The Effect of Random Roughness on the Electromagnetic Flow in a Micropipe.

The features of stationary random processes and the small parameter expansion approach are used in this work to examine the impact of random roughness on the electromagnetic flow in cylindrical micropipes. Utilizing the perturbation method, the analytical solution until second order velocity is achieved. The analytical expression of the roughness function ζ, which is defined as the deviation of the flow rate ratio with roughness to the case having no roughness in a smooth micropipe, is obtained by integrating the spectral density. The roughness function can be taken as the functions of the Hartmann number Ha and the dimensionless wave number λ. Two special corrugated walls of micropipes, i.e., sinusoidal and triangular corrugations, are analyzed in this work. The results reveal that the magnitude of the roughness function rises as the wave number increases for the same Ha. The magnitude of the roughness function decreases as the Ha increases for a prescribed wave number. In the case of sinusoidal corrugation, as the wave number λ increases, the Hartmann number Ha decreases, and the value of ζ increases. We consider the λ ranging from 0 to 15 and the Ha ranging from 0 to 5, with ζ ranging from -2.5 to 27.5. When the λ reaches 15, and the Ha is 0, ζ reaches the maximum value of 27.5. At this point, the impact of the roughness on the flow rate reaches its maximum. Similarly, in the case of triangular corrugation, when the λ reaches 15 and the Ha is 0, ζ reaches the maximum value of 18.7. In addition, the sinusoidal corrugation has a stronger influence on the flow rate under the same values of Ha and λ compared with triangular corrugation.

Stability of a liquid film on inclined flexible substrates: Effect of the spontaneous odd viscosity.

We report the stability of a falling incompressible odd viscosity fluid on flexible substrates when the time-reversal symmetry is broken. The flexible wall equation incorporates the contribution of odd viscosity, where the stress at an interface is determined by the viscosities of the adjacent fluids. The Orr-Sommerfeld (OS) equation is derived using the modified linear flexible wall equation taking the inertia, flexural rigidity, and spring stiffness effects of the elastic plate into account. Here, we solve the above eigenvalue problem using Chebyshev collocation methods to obtain the neutral curve in the k-Re plane and the temporal growth rate under varying values of odd viscosity. There is an interesting finding that, for moderate Reynolds numbers, the presence of odd viscosity leads to an increase in instability when the stiffness coefficient A_{K} is small. However, as the value of the stiffness coefficient A_{K} rises, the effect of odd viscosity changes to suppress the onset of instability. Additionally, at higher Reynolds numbers and extremely small inclination angles, both shear and wall modes of falling film are observed. The results demonstrate that the unstable domain for the wall mode increases as the odd viscosity coefficient value rises, while an opposite trend occurs in the shear mode.

Electromagnetohydrodynamic (EMHD) Flow in a Microchannel with Random Surface Roughness.

This study investigates the effect of small random transverse wall roughness on electromagnetohydrodynamic (EMHD) flow is in a microchannel, employing the perturbation method based upon stationary random function theory. An exact solution of a random corrugation function ξ, which is a measure of the flow rate deviated from the case without the roughness of two plates, is obtained by integrating the spectral density. After the sinusoidal, triangular, rectangular, and sawtooth functions that satisfy the Dirichlet condition are expanded into the Fourier sine series, the spectral density of the sine function is used to represent the corrugation function. Interestingly, for sinusoidal roughness, the final expression of the corrugation function is in good agreement with our previous work. Results show that no matter the shape of the wall roughness, the flow rate always decreases due to the existence of wall corrugation. Variations of the corrugation function and the flow rate strongly depend on fluid wavenumber λ and Hartmann number Ha. Finally, the flow resistance is found to become small, and the flow rate increases with roughness that is in phase (θ = 0) compared with the one that is out of phase (θ = π).

Micro Electro-Osmotic Thrusters of Power-Law Fluids for Space Propulsion.

