1,720,975 research outputs found
Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua
No full textA critical, albeit simple experimental and/or molecular-dynamic (MD) simulation test is proposed whose outcome would, in principle, establish the viability of the Navier-Stokes-Fourier (NSF) equations for compressible fluid continua. The latter equation set, despite its longevity as constituting the fundamental paradigm of continuum fluid mechanics, has recently been criticized on the basis of its failure to properly incorporate volume transport phenomena—as embodied in the proposed bivelocity paradigm [ H. Brenner Int. J. Eng. Sci. 54 67 (2012)]—into its formulation. Were the experimental or simulation results found to accord, even only qualitatively, with bivelocity predictions, the temperature distribution in a gas-filled, thermodynamically and mechanically isolated circular cylinder undergoing steady rigid-body rotation in an inertial reference frame would not be uniform; rather, the temperature would be higher at the cylinder wall than along the axis of rotation. This radial temperature nonuniformity contrasts with the uniformity of the temperature predicted by the NSF paradigm for these same circumstances. Easily attainable rates of rotation in centrifuges and readily available tools for measuring the expected temperature differences render experimental execution of the proposed scheme straightforward in principle. As such, measurement—via experiment or MD simulation—of, say, the temperature difference ΔT between the gas at the wall and along the axis of rotation would provide quantitative tests of both the NSF and bivelocity hydrodynamic models, whose respective solutions for the stated set of circumstances are derived in this paper. Independently of the correctness of the bivelocity model, any temperature difference observed during the proposed experiment or simulation, irrespective of magnitude, would preclude the possibility of the NSF paradigm being correct for fluid continua, except for incompressible flows
Phoresis in fluids
No full textThis paper presents a unified theory of phoretic phenomena in single-component fluids. Simple formulas are given for the phoretic velocities of small inert force-free non-Brownian particles migrating through otherwise quiescent single-component gases and liquids and animated by a gradient in the fluid's temperature (thermophoresis), pressure (barophoresis), density (pycnophoresis), or any combination thereof. The ansatz builds upon a recent paper [ Phys. Rev. E 84 046309 (2011)] concerned with slip of the fluid's mass velocity at solid surfaces—that is, with phenomena arising from violations of the classical no-slip fluid-mechanical boundary condition. Experimental and other data are cited in support of the phoretic model developed herein
Fluid mechanics in fluids at rest
No full textUsing readily available experimental thermophoretic particle-velocity data it is shown, contrary to current teachings, that for the case of compressible flows independent dye- and particle-tracer velocity measurements of the local fluid velocity at a point in a flowing fluid do not generally result in the same fluid velocity measure. Rather, tracer-velocity equality holds only for incompressible flows. For compressible fluids, each type of tracer is shown to monitor a fundamentally different fluid velocity, with (i) a dye (or any other such molecular-tagging scheme) measuring the fluid's mass velocity v appearing in the continuity equation and (ii) a small, physicochemically and thermally inert, macroscopic (i.e., non-Brownian), solid particle measuring the fluid's volume velocity v[subscript v]. The term “compressibility” as used here includes not only pressure effects on density, but also temperature effects thereon. (For example, owing to a liquid's generally nonzero isobaric coefficient of thermal expansion, nonisothermal liquid flows are to be regarded as compressible despite the general perception of liquids as being incompressible.) Recognition of the fact that two independent fluid velocities, mass- and volume-based, are formally required to model continuum fluid behavior impacts on the foundations of contemporary (monovelocity) fluid mechanics. Included therein are the Navier-Stokes-Fourier equations, which are now seen to apply only to incompressible fluids (a fact well-known, empirically, to experimental gas kineticists). The findings of a difference in tracer velocities heralds the introduction into fluid mechanics of a general bipartite theory of fluid mechanics, bivelocity hydrodynamics [ Brenner Int. J. Eng. Sci. 54 67 (2012)], differing from conventional hydrodynamics in situations entailing compressible flows and reducing to conventional hydrodynamics when the flow is incompressible, while being applicable to both liquids and gases
