Ratio Of Relaxation Time Research Articles

A meniscus fingering instability in viscoelastic fluids

We report experiments where a viscoelastic fingering instability develops at the free interface between air and a model viscoelastic fluid confined in a Hele-Shaw cell. The fluid is symmetrically stretched with constant velocity along two opposite directions, leading to the inflation of a two-dimensional air bubble growing from a millimetric centered hole. The instability is observed when the circumferential stretch of the inflating bubble reaches a threshold that depends on the viscoelastic properties of the fluid through the ratio of the material relaxation time to the time elapsed before the fingers start to develop. The critical stretch of the bulk fingering instability of a stretchable elastic solid [B. Saintyves, O. Dauchot, and E. Bouchaud, “Bulk elastic fingering instability in Hele-Shaw cells,” Phys. Rev. Lett. 111, 047801 (2013)] is recovered for large values of this ratio.

Influence of Strain on the Microstructure and Transverse Relaxation Characteristics of HTPB Coating Using Low-Field <sup>1</sup>H NMR Spectroscopy

During the storage process, the HTPB (hydroxyl-terminated polybutadiene) coating is continuously affected by the strain, and the microstructure and mechanical properties will be degraded, which will seriously affect the performance of composite solid propellant and solid rocket motor and cause great harm. In order to analyze the microstructure and transverse relaxation characteristics of HTPB coating under different strains, low-field 1H NMR tests was carried out under 0%, 5%, 10% and 15% strain conditions, and the crosslinking density and transverse relaxation parameters of HTPB coating were analyzed. The results show that, the transverse relaxation decay can be divided into two segmental mobilities corresponding to two distinct transverse relaxation times. With the increase of strain, the crosslinking density shows a decline tendency, the transverse relaxation decay amplitude slows down, and the inversion curve has a tendency to move to the right. The ratio of the fast transverse relaxation time and the peak area are much larger than the slow transverse relaxation time, and the proportion of the fast relaxation time and the peak area enlarge with the increase of the strain, while the proportion of slow transverse relaxation time is reduced. With the increase of strain, there is a transition from slow transverse relaxation to fast transverse relaxation, and there is an inverse linear relationship between crosslinking density and transverse relaxation time.

Shear and extensional rheology of aqueous solutions of cocamidopropyl betaine and sodium dodecyl sulfate mixture

The paper presents the results obtained for aqueous solutions of a mixture of cocamidopropyl betaine (CAPB) and sodium dodecyl sulfate (SDS) in rheological tests in the shear and extensional flow. The rheological measurements in the extensional flow were conducted using a capillary breakup extensional rheometer. The description of the mechanical spectra required the application of the multi-mode Maxwell model, which demonstrates that stress relaxation occurs via reptation – as in entangled polymer solutions. The rheological properties of aqueous CAPB/SDS solutions in the extensional flow were also found to be qualitatively consistent with the properties of entangled polymer solutions. The ratio of the extensional relaxation time to the transient shear relaxation time was considerably lower than one, and the range of elasto-capillary thinning appeared at a Weissenberg number of 2/3. The difference between polymer solutions and CAPB/SDS solutions is noted at late times, when the transient extensional viscosity of the solutions of polymers and wormilke cationic surfactants reaches a constant value, whereas in CAPB/SDS solutions it drops rapidly. The decrease in transient extensional viscosity in this range may be due to the break-up of wormlike micelles under the influence of high transient extensional stresses.

Dynamic cavity effects in topological insulator Bi2Te3 based passive Q-switched solid state laser

In this work, a comprehensive investigation of dynamic evolution for pulsed solid state laser using topological insulator as saturable absorber (SA) is reported. Without material damage, dynamic transition from Q-switched (QS) state to continuous wave (CW) state in the laser cavity is observed when the pumping rate to the Nd3+:YAG laser crystal increases. With a sufficiently large pumping rate, the initiated laser spiking damps and relaxes to CW state similar to a laser system without intra-cavity SA. Formulated by well-known laser rate equations, analysis of the perturbations around fixed points reveals the instability spectrum that is able to explain the observed transition in experiments. Theoretically, the parameters space to support QS operation are given in terms of the ratio of saturation intensity of laser gain media over the saturation intensity of SA, pumping speed, the ratio of relaxation time of laser gain media over cavity lifetime and the modulation depth of the SA. The result of this work suggests a simple approach to understand passive Q-switched (PQS) laser with SAs of low saturation intensity and guidelines to the design of laser system employing low-saturation materials as SA, such as two-dimensional TI material.