In this article, electro-osmotic thrusters (EOTs), which are full of non-Newtonian power-law fluids with a flow behavior index n of the effective viscosity, are theoretically investigated in a microchannel. Different values of the flow behavior index represent two kinds of non-Newtonian power-law fluids, pseudoplastic fluids (n < 1) and dilatant fluids (n > 1), which have not yet been considered to be used as propellants in micro-thrusters. Analytical solutions of the electric potential and flow velocity are obtained using the Debye-Hückel linearization assumption and the approximate scheme of hyperbolic sine function. Then, thruster performances of power-law fluids, including specific impulse, thrust, thruster efficiency, and thrust-to-power ratio, are explored in detail. Results show that these performance curves strongly depend on the flow behavior index and electrokinetic width. It is noted that the non-Newtonian pseudoplastic fluid is most suitable as a propeller solvent in micro electro-osmotic thrusters owing to its improving or optimizing deficiencies in the performances of the existing Newtonian fluid thrusters.

Alternating Current Electroosmotic Flow of Maxwell Fluid in a Parallel Plate Microchannel with Sinusoidal Roughness.

The EOF of a viscoelastic Maxwell fluid driven by an alternating pressure gradient and electric field in a parallel plate microchannel with sinusoidal roughness has been investigated within the Debye-Hückel approximation based on boundary perturbation expansion and separation of variables. Perturbation solutions were obtained for the potential distribution, the velocity and the mean velocity, and the relation between the mean velocity and the roughness. There are significant differences in the velocity amplitudes of the Newtonian and Maxwell fluids. It is shown here that the velocity distribution of the viscoelastic fluid is significantly affected by the roughness of the walls, which leads to the appearance of fluctuations in the fluid. Also, the velocity is strongly dependent on the phase difference θ of the roughness of the upper and lower plates. As the oscillation Reynolds number ReΩ increases, the velocity profile and the average velocity um(t) of AC EOF oscillate rapidly but the velocity amplitude decreases. The Deborah number De plays a similar role to ReΩ, which makes the AC EOF velocity profile more likely to oscillate. Meanwhile, phase lag χ (representing the phase difference between the electric field and the mean velocity) decreases when G and θ are increased. However, for larger λ (e.g., λ > 3), it almost has no phase lag χ.

Thermal and Flow Analysis of Fully Developed Electroosmotic Flow in Parallel-Plate Micro- and Nanochannels with Surface Charge-Dependent Slip.

This study analytically investigates the coupled effects of surface charge and boundary slip on the fully developed electroosmotic flow and thermal transfer in parallel plate micro and nanochannels under the high zeta potential. The electric potential, velocity, temperature, flow rate, and Nusselt number are obtained analytically. The main results are that the velocity of bulk flow is significantly reduced in the presence of the surface charge-dependent slip. Moreover, the maximum velocity at ζ = -125 mV is approximately twice as large as that at ζ = -25 mV. The velocity and dimensionless temperature increase as the zeta potential increases. The dimensionless temperature of the surface charge-dependent slip flow is larger than that of the surface charge-independent slip flow. For the surface charge-dependent slip flow, the maximum temperature at ζ = -125 mV is approximately four times larger than that at ζ = -25 mV. The Nusselt number decreases with Joule heating and increases with a positive heat transfer coefficient. The Nusselt number decreases as the electric field and the magnitude of the zeta potential increase. In the surface charge-dependent slip flows, the Nusselt number is smaller than that in the surface charge-independent slip flows.

The Impacts of Viscoelastic Behavior on Electrokinetic Energy Conversion for Jeffreys Fluid in Microtubes.

In this paper, the electrokinetic energy conversion (EKEC) efficiency, streaming potential of viscoelastic fluids in microtubes under an external transversal magnetic field, and an axial pressure gradient are investigated. The Jeffreys fluid is applied to model the viscoelastic fluid, and the analytic solution of velocity field is obtained using the Green's function method. The influence of different dimensionless parameters, for instance, the Deborah numbers De and De*, which are related to the relaxation time and retardation time, respectively; the dimensionless electro-kinetic width K; the dimensionless frequency ω; the volume fraction of the nanoparticles φ and the dimensionless Hartmann number Ha; and three different imposed axial periodic pressure gradients (cosine, triangular, and square) on fluid dynamics are discussed. The physical quantities are graphically described, and the influence of different parameters on the EKEC is analyzed. The results indicate that De promotes the streaming potential and EKEC efficiency of the microtube, while De* inhibits them.

Space Electroosmotic Thrusters in Ion Partitioning Soft Nanochannels.

