Conduction-only transport phenomena in compressible bivelocity fluids: diffuse interfaces and Korteweg stresses.

"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.

Fullerene embedded shape memory nanolens array.

Securing 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.

Multiplex particle focusing via hydrodynamic force in viscoelastic fluids.

We 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.

Proposal of a critical test of the Navier-Stokes-Fourier paradigm for compressible fluid continua.

A 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.

Thermal and viscous effects on sound waves: revised classical theory.

In this paper the recently developed, bi-velocity model of fluid mechanics based on the principles of linear irreversible thermodynamics (LIT) is applied to sound propagation in gases taking account of first-order thermal and viscous dissipation effects. The results are compared and contrasted with the classical Navier-Stokes-Fourier results of Pierce for this same situation cited in his textbook. Comparisons are also made with the recent analyses of Dadzie and Reese, whose molecularly based sound propagation calculations furnish results virtually identical with the purely macroscopic LIT-based bi-velocity results below, as well as being well-supported by experimental data.

Predicting enhanced mass flow rates in gas microchannels using nonkinetic models.

Different 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.

Fluid mechanics in fluids at rest.

Using 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.

Phoresis in fluids.

This 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.

Beyond the no-slip boundary condition.

This 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(m))(slip)=-α∂lnρ/∂s|(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.

Self-thermophoresis and thermal self-diffusion in liquids and gases.

This 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).

A critical test of bivelocity hydrodynamics for mixtures.

The present paper provides direct noncircumstantial evidence in support of the existence of a diffuse flux of volume j(v) in mixtures. As such, it supersedes an earlier paper [H. Brenner, J.

Circumstantial evidence in support of bivelocity hydrodynamic theory for mixtures.

Based upon findings with respect to the viability of the expression j(v)=-rhoD(v)nablav hypothesized to represent the constitutive equation for the diffusive volume flux in ideal binary mixtures (rho=mass density, v=1/rho=specific volume, and D(v)=volume diffusion coefficient), implicit evidence is offered in support of the recently developed theory of bivelocity continuum hydrodynamics for mixtures. Present findings for the case of mixtures add to existing evidence already available for the single-component case, thus supporting the viability of bivelocity hydrodynamic theory in general.

Dispersion phenomena in helical flow in a concentric annulus.

We examined dispersion phenomena of solutes in helical flow in a concentric annulus through a multiscale approach. The helical flow was developed by the combination of the Poiseuille flow and Couette flow. Here, we present an analytic model that can address the multidimensional Taylor dispersion in the helical flow under a lateral field of thermophoresis (or thermal diffusion) in the gapwise direction.

Multiscale analysis of thermal field flow fractionation through macrotransport approach.

We introduce the general theory of macrotransport processes to analyze thermal field flow fractionation (ThFFF). Multiscale analysis is carried out by adopting local and total moments. It is shown that the scheme of macrotransport processes is easier to apply and mathematically straightforward than exiting microscopic methods.

Elementary kinematical model of thermal diffusion in liquids and gases.

An elementary hydrodynamic and Brownian motion model of the thermal diffusivity D(T) of a restricted class of binary liquid mixtures, previously proposed by the author, is given a more transparent derivation than originally, exposing thereby the strictly kinematic-hydrodynamic nature of an important class of thermodiffusion separation phenomena. Moreover, it is argued that the solvent's thermometric diffusivity alpha appearing in that theory as one of the two fundamental parameters governing D(T) should be replaced by the solvent's (isothermal) self-diffusivity D(S). In addition, a corrective multiplier of O(1) is inserted to reflect the general physicochemical noninertness of the solute relative to the solvent, thus enhancing the applicability of the resulting formula D(T)=lambdaD(S)beta to "nonideal" solutions.

Nonisothermal Brownian motion: Thermophoresis as the macroscopic manifestation of thermally biased molecular motion.

A quiescent single-component gravity-free gas subject to a small steady uniform temperature gradient T, despite being at rest, is shown to experience a drift velocity UD=-D* gradient ln T, where D* is the gas's nonisothermal self-diffusion coefficient. D* is identified as being the gas's thermometric diffusivity alpha. The latter differs from the gas's isothermal isotopic self-diffusion coefficient D, albeit only slightly.