Methods for Local Recovery of Tectonic Stresses Based on Kinematic Data: Physical Inconsistency and False Objectives. Part I

This work criticizes the entrenched views according to which the orientation of the principal tectonic stress axes can be determined from local (in time and space) observations of the kinematic indicators which jointly allow estimating the strain rate of a crustal block under study. The criticized approach ignores or replaces by subjective assumptions the following factors: (1) The block’s interaction with a hosting medium expressed in terms of the equilibrium conditions of the block; (2) The stress rate which (in addition to stresses) can affect the strain rate; (3)The specific macroscopic mechanical properties of the block’s material under the unknown sought stresses, including the ratio of the stress relaxation time to the period of observations. This approach, which is developed in some Solid Earth sciences and mainly in tectonophysics, is referred to in our paper as the method of local kinematic reconstruction (MLKR) of stresses. After briefly surveying the concept of forces and stresses and discussing the importance of studying the tectonic stresses, this paper refutes the MLKR notions based on general arguments and by the example of certain thought experiments. It is shown that the use of the MLKR for the conditions of the Earth’s interior does not guarantee against obtaining the results that fundamentally and drastically differ from the true tectonic stresses. In the studied rock block, depending on the factors ignored in the MLKR, the principal axes of the strain rate tensor, on one hand, and the principal stress axes, on the other hand, can be oriented discordantly in any arbitrary given fashion. In particular, in the processes accompanied by the release of elastic energy, the maximal rate of elongation can be oriented along the axis of maximal compression, whereas the maximal rate of shortening can be aligned with the axis of the maximal tension. In this paper, the deformation processes that are most detrimental to the results of stress reconstruction by the MLKR are revealed. We introduce the notion of the inherited stress-state regime in which the orientation of the axes of principal stresses during the observation period does not depend on the deformation process and, hence, cannot be in principle determined by the MLKR. An attempt to directly locally recover the stress axes from the kinematic data is a false objective because neither the physical meaning of the stress tensor nor the way it is introduced has anything to do with strains. It is concluded that the MLKR is physically inadequate and that the tectonophysical concept of locality should be abandoned in favor of returning to the notions of classical physics, namely, to using the conservation laws. By the example of several guides on tectonophysics, this paper exposes typical errors in understanding the stress reconstruction problem.

Lie point symmetries for biological magneto-Jeffrey fluid flow in expanding or contracting permeable walls: a blood vessel model

ABSTRACTThis article addresses biological flow in expanding or contracting blood vessels. The alternate contraction and expansion of vessels is known to act as a physiological pump to generate flow. When muscles compress blood vessel walls, the valve at the end of the source is closed, and the downstream end opens; for this reason, blood is pumped in the downstream direction. To study this situation, a model has been developed here that consists of the unsteady two-dimensional flow of an incompressible magneto-Jeffrey fluid in a porous semi-infinite channel with expanding or contracting walls; the channel is closed from one end by a compliant membrane. The Lie group analysis method was used to transform a system of nonlinear partial differential equations into nonlinear ordinary differential equations that were solved using the perturbation method. The effects of Jeffrey parameters (, which is the ratio of relaxation time to retardation time, and Deborah parameter ) and other physical parameters are plotted and discussed. We find that the axial velocity of a Newtonian fluid is greater than that of a non-Newtonian fluid if the walls are in contraction and vice versa if the walls are in expansion. If the walls are expanded, the blood is distributed in a large area, and thus, the normal pressure decreases, while if the walls are contracted, blood is distributed in less space, and thus, the pressure increases. Normal pressure in expanding blood vessels is less than that in contracting blood vessels.

Investigating the effect of electrical conductivity on electrospray modes

This study investigated experimentally the effect of electrical conductivity on electro-hydrodynamic (EHD) modes in the electrospray process. The geometric shape of the micro-droplets having different electrical conductivity was studied. For this purpose, three fluids, including acetic acid, ethanol, and toluene, were selected as the representation of three different fluid classifications in terms of electrical conductivity. The difference in conductivity of these fluids can be characterized by α denoting the ratio of electrical relaxation time to the characteristic hydrodynamic time. The experiments showed that the increase in α did not significantly affect the transfer of the EHD modes. In addition, analytical and graphical investigations showed why ethanol as a leaky dielectric fluid produced lower droplet diameters in comparison with acetic acid as a conductive fluid at highest electrical capillary numbers. Also, a pulsation mode was monitored in the experiments related to toluene as a dielectric fluid. Finally, an equation was presented for calculating the dimensionless diameters of ethanol droplets and acetic acid using non-dimensional numbers derived from the experimental data.