Space electroosmotic thrusters (EOTs) are theoretically investigated in a soft charged nanochannel with a dense polyelectrolyte layer (PEL), which is considered to be more realistic than a low-density PEL. When the PEL is dense, its permittivity is smaller than the one of the electrolyte solution layer, leading to rearrangement of ions in the channel, which is denoted as the ion partitioning effect. It is noted that fluid viscosity becomes high within the PEL owing to the hydration effect. An analytical solution for electroosmotic velocity through the channel is obtained by utilizing the Debye-Hückel linearization assumption. Based on the fluid motion, thruster performances, including thrust, specific impulse, thrust-to-power ratio, and efficiency, are calculated. The ion partitioning effect leads to enhancement of the thruster velocity, while increase of the dynamic viscosity inside the PEL reduces the flow rate of the fluid. Therefore, these performances are further impacted by the dense soft material, which are discussed in detail. Moreover, changes or improvements of the thruster performances from the dense PEL to the weak PEL are presented and compared, and distributions of various energy items are also provided in this study. There is a good result whereby the increase in electric double layer thickness promotes the development of thruster performances. Ultimately, the simulated EOTs produce thrust of about 0 to 20 µN and achieve thruster efficiency of 90.40%, while maintaining an appropriate thrust-power ratio of about 1.53 mN/W by optimizing all design parameters.

Odd-viscosity-induced instability of a falling thin film with an external electric field.

The influence of odd viscosity of Newtonian fluid on the instability of thin film flowing along an inclined plane under a normal electric field is studied. By odd viscosity, we mean apart from the well-known coefficient of shear viscosity, a classical liquid with broken time-reversal symmetry is endowed with a second viscosity coefficient in biological, colloidal, and granular systems. Under the long wave approximation, a nonlinear evolution equation of the free surface is derived by the method of systematic asymptotic expansion. The effects of the odd viscosity and external electric field are considered in this evolution equation and an analytical expression of critical Reynolds number is obtained. It is interesting to find that, by linear stability analysis, the critical Reynolds number increases with odd viscosity and decreases with external strength of electric field. In other words, odd viscosity has a stable effect and electric field has a destabilized effect on flowing of thin film. In addition, through nonlinear analysis, we obtain a Ginsburg-Landau equation and find that the film has not only the supercritical stability zone and the subcritical instability zone but also the unconditional stability zone and the explosive zone. The variations of each zone with related parameters, such as the strength of electric field, odd viscosity, and Reynolds number, etc., are investigated. The results are conducive to the further development of related experiments.

The Streaming Potential of Fluid through a Microchannel with Modulated Charged Surfaces.

In this paper, the effects of asymmetrically modulated charged surfaces on streaming potential, velocity field and flow rate are investigated under the axial pressure gradient and vertical magnetic field. In a parallel-plate microchannel, modulated charged potentials on the walls are depicted by the cosine function. The flow of incompressible Newtonian fluid is two-dimensional due to the modulated charged surfaces. Considering the Debye-Hückel approximation, the Poisson-Boltzmann (PB) equation and the modified Navier-Stokes (N-S) equation are established. The analytical solutions of the potential and velocities (u and v) are obtained by means of the superposition principle and stream function. The unknown streaming potential is determined by the condition that the net ionic current is zero. Finally, the influences of pertinent dimensionless parameters (modulated potential parameters, Hartmann number and slip length) on the flow field, streaming potential, velocity field and flow rate are discussed graphically. During the flow process and under the impact of the charge-modulated potentials, the velocity profiles present an oscillating characteristic, and vortexes are generated. The results show that the charge-modulated potentials are beneficial for the enhancement of the streaming potential, velocity and flow rate, which also facilitate the mixing of fluids. Meanwhile, the flow rate can be controlled through the use of a low-amplitude magnetic field.

Electromagnetohydrodynamic Electroosmotic Flow and Entropy Generation of Third-Grade Fluids in a Parallel Microchannel.