Conduction-only transport phenomena in compressible bivelocity fluids: Diffuse interfaces and Korteweg stresses
No full text“Diffuse interface” theories for single-component fluids—dating back to van der Waals, Korteweg, Cahn-Hilliard, and many others—are currently based upon an ad hoc combination of thermodynamic principles (built largely upon Helmholtz's free-energy potential) and so-called “nonclassical” continuum-thermomechanical principles (built largely upon Newtonian mechanics), with the latter originating with the pioneering work of Dunn and Serrin [Arch. Ration. Mech. Anal. 88, 95 (1985)]. By introducing into the equation governing the transport of energy the notion of an interstitial work-flux contribution, above and beyond the usual Fourier heat-flux contribution, namely, j[subscript q] = −k∇T, to the energy flux, Dunn and Serrin provided a rational continuum-thermomechanical basis for the presence of Korteweg stresses in the equation governing the transport of linear momentum in compressible fluids. Nevertheless, by their failing to recognize the existence and fundamental need for an independent volume transport equation [Brenner, Physica A 349, 11 (2005)]—especially for the roles played therein by the diffuse volume flux j[subscript v] and the rate of production of volume π[subscript v] at a point of the fluid continuum—we argue that diffuse interface theories for fluids stand today as being both ad hoc and incomplete owing to their failure to recognize the need for an independent volume transport equation for the case of compressible fluids. In contrast, we point out that bivelocity hydrodynamics, as it already exists [Brenner, Phys. Rev. E 86, 016307 (2012)], provides a rational, non-ad hoc, and comprehensive theory of diffuse interfaces, not only for single-component fluids, but also for certain classes of crystalline solids [Danielewski and Wierzba, J. Phase Equilib. Diffus. 26, 573 (2005)]. Furthermore, we provide not only what we believe to be the correct constitutive equation for the Korteweg stress in the class of fluids that are constitutively Newtonian in their rheological response to imposed stresses but, equally importantly, we establish the explicit functional forms of Korteweg's phenomenological thermocapillary coefficients appearing therein
Beyond the no-slip boundary condition
No full textThis paper offers a simple macroscopic approach to the question of the slip boundary condition to be imposed upon the tangential component of the fluid velocity at a solid boundary. Plausible reasons are advanced for believing that it is the energy equation rather than the momentum equation that determines the correct fluid-mechanical boundary condition. The scheme resulting therefrom furnishes the following general, near-equilibrium linear constitutive relation for the slip velocity of mass along a relatively flat wall bounding a single-component gas or liquid: (v[subscript ]m)[subscript slip]=−α∂lnρ/∂s|[subscript wall], where α and ρ are, respectively, the fluid's thermometric diffusivity and mass density, while the length δs refers to distance measured along the wall in the direction in which the slip or creep occurs. This constitutive relation is shown to agree with experimental data for gases and liquids undergoing thermal creep or pressure-driven viscous creep at solid surfaces
Self-thermophoresis and thermal self-diffusion in liquids and gases
No full textThis paper demonstrates the existence of self-thermophoresis, a phenomenon whereby a virtual thermophoretic force arising from a temperature gradient in a quiescent single-component liquid or gas acts upon an individual molecule of that fluid in much the same manner as a “real” thermophoretic force acts upon a macroscopic, non-Brownian body immersed in that same fluid. In turn, self-thermophoresis acting in concert with Brownian self-diffusion gives rise to the phenomenon of thermal self-diffusion in single-component fluids. The latter furnishes quantitative explanations of both thermophoresis in pure fluids and thermal diffusion in binary mixtures (the latter composed of a dilute solution of a physicochemically inert solute whose molecules are large compared with those of the solvent continuum). Explicitly, the self-thermophoretic theory furnishes a simple expression for both the thermophoretic velocity U of a macroscopic body in a single-component fluid subjected to a temperature gradient ∇T, and the intimately related binary thermal diffusion coefficient DT for a two-component colloidal or macromolecular mixture. The predicted expressions U=−DT∇T≡−βDS∇T and DT=βDS (with β and DS the pure solvent’s respective thermal expansion and isothermal self-diffusion coefficients) are each noted to accord reasonably well with experimental data for both liquids and gases. The likely source of systematic deviations of the predicted values of DT from these data is discussed. This appears to be the first successful thermodiffusion theory applicable to both liquids and gases, a not insignificant achievement considering that the respective thermal diffusivities and thermophoretic velocities of these two classes of fluids differ by as much as six orders of magnitude