Theoretical investigation of heterogeneous wettability in porous media using NMR

It is highly important to understand the heterogeneous wettability properties of porous media for enhanced oil recovery (EOR). However, wettability measurements are still challenging in directly investigating the wettability of porous media. In this paper, we propose a multidimensional nuclear magnetic resonance (NMR) method and the concept of apparent contact angles to characterize the heterogeneous wettability of porous media. The apparent contact angle, which is determined by both the wetting surface coverage and the local wettability (wetting contact angles of each homogeneous wetting regions or wetting patches), is first introduced as an indicator of the heterogeneous wettability of porous media using the NMR method. For homogeneously wetting patches, the relaxation time ratio T1/T2 is employed to probe the local wettabiity of wetting patches. The T2 − D is introduced to obtain the wetting surface coverage using the effective relaxivity. Numerical simulations are conducted to validate this method.

Valley Hall transport of photon-dressed quasiparticles in two-dimensional Dirac semiconductors

We present a theory of the photovoltaic valley-dependent Hall effect in a two-dimensional (2D) Dirac semiconductor subject to an intense near-resonant electromagnetic field. Our theory captures and elucidates the influence of both the field-induced resonant interband transitions and the nonequilibrium carrier kinetics on the resulting valley Hall transport in terms of photon-dressed quasiparticles (PDQs). The non-perturbative renormalization effect of the pump field manifests itself in the dynamics of the PDQs, with a quasienergy spectrum characterized by dynamical gaps δη (η is the valley index) that strongly depend on field amplitude and polarization. Nonequilibrium carrier distribution functions are determined by the pump field frequency ω as well as the ratio of intraband relaxation time τ and interband recombination time τrec. We obtain analytic results in three regimes, when (I) all relaxation processes are negligible, (II) τ ≪ τrec, and (III) τ ≫ τrec, and display corresponding asymptotic dependences on δη and ω. We then apply our theory to 2D transition-metal dichalcogenides, and find a strong enhancement of valley-dependent Hall conductivity as the pump field frequency approaches the transition energies between the pair of spin-resolved conduction and valence bands at the two valleys.

Associations Between Slower Walking Speed and T1ρ Magnetic Resonance Imaging of Femoral Cartilage Following Anterior Cruciate Ligament Reconstruction.

To determine whether walking speed, collected at 6 and 12 months following anterior cruciate ligament reconstruction (ACLR), is associated with inter-extremity differences in proteoglycan density, measured via T1ρ magnetic resonance imaging, in tibiofemoral articular cartilage 12 months following ACLR. Twenty-one individuals with a unilateral patellar-tendon autograft ACLR (10 women and 11 men, mean ± SD age 23.9 ± 2.7 years, mean ± SD body mass index 23.9 ± 2.7 kg/m2 ) were recruited for participation in this study. Walking speed was collected using 3-dimensional motion capture at 6 and 12 months following ACLR. The articular cartilage of the medial femoral condyle (MFC) and lateral femoral condyle and medial and lateral tibial condyles was manually segmented and subsectioned into 3 regions of interest (anterior, central, and posterior) based on the location of the meniscus in the sagittal plane. Inter-extremity mean T1ρ relaxation time ratios (T1ρ ACLR extremity / T1ρ contralateral extremity) were calculated and used for analysis. Pearson product-moment correlations were used to determine associations between walking speed and inter-extremity differences in T1ρ relaxation time ratios. Slower walking speed 6 months post-ACLR was significantly associated with higher T1ρ relaxation time ratios in the MFC of the ACLR extremity 12 months following ACLR (posterior MFC, r = -0.51, P = 0.02; central MFC, r = -0.47, P = 0.04). Similarly, slower walking speed at 12 months post-ACLR was significantly associated with higher T1ρ relaxation time ratios in the posterior MFC ACLR extremity (r = -0.47, P = 0.04) 12 months following ACLR. Slower walking speed at 6 and 12 months following ACLR may be associated with early proteoglycan density changes in medial femoral compartment cartilage health in the first 12 months following ACLR.

