Low Viscosity Region Research Articles

Study of the impurity dissolution kinetics, rheological characterization, and hydrodynamic aspects during the bioleaching of iron ore pulp in a bioreactor

AbstractThis research aims to study the rheological behavior and impurities dissolution kinetics in a bioleaching process of two particle sizes and three different pulp densities, which are analyzed and compared. It was found that the small particle size with 40% (w/w) pulp density provides the maximum dissolution of impurities in the shortest bioleaching time (in 2 days). Furthermore, through a CFD simulation in a system with 40% (w/w) pulp density and 44 μm particle size, a stirring speed of 700 rpm provides the best mixing conditions in the bioreactor, enabling good distribution of recirculation zones and adequate streamline patterns with a viscosity map that minimizes regions of high and low viscosity. Graphical abstract

Robust surface light scattering spectroscopy for fluid interfaces

Surface Light Scattering Spectroscopy (SLSS) can characterize the dynamics of an interface between two immiscible fluids by measuring the frequency spectrum of coherent light scattered from thermophysical fluctuations—‘ripplons’. In principle, and for many interfaces, SLSS can simultaneously measure surface tension and viscosity, with the potential for higher-order properties, such as surface elasticity and bending moments. Previously, this has been challenging. We describe and present some measurements from an instrument with improvements in optical design, specimen access, vibrational stability, signal-to-noise ratio, electronics, and data processing. Quantitative improvements include total internal reflection at the interface to enhance the typically available signal by a factor of order 40 and optical improvements that minimize adverse effects of sloshing induced by external vibrations. Information retrieval is based on a comprehensive surface response function, an instrument function, which compensates for real geometrical and optical limitations, and processing of almost real-time data to report results and their likely accuracy. Detailed models may be fit to the power spectrum in real time. The raw one-dimensional digitized data stream is archived to allow post-experiment processing. This paper reports a system design and implementation that offers substantial improvements in accuracy, simplicity, ease of use, and cost. The presented data are for systems in regions of low viscosity where the ripplons are underdamped, but the hardware described is more widely applicable.

Experimental Study on Droplet Splash and Receding Breakup on a Smooth Surface at Atmospheric Pressure.

Droplet impact on a smooth solid surface at atmospheric pressure was experimentally studied and physically interpreted. A particular emphasis of the study is on the effects of liquid viscosity on the transition between droplet deposition (or droplet spreading without breakup) and droplet disintegration (including droplet splash and receding breakup). Specifically, the critical Weber number separating droplet deposition from droplet disintegration decreases and then increases with increasing Ohnesorge number (Oh). The splash in the low-Oh region and the receding breakup in the high-Oh region were analyzed qualitatively based on the unbalanced forces acting on the rim of the spreading or receding liquid film. A semiempirical correlation of droplet deposition/disintegration thresholds is proposed and well fits the experimental results from previous and present studies over a wide range of liquid viscosity.

Green algae scatter off sharp viscosity gradients

We study the behaviour of the green alga Chlamydomonas reinhardtii (CR) in the presence of neighbouring regions of different viscosity. We show that the velocity and angular diffusion of the algae decreases when the viscosity of the surrounding medium is increased. We report on a phenomenon occurring when the algae try to cross from a region of low viscosity to a highly viscous one, which causes CR to re-orient and scatter away from the interface if it is approached at a sufficiently small angle. We highlight that the effect does not occur for CR crossing from high to low viscosity regions. Lastly we show that algae do not concentrate in the region of high viscosity despite them swimming slower there. On the contrary, they concentrate in the region of low viscosity or maintain a uniform concentration profile, depending on the viscosity ratio between the two regions.

Mixing behavior in a confined jet with disparate viscosity and implications for complex reactions

Turbulent shear-driven mixing in a coaxial and co-flowing configuration is studied using experiments and computations to understand and model the effect of viscosity gradients in the flow field. Two liquids with a large disparity in dynamic viscosity are mixed, with a low viscosity, high momentum jet directed into a high viscosity, low momentum co-flow in a pipe. Simultaneous experimental measurements of the velocity and concentration fields are made using high-resolution PIV and PLIF to obtain their turbulent cross-correlation statistics for viscosity ratios of 1 and 40. LES simulations are also performed using dynamic mixing sub-grid model to investigate the three dimensional mixing structure of the flow for the two cases. The overall structure of turbulent mixing in the coaxial confined jet configuration is studied to identify the mixing regions of the flow and the effect of viscosity gradients on the dynamics of the same. Besides the effect of Reynolds number between the two cases that manifests as reduced mixing, it was noted that the transport of turbulent kinetic energy and scalar concentration variance shows significant asymmetries that arise from the viscosity gradients in the field. The scalar mixing structure between the two cases is studied in detail with relevance to complex mixing-limited reactions frequently encountered in such environments. It was found that turbulence production and associated scalar mixing is highly skewed in variable viscosity flows, where the low viscosity regions show enhanced turbulence activity. The implications of such turbulence skewness on the chemistry of reaction systems involving variable viscosity environments are discussed in further detail.