Predicting enhanced mass flow rates in gas microchannels using nonkinetic models
No full textDifferent nonkinetic approaches are adopted in this paper towards theoretically predicting the experimentally observed phenomenon of enhanced mass flow rates accompanying pressure-driven rarefied gas flows through microchannels. Our analysis utilizes a full set of mechanically consistent volume-diffusion hydrodynamic equations, allowing complete, closed-form, analytical solutions to this class of problems. As an integral part of the analysis, existing experimental data pertaining to the subatmospheric pressure dependence of viscosity were analyzed. The several nonkinetic approaches investigated were (1) pressure-dependent viscosity exponent model, (2) slip-velocity models, and (3) volume diffusion model. We explored the ability to predict the gas's mass flow rate over the full range of Knudsen numbers, including furnishing a physically sound interpretation of the well-known Knudsen minimum observed in the mass flow rate. Matching of a pressure-dependent viscosity model, one that follows the standard temperature-viscosity power law and its supporting single momentum diffusion mechanism, did not allow an accurate interpretation of the data. Rather, matching of this model with the flow rate was found to mismatch the experimental pressure dependence of the viscosity. An additional transport mechanism model, one based on volume diffusion, offered a comprehensive understanding of the Knudsen minimum, while also resulting in excellent agreement with experimental data well into the transition regime (up to a Knudsen number of 5)
Fullerene Embedded Shape Memory Nanolens Array
No full textSecuring fragile nanostructures against external impact is indispensable for offering sufficiently long lifetime in service to nanoengineering products, especially when coming in contact with other substances. Indeed, this problem still remains a challenging task, which may be resolved with the help of smart materials such as shape memory and self-healing materials. Here, we demonstrate a shape memory nanostructure that can recover its shape by absorbing electromagnetic energy. Fullerenes were embedded into the fabricated nanolens array. Beside the energy absorption, such addition enables a remarkable enhancement in mechanical properties of shape memory polymer. The shape memory nanolens was numerically modeled to impart more in-depth understanding on the physics regarding shape recovery behavior of the fabricated nanolens. We anticipate that our strategy of combining the shape memory property with the microwave irradiation feature can provide a new pathway for nanostructured systems able to ensure a long-term durability
Comment on “No-Slip Condition for a Mixture of Two Liquids”
Full text linkA Comment on the Letter by Joel Koplik and Jayanth R. Banavar, Phys. Rev. Lett. 80, 6125 (1998). The authors of the Letter offer a Reply
Multiplex Particle Focusing via Hydrodynamic Force in Viscoelastic Fluids
No full textWe introduce a multiplex particle focusing phenomenon that arises from the hydrodynamic interaction between the viscoelastic force and the Dean drag force in a microfluidic device. In a confined microchannel, the first normal stress difference of viscoelastic fluids results in a lateral migration of suspended particles. Such a viscoelastic force was harnessed to focus different sized particles in the middle of a microchannel, and spiral channel geometry was also considered in order to take advantage of the counteracting force, Dean drag force that induces particle migration in the outward direction. For theoretical understanding, we performed a numerical analysis of viscoelastic fluids in the spiral microfluidic channel. From these results, a concept of the ‘Dean-coupled Elasto-inertial Focusing band (DEF)’ was proposed. This study provides in-depth physical insight into the multiplex focusing of particles that can open a new venue for microfluidic particle dynamics for a concrete high throughput platform at microscale
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