Lesser Mechanical Loading During Walking Gait Associates with Worse Proteoglycan Density 6 months Following Anterior Cruciate Ligament Reconstruction

Optimal mechanical loading is necessary to decrease the risk of posttraumatic osteoarthritis (PTOA) following anterior cruciate ligament reconstruction (ACLR) and lesser mechanical loading early following ACLR may increase the risk for PTOA onset. T1ρ magnetic resonance imaging (MRI) has been used to measure cartilage composition at early time points following ACLR. PURPOSE: To determine the association between proteoglycan density of femoral cartilage derived from T1ρ MRI relaxation times and peak vertical ground reaction force (vGRF) and instantaneous vGRF loading rate (vGRF-LR) during walking gait 6 months following ACLR. METHODS: Twenty-nine individuals (52% female, BMI = 24±3 kg/m2) with a unilateral patellar-tendon autograft ACLR participated in this study. Five trials of walking gait at self-selected speed were performed 6 months following ACLR. Peak vGRF and instantaneous vGRF-LR were extracted from the first 50% of the stance phase in both limbs. T1ρ relaxation times were calculated for articular cartilage in the medial and lateral condyles (MFC & LFC) by fitting a monoexponential model. The weight bearing MFC and LFC cartilage was manually segmented into posterior, central, and anterior regions of interest (ROI) based on the location of the meniscus in the sagittal plane. Affine and deformable registration techniques were used to register the ACLR limb to the uninjured limb. Inter-limb mean T1ρ relaxation time ratios (RTR = ACLR limb / uninjured limb) were calculated for each ROI. Separate, stepwise linear regressions were used to determine the unique associations between vGRF outcomes and T1ρ RTR in each ROI after accounting for walking speed and meniscal injury (ΔR2; P≤ 0.05). RESULTS: In the ACLR limb, lesser vGRF during gait was associated with lesser proteoglycan density in the posterior (ΔR2=0.22, P=0.02) and central LFC (ΔR2=0.22, P=0.02), as well as the posterior (ΔR2=0.12, P=0.05) and central MFC (ΔR2=0.21, P=0.01). vGRF-LR in the ACLR limb and all vGRF outcomes in the contralateral limb did not significantly associate with T1ρ RTR for any ROI. CONCLUSIONS: Individuals with lesser vGRF in the ACLR limb presented with T1ρ MRI findings consistent with deteriorating cartilage health. Understanding how loading affects joint health is critical to developing interventions to delay PTOA onset.

Spatial instability of double-layer viscoelastic liquid sheets in a viscous gas medium

The spatial instability of double-layer viscoelastic liquid sheets in a viscous gas medium is investigated. A linear stability analysis is used to simplify the governing equations and boundary conditions combined with the Oldroyd-B model for describing the viscoelastic liquid. The growth rate and the cut-off wavenumber have been studied by analyzing the dispersion curve which is based on the spectral collocation method. Moreover, we use the decomposition of growth rate to interpret some special cases. We conclude that the thickness ratio, the liquid density ratio, the liquid viscosity ratio, and the gas-to-liquid viscosity ratio stabilize the liquid sheets, while the gas-to-liquid density ratio, the Reynolds number, and the Weber number destabilize the liquid sheets. The dispersion curves are nearly-identical when the surface tension ratio is smaller than one, while the surface tension ratio is a stabilizing factor when the ratio is larger than one, but the second maximum and the counterintuitive destabilization exist in the large wavenumber region. As specific parameters concerning the viscoelasticity, the elasticity number transforms from the destabilizing factor into the stabilizing factor with the increased Reynolds number in the region nearby the cut-off wavenumber, because the relationship between the change rates of viscous dissipation terms and elasticity terms in the decomposition of the growth rate is varying. Besides, it is discovered that the trend of the change of the growth rate under the varying stress relaxation time ratio is non-monotonic and double-layer liquid sheets are most stable when the stress relaxation time ratio is near 3 (not 1), because the difference between the change rate of the viscous dissipation and the deformation retardation dissipation determines the most stable region (not the elasticity difference), which can also be interpreted with the variation of the energy terms.