Swimming sheet in a viscosity-stratified fluid

In this work, we theoretically investigate the motion of a Taylor swimming sheet immersed in a viscosity-stratified fluid. The propulsion of the swimmer disturbs the surrounding fluid, which influences the transport of the stratifying agent described by the advection–diffusion equation. We employ a regular perturbation scheme to solve the coupled differential equations of motion up to the second order with the small parameter given by the ratio of the wave amplitude and the wavelength. The expression for the swimming velocity is linear in the magnitude of the viscosity gradient, while depending on the Peclet number in a non-monotonic way. Interestingly, we find that the Peclet number governs the propensity of the sheet to propel towards regions of favourable viscosities. In particular, for small Peclet numbers ( $0<Pe<3$ ), the swimmer prefers regions of low viscosity, while for high Peclet numbers ( $Pe>3$ ), the swimmer prefers regions of high viscosity. Our analysis shows that purely hydrodynamic effects might be responsible for the experimentally observed accumulation of swimmers near favourable viscosity regions. We find that viscosity gradients influence other motility characteristics of the swimmer, such as power expenditure and hydrodynamic efficiency, and provide analytical expressions for both.

Toward a boot strap hypothesis of plate tectonics: Feedbacks between plates, the asthenosphere, and the wavelength of mantle convection

The solid Earth system is characterized by plate tectonics, a low viscosity zone beneath plates (the asthenosphere), and long wavelength flow in the convecting mantle. We use suites of numerical experiments to show: 1) How long wavelength flow and the operation of plate tectonics can generate and maintain an asthenosphere, and 2) How an asthenosphere can maintain long wavelength flow and plate tectonics. Plate subduction generates a sub-adiabatic temperature gradient in the mantle which, together with temperature-dependent viscosity, leads to a viscosity increase from the upper to the lower mantle. This allows mantle flow to channelize in a low viscosity region beneath plates (an asthenosphere forms dynamically). Flow channelization, in turn, stabilizes long wavelength convection. The degree of dynamic viscosity variations from the upper to the lower mantle increases with the wavelength of convection and drops toward zero if the system transitions from plate tectonics to a single plate planet. The plate margin strength needed to initiate that transition increases for long wavelength cells (long wavelength flow allows plate tectonics to exist over a wider range of plate margin strength). The coupled feedbacks allow for a linked causality between plates, the asthenosphere, and the wavelength of mantle flow, with none being more fundamental than the others and the existence of each depending on the others. Under this hypothesis, the asthenosphere is defined by an active process, plate tectonics, which maintains it and is maintained by it and plate tectonics is part of an emergent, self-sustaining flow system that bootstraps itself into existence.

Focusing and splitting streams of soft particles in microflows via viscosity gradients.

Microflows are intensively used for investigating and controlling the dynamics of particles, including soft particles such as biological cells and capsules. A classic result is the tank-treading motion of elliptically deformed soft particles in linear shear flows, which do not migrate across straight streamlines in the bulk. However, soft particles migrate across straight streamlines in Poiseuille flows. In this work we describe a new mechanism of cross-streamline migration by using soft capsules with a spherical equilibrium shape. If the viscosity varies perpendicular to the streamlines then the soft particles migrate across streamlines towards regions of a lower viscosity, even in linear shear flows. An interplay with the repulsive particle-boundary interaction causes then focusing of particles in linear shear flows with the attractor streamline closer to the wall in the low viscosity region. Viscosity variations perpendicular to the streamlines in Poiseuille flows leads either to a shift of the particle attractor or even to a splitting of particle attractors, which may give rise to interesting applications for particle separation. The location of attracting streamlines depend on the particle properties, like their size and elasticity. The cross-stream migration induced by viscosity variations is explained by analytical considerations, Stokesian dynamics simulations with a generalized Oseen tensor and lattice-Boltzmann simulations.