Is the tracer velocity of a fluid continuum equal to its mass velocity?

Owing to its size independence in the so-called near-continuum vanishingly small Knudsen number regime (Kn<<1) , thermophoretic particle motion occurring in an otherwise quiescent gas under the influence of a temperature gradient is here interpreted as representing the motion of a tracer, namely, an effectively point-size test particle monitoring the local velocity of the undisturbed, particle-free, compressible gas continuum through space. "Compressibility" refers here not to the usual effect of pressure on the gas's mass density rho but rather to the effect thereon of temperature. Our unorthodox continuum interpretation of thermophoresis differs from the usual one, which regards the existence of thermophoretic forces in gases as a strictly noncontinuum phenomenon, involving thermal stress-induced Maxwell slip ("thermal creep") of the gas's mass velocity vm at the surface of the particle, with vm denoting the velocity appearing in the continuity equation expressing the law of conservation of mass.

Separation mechanisms underlying vector chromatography in microlithographic arrays.

Micropatterned chips possessing an asymmetric, spatially periodic array of obstacles enable the vector (directional) chromatographic separation of charged particles animated by an external electric field. We apply a network theory to analyze the chip-scale (L-scale) transport of finite-size Brownian particles in such devices and identify those factors that break the symmetry of the chip-scale particle mobility tensor, most importantly the hydrodynamic wall effects between the particles and the obstacle surfaces. Our analysis contrasts with prevailing separation theories, which are limited to effectively point-size particles, for which wall effects are negligible.

Body versus surface forces in continuum mechanics: is the Maxwell stress tensor a physically objective Cauchy stress?

The Maxwell stress tensor (MST) T(M) plays an important role in the dynamics of continua interacting with external fields, as in the commercially and scientifically important case of "ferrofluids." As a conceptual entity in quasistatic systems, the MST derives from the definition f(M)def=inverted Delta x T(M), where f(M)(x) is a physically objective volumetric external body-force density field at a point x of a continuum, derived from the solution of the pertinent governing equations. Beginning with the fact that T(M) is not uniquely defined via the preceding relationship from knowledge of f(M), we point out in this paper that the interpretation of T(M) as being a physical stress is not only conceptually incorrect, but that in commonly occuring situations this interpretation will result in incorrect predictions of the physical response of the system.

Generalized Taylor-Aris dispersion in discrete spatially periodic networks: microfluidic applications.

A theory is presented for the lumped parameter, convective-diffusive transport of individual, noninteracting Brownian solute particles ("macromolecules") moving within spatially periodic, solvent-filled networks--the latter representing models of chip-based microfluidic chromatographic separation devices, as well as porous media. Using graph-theoretical techniques, the composite medium is conceptually decomposed into a network of channels (the edges) through which the solute is transported by a combination of molecular diffusion and either "piggyback" entrainment within a flowing solvent or an externally applied force field acting upon the solute molecules. A probabilistic choice of egress channel for a solute particle exiting the intersection (vertex) of the channels is furnished by an imperfect mixing model.

"Vector Chromatography": Modeling Micropatterned Separation Devices.

A repetitive sequence of quiescent fluid layers of differing viscosities through which small spherical Brownian particles move is analyzed in order to illustrate in a simple context how the theory of macrotransport processes, a generalization of Taylor dispersion theory, may be employed to rigorously analyze spatially periodic micropatterned chromatographic separation devices for circumstances in which the solute species to be separated are animated by the action of species-specific external forces oriented asymmetrically relative to the body-fixed pattern. In the generic "vector" separation scheme, illustrated by our elementary example, the different species undergoing separation move, on average, in different directions relative to pattern-fixed axes, whence their chromatographic sorting is effected according to their different mean angular trajectories through the device. This scheme differs fundamentally from traditional "scalar" chromatographic separation schemes, wherein all species move on average parallel to the animating force (including circumstances in which they are passively entrained in a unidirectional solvent flow) and hence for which the sorting is effected by the relative speeds of the several species through the chromatographic column.