The present paper discusses the electromagnetohydrodynamic (EMHD) electroosmotic flow (EOF) and entropy generation of incompressible third-grade fluids in a parallel microchannel. Numerical solutions of the non-homogeneous partial differential equations of velocity and temperature are obtained by the Chebyshev spectral collocation method. The effects of non-Newtonian parameter Λ, Hartman number Ha and Brinkman number Br on the velocity, temperature, Nusselt number and entropy generation are analyzed in detail and shown graphically. The main results show that both temperature and Nusselt number decrease with the non-Newtonian physical parameter, while the local and total entropy generation rates exhibit an adverse trend, which means that non-Newtonian parameter can provoke the local entropy generation rate. In addition, we also find that the increase of non-Newtonian parameter can lead to the increase of the critical Hartman number Hac.

Effects of surface charge and boundary slip on time-periodic pressure-driven flow and electrokinetic energy conversion in a nanotube.

Time-periodic pressure-driven slip flow and electrokinetic energy conversion efficiency in a nanotube are studied analytically. The slip length depends on the surface charge density. Electric potential, velocity and streaming electric field are obtained analytically under the Debye-Hückel approximation. The electrokinetic energy conversion efficiency is computed using these results. The effects of surface charge-dependent slip and electroviscous effect on velocity and electrokinetic energy conversion efficiency are discussed. The main results show that the velocity amplitude and the electrokinetic energy conversion efficiency of the surface charge-dependent slip flow are reduced compared with those of the surface charge-independent slip flow.

Spectral CT Imaging in the Differential Diagnosis of Small Bowel Adenocarcinoma From Primary Small Intestinal Lymphoma.

PURPOSE: To investigate the value of dual-energy spectral computed tomography (CT) imaging in the differential diagnosis of small bowel adenocarcinoma (SBA) from primary small intestinal lymphoma (PSIL). MATERIALS AND METHODS: We retrospectively analyzed the images of 27 SBA cases and 15 PSIL cases. These patients underwent spectral CT imaging in the arterial phase (AP) and venous phase (VP). CT attenuation values of tumors at different energy levels were measured to generate spectral attenuation curve and to calculate curve slope (λHU). Iodine concentration (IC) in tumors at AP and VP were measured and normalized to that of aorta as normalized iodine concentration (NIC). Independent samples t test was used to analyze the spectral CT parameters; Receiver operating characteristic curves were generated to evaluate the diagnostic efficacy of each parameter. RESULTS: There were significant differences between SBA and PSIL in IC (2.09 ± 0.71 vs 1.33 ± 0.15 mg/ml), NIC (0.20 ± 0.06 vs 0.13 ± 0.02) and slope (λHU) (2.78 ± 1.06 vs 1.86 ± 0.30) in AP and (1.86 ± 0.68 vs 1.37 ± 0.18 mg/ml for IC; 0.47 ± 0.13 vs 0.33 ± 0.02 for NIC and 2.00 ± 0.56 vs 1.50 ± 0.26 for λHU) in VP (all p < 0.05). For the CT value measurement, there were significant differences between SBA and PSIL in the 40-60keV energy range (p < 0.05), but not in the 70-140keV range (p > 0.05). Using 1.38 mg/ml as a threshold value for iodine concentration at AP, one could obtain the area-under-curve of 0.93 for receiver operating characteristic study and sensitivity of 94% and specificity of 85% for differentiating SBA from PSIL. The sensitivity and specificity values were significantly higher than the respective values of 62% and 60% with the conventional CT numbers at 70keV. CONCLUSION: Quantitative parameters obtained in spectral CT, especially iodine concentration in AP, provide high accuracy for differentiating SBA from PSIL.

Heat Transport of Electrokinetic Flow in Slit Soft Nanochannels.

Soft nanochannels are defined as nanochannels with a polyelectrolyte layer (PEL) on the rigid walls. In the present study, the thermal transport properties of the fluids through slit soft nanochannels are investigated under the combined influences of pressure-driven and streaming potential. Based on the analytical solutions of electric potential and velocity distributions, a dimensionless temperature of electrolyte solution in soft nanochannels is obtained by resolving the energy equation. Then, a finite difference method is used to compute the energy equation and test the validity of the analytical solution. Results show that the temperature increases with the decrease of dimensionless velocity and the heat transfer rate for rigid nanochannel are higher than that for the soft one. Moreover, we find the total entropy generation decreases with the increases of the ratio Kλ of the electrical double layer (EDL) thickness in PEL to the EDL thickness on the solid wall.

Electrokinetic energy conversion efficiency of viscoelastic fluids in a polyelectrolyte-grafted nanochannel.