Three-dimensional Couette flow of a Jeffrey fluid along periodic injection/suction

Three-dimensional Couette flow of an incompressible Jeffrey fluid is formulated and discussed analytically and graphically. The suction is applied over uniformly moving upper plate and its equivalent deduction by injection at the lower stationary plate. Because of this type of suction/injection, this flow turns into three-dimensional. An analytical method is applied to get main flow velocity, secondary flows velocities and pressure components. Also skin friction components along the main and secondary flow directions have been calculated. The effects of different physical parameters, for example, the Deborah number, suction/injection parameter, the ratio of relaxation time to the retardation time and Reynolds number have been discussed graphically. It is witnessed that the Deborah number plays vital role to control the main flow velocity.

Associations between cartilage proteoglycan density and patient outcomes 12 months following anterior cruciate ligament reconstruction

BackgroundLower proteoglycan density (PGD) of the articular cartilage may be an early marker of osteoarthritis following anterior cruciate ligament (ACL) reconstruction (ACL-R). The purpose this study was to determine associations between the Knee Injury and Osteoarthritis Outcomes Score (KOOS) and PGD of the articular cartilage in the femur and tibia 12-months following ACL-R. MethodsWe evaluated KOOS pain, symptoms, function in activities of daily living (ADL), function in sport and recreation (Sport), and quality of life (QOL), as well as PGD using T1rho magnetic resonance imaging in 18 individuals 12.50±0.70months (these are all mean±standard deviation) following unilateral ACL-R (10 females, eight males; 22.39±4.19years; Marx Score=10.93±3.33). Medial and lateral load-bearing portions of the femoral and tibial condyles were sectioned into three (anterior, central and posterior) regions of interest (ROIs). T1rho relaxation times in the ACL-R knee were normalized to the same regions of interest in the non-surgical knees. Alpha levels were set at P≤0.05. ResultsWorse KOOS outcomes were significantly associated with greater T1rho relaxation time ratios in the posterior-lateral femoral condyle [pain (r=−0.54), ADL (r=−0.56), Sport (r=−0.62) and QOL (r=−0.59)] central-lateral femoral condyle [Sport (r=−0.48) and QOL (r=−0.42)], and the anterior-medial femoral condyle [Sport (r=−0.46) and QOL (r=−0.40)].There were no significant associations between the KOOS and T1rho outcomes for tibial ROI. ConclusionsLower PGD of the femoral cartilage in the ACL-R knees was associated with worse patient-reported outcomes.

Exploring sensitivity of the extensional flow to wormlike micellar structure

The non-linear dynamics of a series of salt-free surfactant solutions is investigated via a combination of TEM imaging, shear rheology and capillary breakup extensional rheometry. Surfactant solutions contain Hexadecyltrimethylammonium p-toluenesulfonate (CTAT) in de-ionized water. At low surfactant concentrations, 0.7 wt% < c < 1.1 wt%, solutions exhibit shear thickening behavior and the transient extensional measurements lead to formation of long lasting elastic filaments with a fairly constant extensional relaxation time λE ≈ 0.03 s. At higher concentrations, 1.1 wt% ≤ c < 2 wt%, solutions exhibit strong viscoelastic behavior evidenced by dramatic increase in shear relaxation time. However, for concentrations above 2 wt%, the shear relaxation time decreases, while the zero shear viscosity reaches an asymptotic value. TEM images suggest that below the critical concentration, a polydisperse micellar structure with fairly long, short and spherical micelles co-exist. However, above the critical concentration, a dense micellar network forms with no indication of branched micelles. Using shear rheology data, we demonstrate that the micellar chain length decreases beyond the critical concentration, while the entanglement number remains fairly constant. On the other hand, the maximum Trouton ratio measured in transient extensional experiments decreases as surfactant concentration is increased to c ≈ 3 wt%, and remains fairly constant around Tr ≈ 3, for higher concentrations. This finding is in-line with the structural parameters inferred from the shear rheology and also the TEM images. Therefore, we confirm that the extensional rheology is sensitive to structural transitions near the critical concentration. Finally, we show that the ratio of the extensional relaxation time to the shear relaxation time, λE/λ, is always less than unity regardless of whether relaxation is dominated by reptation or breakage of the wormlike micelles.

