Ray theory for high-Péclet-number convection-diffusion

Asymptotic methods based on those of geometrical optics are applied to some steady convection-diffusion streamed flows at a high Péclet number. Even with the assumption of inviscid, irrotational flow past a body with uniform ambient conditions, the rays from which the solution is constructed can only be found after local analyses have been carried out near the stagnation points. In simple cases, the temperature away from the body is the sum of contributions from each stagnation point

Modeling non-equilibrium mass transport in biologically reactive porous media.

We develop a one-equation non-equilibrium model to describe the Darcy-scale transport of a solute undergoing biodegradation in porous media. Most of the mathematical models that describe the macroscale transport in such systems have been developed intuitively on the basis of simple conceptual schemes. There are two problems with such a heuristic analysis. First, it is unclear how much information these models are able to capture; that is, it is not clear what the model's domain of validity is. Second, there is no obvious connection between the macroscale effective parameters and the microscopic processes and parameters. As an alternative, a number of upscaling techniques have been developed to derive the appropriate macroscale equations that are used to describe mass transport and reactions in multiphase media. These approaches have been adapted to the problem of biodegradation in porous media with biofilms, but most of the work has focused on systems that are restricted to small concentration gradients at the microscale. This assumption, referred to as the local mass equilibrium approximation, generally has constraints that are overly restrictive. In this article, we devise a model that does not require the assumption of local mass equilibrium to be valid. In this approach, one instead requires only that, at sufficiently long times, anomalous behaviors of the third and higher spatial moments can be neglected; this, in turn, implies that the macroscopic model is well represented by a convection–dispersion–reaction type equation. This strategy is very much in the spirit of the developments for Taylor dispersion presented by Aris (1956). On the basis of our numerical results, we carefully describe the domain of validity of the model and show that the time-asymptotic constraint may be adhered to even for systems that are not at local mass equilibrium

Microfluidics: Fluid physics at the nanoliter scale

Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Péclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world

Upscaling of non-isothermal reactive porous media flow under dominant Péclet number : the effect of changing porosity

Motivated by rock-fluid interactions occurring in a geothermal reservoir, we present a two-dimensional pore scale model of a thin strip consisting of void space and grains, with fluid flow through the void space. Ions in the fluid are allowed to precipitate onto the grains, while minerals in the grains are allowed to dissolve into the fluid, taking into account the possible change in the aperture of the strip that these two processes cause. Temperature variations and possible effects of the temperature in both fluid density and viscosity and in the mineral precipitation and dissolution reactions are included. For the pore scale model equations, we investigate the limit as the width of the strip approaches zero, deriving onedimensional effective equations. We assume that the convection is dominating over diffusion in the system, resulting in Taylor dispersion in the upscaled equations and a Forchheimer-type term in Darcy’s law. Some numerical results where we compare the upscaled model with three simpler versions are presented; two still honoring the changing aperture of the strip but not including Taylor dispersion, and one where the aperture of the strip is fixed but contains dispersive terms

Influence of asperities on fluid and thermal flow in a fracture: a coupled Lattice Boltzmann study

The characteristics of the hydro-thermal flow which occurs when a cold fluid is injected into a hot fractured bedrock depend on the morphology of the fracture. We consider a sharp triangular asperity, invariant in one direction, perturbing an otherwise flat fracture. We investigate its influence on the macroscopic hydraulic transmissivity and heat transfer efficiency, at fixed low Reynolds number. In this study, numerical simulations are done with a coupled lattice Boltzmann method that solves both the complete Navier-Stokes and advection-diffusion equations in three dimensions. The results are compared with those obtained under lubrication approximations which rely on many hypotheses and neglect the three-dimensional (3D) effects. The lubrication results are obtained by analytically solving the Stokes equation and a two-dimensional (integrated over the thickness) advection-diffusion equation. We use a lattice Boltzmann method with a double distribution (for mass and energy transport) on hypercubic and cubic lattices. Beyond some critical slope for the boundaries, the velocity profile is observed to be far from a quadratic profile in the vicinity of the sharp asperity: the fluid within the triangular asperity is quasi-static. We find that taking account of both the 3D effects and the cooling of the rock, are important for the thermal exchange. Neglecting these effects with lubrication approximations results in overestimating the heat exchange efficiency. The evolution of the temperature over time, towards steady state, also shows complex behavior: some sites alternately reheat and cool down several times, making it difficult to forecast the extracted heat.Comment: In Journal of Geophysical Research B (2013) online firs

Upscaling of non-isothermal reactive porous media flow under dominant Péclet number : the effect of changing porosity