In order to conduct extensive investigation of energy harvesting capabilities of nanofluidic devices, we provide analytical solutions for streaming potential and electrokinetic energy conversion (EKEC) efficiency through taking the combined consequences of soft nanochannel, a rigid nanochannel whose surface is covered by charged polyelectrolyte layer, and viscoelastic rheology into account. The viscoelasticity of the fluid is considered by employing the Maxwell constitutive model when the forcing frequency of an oscillatory driving pressure flow matches with the inverse of the relaxation time scale of a typical viscoelastic fluid. We compare the streaming potential and EKEC efficiency with those of a rigid nanochannel, having zeta potential equal to the electrostatic potential at the solid-polyelectrolyte interface of the soft nanochannels. Within the present selected parameter ranges, it is shown that the different peaks of maximal streaming potential and EKEC efficiency for the rigid nanochannel are larger than those for the soft nanochannel when forcing frequencies of the driving pressure gradient are close to resonating frequencies. However, more enhanced streaming potential and EKEC efficiency for a soft nanochannel can be found in most of the regions away from these resonant frequencies. Moreover, the influence of several dimensionless parameters on EKEC efficiency is discussed in detail. Finally, within the given parametric regions, the maximum efficiency at some resonant frequency obtained in present analysis is about 25%.

Alternating current electroosmotic flow in polyelectrolyte-grafted nanochannel.

In this work, we investigate the time periodic electroosmotic flow (EOF) of an electrolyte solution through a slit polyelectrolyte-grafted (PE-grafted) nanochannel under applied alternating current (AC) electrical field. The PE-grafted nanochannel is represented by a rigid surface covered by a polyelectrolyte layer (PEL) in a brush-like configuration. Under Debye-Hückel approximation, we obtain analytical solutions of electrical potential in decoupled regime of PE-grafted nanochannel, where the thickness of PEL is independent of the electrostatic effects triggered by polyelectrolyte charges. Based upon the electrical potential obtained above, we calculate EOF velocities with uniform and non-uniform drag coefficients for PE-grafted nanochannel and compare their results. The effects of pertinent dimensionless parameters on EOF velocity amplitude are discussed in detail. Moreover, the amplitude of EOF velocity in a PE-grafted nanochannel is compared with that in a rigid one. It is shown that larger EOF velocity and volume flow rate are found for a PE-grafted nanochannel. In addition, AC EOF velocity is further investigated. The oscillation of velocity reduces and is restricted within the region near the PEL-electrolyte interface for higher oscillating Reynolds number Re.

Electroosmotic flow through a microparallel channel with 3D wall roughness.

In this paper, a perturbation method is introduced to study the EOF in a microparallel channel with 3D wall roughness. The corrugations of the two walls are periodic sinusoidal waves of small amplitude in two directions either in phase or half-period out of phase. Based on linearized Poisson-Boltzmann equation, Laplace equation, and the Navier-Stokes equations, the perturbation solutions of velocity, electrical potential, and volume flow rate are obtained. By using numerical computation, the influences of the wall corrugations on the mean velocity are analyzed. The variations of electrical potential, velocity profile, mean velocity, and their dependences on the wave number α and ß of wall corrugations in two directions, the nondimensional electrokinetic width K, and the zeta potential ratio between the lower wall and the upper wall ς are analyzed graphically.

Electromagnetohydrodynamic (EMHD) flow between two transversely wavy microparallel plates.

In this paper, 2D electromagnetohydrodynamic (EMHD) flow in a microparallel channel with slightly transverse corrugated walls is investigated using perturbation method. The corrugations of the two walls are presented by periodic sinusoidal waves with small amplitudes. The perturbation solutions of the stream function and a relation between flow rate and roughness are obtained. It is shown that the flow rate always decreases due to the wall corrugations irrespective of the phase difference. For prescribed Hartmann number and wave number of the wavy walls, the flow resistance increases as the phase difference between the wall corrugations increases. The effect of corrugation on the flow rate decreases with Hartmann number. With the increase of wave number, the effects of corrugations on the flow rate increase. The phase difference of wall corrugations becomes unimportant when the wave number is greater than 4. The obtained results for the flow rates as a function of the applied current are in qualitative agreement with the existing experimental results.