubble

A study of the closed wakes behind large gas bubbles rising between two parallel plates reveals that they are elliptical in shape, rather than circular. Fitting an are of an ellipse, rather than a circle, to the curved upper surface of such a bubble eliminates a discrepancy between theory and experiment noted by Collins (1965a). Collins’ analysis of the effect of finite channel width is extended to the elliptical case, and the stability of the closed wake is examined.

A statistical approach to the choice of channel-width in gamma-ray spectrometry using empirical relations between resolution and gamma-ray energy

The problem of extra peak-broadening caused by the finite channel-width in multichannel gamma-ray spectrometry is discussed, using empirical equations for the relations between resolution and energy for NaI(T1) scintillation detectors and Ge(Li) drift detectors. Relations are derived and graphs designed to estimate the extra peak-broadening at a certain energy, caused by the compromise necessary when using a chosen energy scale in as few channels as possible.

Monoenergetic Absorption Peaks Obtained with a Scintillation Spectrometer

The effect of finite channel width in distorting intensities of monoenergetic lines in a scintillation spectrometer is considered. It is found that peak area divided by channel width gives the rate of monoenergetic absorptions in the crystal. A correction to intensities proportional to the square root of the pulse height is not applicable.