Motivated by rock-fluid interactions occurring in a geothermal reservoir, we present a two-dimensional pore scale model of a thin strip consisting of void space and grains, with fluid flow through the void space. Ions in the fluid are allowed to precipitate onto the grains, while minerals in the grains are allowed to dissolve into the fluid, taking into account the possible change in the aperture of the strip that these two processes cause. Temperature variations and possible effects of the temperature in both fluid density and viscosity and in the mineral precipitation and dissolution reactions are included. For the pore scale model equations, we investigate the limit as the width of the strip approaches zero, deriving onedimensional effective equations. We assume that the convection is dominating over diffusion in the system, resulting in Taylor dispersion in the upscaled equations and a Forchheimer-type term in Darcy’s law. Some numerical results where we compare the upscaled model with three simpler versions are presented; two still honoring the changing aperture of the strip but not including Taylor dispersion, and one where the aperture of the strip is fixed but contains dispersive terms

Dynamo cycles in global convection simulations of solar-like stars

Several solar-like stars exhibit cyclic magnetic activity similar to the Sun as found in photospheric and chromospheric emission. We want to understand the physical mechanism involved in rotational dependence of these activity cycle periods. We use three-dimensional magnetohydrodynamical simulations of global convective dynamos models of solar-like stars to investigate the rotational dependency of dynamos. We further apply the test-field method to determine the $\alpha$ effect in these simulations. We find dynamo with clear oscillating mean magnetic fields for moderately and rapidly rotating runs. For slower rotation, the field is constant or exhibit irregular cycles. In the moderately and rapidly rotating regime the cycle periods increase weakly with rotation. This behavior can be well explained with a Parker-Yoshimura dynamo wave traveling equatorward. Even though the $\alpha$ effect becomes stronger for increasing rotation, the shear decreases steeper, causing this weak dependence on rotation. Similar as other numerical studies, we find no indication of activity branches as suggested by Brandenburg et al. (1998). However, our simulation seems to agree more with the transitional branch suggested by Distefano et al. (2017) and Olspert et al. (2017). If the Sun exhibit a dynamo wave similar as we find in our simulations, it would operate deep inside the convection zone.Comment: 11 pages, 10 figures, accepted for publication in A&

Influence of Gravity on Atomic Mobility in a Liquid

Measurements of diffusion and thermodiffusion in liquids are very sensitive to convection caused for example by buoyancy. To reduce the impact of buoyancy-driven convection, benchmark experiments are performed in microgravity conditions. Here, we discuss the general influence of gravity on atomic mobility. The gravitational Peclet number and the gravitational length can be used to assess this influence. They show that the diffusion processes of atoms in a liquid is not affected by Earth’s gravitational force but that the process is dominated by the thermal energy of the atoms. Data from experiments under different gravity conditions ranging from 10^-5 g to 10^6 g are summarized. They confirm that interdiffusion is only influenced by accelerations that are orders of magnitude larger than Earth’s gravity

Understanding the Role of Gravity in the Crystallization Suppression of ZBLAN Glass

Fluorozirconate glasses, such as ZBLAN (ZrF4-BaF2-LaF3-AlF3-NaF), have the potential for optical transmission from 0.3 μm in the UV to 7 μm in the IR region. However, crystallites formed during the fiber drawing process prevent this glass from achieving its low loss-capability. Other researchers have shown that microgravity processing leads to suppressed crystal growth in ZBLAN glass, which can lead to lower transmission loss in the desired mid-IR range. However, the mechanism governing crystal growth suppression has not been thoroughly investigated. In the present research multiple ZBLAN samples were subjected to a heating and quenching test apparatus on a parabolic aircraft under controlled μ-g and hyper-g environments and compared with 1-g ground tests. Optical microscopy (transmission and polarized) along with SEM examination elucidates that crystal growth in ZBLAN is suppressed when processed in a microgravity environment. Hence crystallization occurs at a higher temperature in μ-g and the working temperature range at which the fiber can be manufactured has been extended. We postulate that the fundamental process of nano-scale mass transfer (lack of buoyancy driven convection) in the viscous glass is the mechanism responsible for crystal growth suppression in microgravity. Suppressing molecular mobility within the semi-molten glass starves nucleating crystallites and prevents any further growth. A COMSOL Multi-Physics model was developed to show the velocity contours due to convection processes in a 1-g, μ-g, and hyper-g environment. Analytical models show that while suppressing convection is relevant at fiber drawing temperatures (360°C), mass transfer due to diffusion dominates at higher temperatures leading to crystal growth at temperatures 65400°C. ZBLAN fibers are also known for their poor handling ability. Therefore an analysis of the thermal degradation of ZBLAN optical fibers based on fracture mechanics was also conducted. Conditions of crack initiation and stable versus unstable crack growth leading to fiber fracture were analyzed to explain behavior observed from controlled flexure tests of ZBLAN optical fibers exposed to various temperatures