Multiphase mesh-free particle modeling of local sediment scouring with μ(I) rheology

Abstract Sediment scouring is a common example of highly dynamic sediment transport. Considering its complexities, the accurate prediction of such a highly dynamic multiphase granular flow system is a challenge for the traditional numerical techniques that rely on a mesh system. The mesh-free particle methods are a newer generation of numerical techniques with an inherent ability to deal with the deformations and fragmentations of a multiphase continuum. This study aims at developing and evaluating a multiphase mesh-free particle model based on the weakly compressible moving particle semi-implicit (WC-MPS) formulation for simulation of sediment scouring. The sediment material is considered as a non-Newtonian viscoplastic fluid, whose behavior is predicted using a regularized μ(I) rheological model in combination with pressure-dependent yield criteria. The model is first validated for a benchmark problem of viscoplastic Poiseuille flow. It is then applied and evaluated for the study of two classical sediment scouring cases. The results show that the high-velocity flow currents and the circulations can create a low-viscosity region on the surface of the sediment continuum. Comparing the numerical results with the experimental measurements shows a good accuracy in prediction of the sediment profile, especially the shape and dimensions of the scour hole.

Lattice Boltzmann Simulation of Immiscible Displacement in Porous Media: Viscous Fingering in a Shear-Thinning Fluid

In this work, we investigate immiscible displacement in porous media with the displaced fluid being shear-thinning. We focus on the influence the heterogeneous viscosity field in the shear-thinning fluid brings on viscous fingering, which has received little attention in the existing researches. Lattice Boltzmann simulations of immiscible displacement with a power law model implementation in the displaced fluid are conducted. The lattice Boltzmann algorithm is validated against Newtonian and non-Newtonian flows in a channel. The effects of the shear-thinning property and the viscosity heterogeneity on viscous fingering are considered in the simulations. The results show that with stronger shear-thinning property (lower power law exponent n), there is stronger viscosity heterogeneity in the displaced fluid, and the viscous fingering shows weaker instability. The influence of a heterogeneous viscosity field on viscous fingering is dominated by the viscosity in the low-viscosity regions, while the high-viscosity regions show little influence. The influence of the local viscosity on viscous fingering is dependent upon the local shear rate. A concept of ‘effective field viscosity’ is introduced to quantitatively characterize a heterogeneous viscosity field. A shear rate weighted averaging algorithm is proposed to calculate the effective field viscosity from a heterogeneous viscosity field. The algorithm is tested in several cases and shows good performance to represent the influence of the heterogeneous viscosity field.

Chemorheological behaviors of TDE-85 toughened by low viscosity liquid epoxy for RTM process

In this study, 1,4-cyclohexanedimethanol diglycidyl ether (EP-1) has been synthesized via a two-step process to toughen and lower the viscosity of TDE-85 epoxy first time and suitable for the resin transfer molding (RTM) process. Chemical structure of EP-1 and the reactivity, rheological and mechanical properties of TDE-85/MeTHPA/DMP-30/EP-1 system were studied. When the composition ratio of TDE-85/MeTHPA/EP-1/DMP-30 is 100: 140: 15: 1 and the curing process is 80 °C/2 h + 110 °C/2 h + 140 °C/2 h, the overall performance of the resin system reached to an optimal value. Impact and bending strength of the casting came out to be 27.64 kJ m−2 and 167.2 MPa, which improved 75.16% and 17.50% respectively compared to the pristine resin system without EP-1. Dynamic viscosity analysis of TDE-85/MeTHPA/DMP-30/EP-1 system showed that the viscosity-temperature curve was U-shaped and the platform zone was located around 60–95 °C during which the viscosity was less than 200 mPa s. Dual-Arrhenius and engineering viscosity models were established to predict the viscosity characteristics of the resin. It was found that the dual-Arrhenius model matched better with the experimental data at low temperature and low viscosity region. Whereas when the viscosity increased, the engineering viscosity model became more accurate. The viscosity analysis provided the basis for the window prediction of RTM molding process.

Drop spreading and drifting on a spatially heterogeneous film: capturing variability with asymptotics and emulation

A liquid drop spreading over a thin heterogeneous precursor film (such as an inhaled droplet on the mucus-lined wall of a lung airway) will experience perturbations in shape and location as its advancing contact line encounters regions of low or high film viscosity. Prior work on spatially one-dimensional spreading over a precursor film having a random viscosity field [Xu & Jensen 2016, Proc. Roy. Soc. A 472, 20160270] has demonstrated how viscosity fluctuations are swept into a narrow region behind the contact line, where they can impact drop dynamics. Here we investigate two-dimensional drops, seeking to understand the relationship between the statistical properties of the precursor film and those of the spreading drop. Assuming the precursor film is much thinner than the drop and viscosity fluctuations are weak, we use asymptotic methods to derive explicit predictions for the mean and variance of drop area and the drop's lateral drift. For larger film variability, we use Gaussian process emulation to estimate the variance of outcomes from a restricted set of simulations. Stochastic drift of the droplet is predicted to be greatest when the initial drop diameter is comparable to the correlation length of viscosity fluctuations.