A Jeffrey-fluid model of blood flow in tubes with stenosis

In this paper, we discuss the two-layered Jeffrey-fluid model with mild stenosis in narrow tubes. The blood flow in narrow arteries is treated as a two-fluid model with the suspension of erythrocytes, leukocytes, etc., as a Jeffrey fluid, which is a non-Newtonian fluid, in the core region and plasma, a Newtonian fluid, in the peripheral region. An analytical solution has been obtained for the velocity in the core and peripheral region, volume flow rate, resistance to flow, and wall-shear stress. The effect of Jeffrey-fluid parameters, like the height of stenosis, viscosity, etc., on volume flow rate, resistance to flow (impedance), and wall-shear stress has been discussed graphically. Through the present study, it is found that the wall-shear stress and resistance to flow increases with the increase in height of stenosis and decreases with the increase in the ratio of relaxation time. It is also found that the velocity decreases with an increase in stenosis height in both the core and the peripheral region. A previous result has been also verified.

Magnetohydrodynamic (MHD) nonlinear convective flow of Jeffrey nanofluid over a nonlinear stretching surface with variable thickness and chemical reaction

Main purpose here is to analysis magnetohydrodynamic (MHD) nonlinear convective flow of Jeffrey nanofluid by a nonlinear convectively heated stretching sheet of variable thickness. Nonlinear thermal radiation, heat generation/absorption and chemical reaction are considered. Brownian motion and thermophoresis have been utilized in energy and concentration expressions. Recently suggested condition employing volume fraction of nanoparticle at the surface to be controlled passively rather than actively is utilized. Appropriate variables lead to development of nonlinear ordinary differential systems. Effect of various pertinent variables for velocity, temperature and nanoparticle concentration have been displayed and explored. Skin friction coefficient and local Nusselt number are calculated and addressed. It is revealed that larger values of relaxation and retardation times ratio diminish velocity distribution. Moreover impact of heat generation/absorption on the temperature and heat transfer rate are quite reverse.

Demonstrating microstructural changes of basal ganglia in neonatal bilirubin encephalopathy with MP2RAGE

ObjectivesThis study aims to evaluate the microstructural changes of basal ganglia in neonatal bilirubin encephalopathy (NBE) with two inversion-contrast magnetization-prepared rapid gradient echo (MP2RAGE) sequence. Methods22 patients with NBE and 21 healthy, age-matched control neonates were included in this study. Conventional MRI, DWI, and MP2RAGE sequence were performed for all patients and controls. T1 relaxation time of bilateral globus pallidus (GP) and putamen were measured on the T1 mapping images. ResultsThe 3D T1-weighted high-resolution MP2RAGE contrast image clearly displayed the structure of basal ganglia. Relative hyper-intensity signals were found in bilateral GP on the T1-weighted images in all patients and in 16 (16/21) control neonates. The T1 relaxation time in GP and putamen decreased in the NBE group compared with that in the control group, but the difference was not statistically significant (P > 0.05). The T1-relaxation time ratio of GP and putamen in NBE were shorter than in control neonates (t = 2.38, P < 0.05). The T1 relaxation time ratio of GP and putamen was significantly correlated with the peak level of total serum bilirubin in the NBE group (r = −0.571). ConclusionsThe microstructure of basal ganglia changes in NBE. The T1 relaxation time ratio of GP and putamen is associated with serum bilirubin level. The quantitative T1 relaxation time maps obtained with MP2RAGE could be a promising parameter for diagnosis of NBE.

The effects of changing the electrodes temperature on the tunnel magnetoresistance in the ferromagnetic single electron transistor

Ferromagnetic single electron transistor with electrodes having different temperatures is investigated and the effects of changing electrodes temperature on TMR of system are studied. A modified orthodox theory is used to study the system and to calculate the electron tunneling transition rate. The results show that the temperature of electrodes can be an effective tool to control and tune the tunnel magnetoresistance of FM-SET. Also, the effects of parameters such as resistance ratio of junctions, magnetic polarization and spin relaxation time on the behaviour of the system are studied.

Effects of topological edge states on the thermoelectric properties of Bi nanoribbons

Using first-principles calculations combined with Boltzmann transport theory, we investigate the effects of topological edge states on the thermoelectric properties of Bi nanoribbons. It is found that there is a competition between the edge and bulk contributions to the Seebeck coefficients. However, the electronic transport of the system is dominated by the edge states because of its much larger electrical conductivity. As a consequence, a room temperature ZT value exceeding 3.0 might be achieved for both p- and n-type systems by fine tuning the relaxation time ratio between the edge and the bulk states.