Viscotaxis: Microswimmer Navigation in Viscosity Gradients.

The survival of many microorganisms, like Leptospira or Spiroplasma bacteria, can depend on their ability to navigate towards regions of favorable viscosity. While this ability, called viscotaxis, has been observed in several bacterial experiments, the underlying mechanism remains unclear. We provide a framework to study viscotaxis of biological or synthetic self-propelled swimmers in slowly varying viscosity fields and show that suitable body shapes create viscotaxis based on a systematic asymmetry of viscous forces acting on a microswimmer. Our results shed new light on viscotaxis in Spiroplasma and Leptospira and suggest that dynamic body shape changes exhibited by both types of microorganisms may have an unrecognized functionality: to prevent them from drifting to low viscosity regions where they swim poorly. The present theory classifies microswimmers regarding their ability to show viscotaxis and can be used to design synthetic viscotactic swimmers, e.g., for delivering drugs to a target region distinguished by viscosity.

Giant planet formation at the pressure maxima of protoplanetary disks

In the classical core-accretion planet formation scenario, rapid inward migration and accretion timescales of kilometer size planetesimals may not favor the formation of massive cores of giant planets before the dissipation of protoplanetary disks. On the other hand, the existence of pressure maxima in the disk could act as migration traps and locations for solid material accumulation, favoring the formation of massive cores. We aim to study the radial drift of pebbles and planetesimals and planet migration at pressure maxima in a protoplanetary disk and their implications for the formation of massive cores as triggering a gaseous runaway accretion phase. The time evolution of a viscosity driven accretion disk is solved numerically introducing a a dead zone as a low-viscosity region in the protoplanetary disk. A population of pebbles and planetesimals evolving by radial drift and accretion by the planets is also considered. Finally, the embryos embedded in the disk grow by the simultaneous accretion of pebbles, planetesimals and the surrounding gas. Our simulations show that the pressure maxima generated at the edges of the low-viscosity region of the disk act as planet migration traps, and that the pebble and planetesimal surface densities are significantly increased due to the radial drift towards pressure maxima locations. However, our simulations also show that migration trap locations and solid material accumulation locations are not exactly at the same positions. Thus, a planet's semi-major axis oscillations around zero torque locations, predicted by MHD and HD simulations, are needed for the planet to accrete all the available material accumulated at the pressure maxima. Pressure maxima generated at the edges of a low-viscosity region of a protoplanetary disk seem to be preferential locations for the formation and trap of massive cores.

Timing of water plume eruptions on Enceladus explained by interior viscosity structure

Water plume eruptions on Saturn’s icy moon Enceladus are delayed relative to the peak tidal stresses. Simulations suggest the delay can be explained by the moon’s interior structure and the presence of a subsurface ocean. At the south pole of Saturn’s icy moon Enceladus, eruptions of water vapour and ice emanate from warm tectonic ridges1,2,3,4. Observations in the infrared5 and visible6 spectra have shown an orbital modulation of the plume brightness, which suggests that the eruption activity is influenced by tidal forces. However, the observed activity seems to be delayed by several hours with respect to predictions based on simple tidal models6,7. Here we simulate the viscoelastic tidal response of Enceladus with a full three-dimensional numerical model8,9 and show that the delay in eruption activity may be a natural consequence of the viscosity structure in the south-polar region and the size of the putative subsurface ocean. By systematically comparing simulations of variations in normal stress along faults with plume brightness data, we show that the observed activity is reproduced for two classes of interior models with contrasting thermal histories: a low-viscosity convective region above a polar sea extending about 45°–60° from the south pole at a depth below the surface as small as 30 km, or a convecting ice shell of 60–70 km in thickness above a global ocean. Our analysis further shows that the eruption activity is controlled by the average normal stress applied across the cracks, thus providing a constraint on the eruption mechanism.

Viscosity of Molten Alkaline-Earth Fluorides

The viscosities of molten alkaline-earth fluorides \((\hbox {MgF}_{2}, \hbox {CaF}_{2}, \hbox {SrF}_{2},\)\(\hbox {BaF}_{2})\) were measured using the oscillating crucible method, which is especially suitable for measuring molten salts with low viscosity. The results showed a good Arrhenius linearity over a wide temperature range. The measured viscosities and activation energies increased in the following order: \(\hbox {MgF}_{2} < \hbox {CaF}_{2} < \hbox {BaF}_{2} < \hbox {SrF}_{2}\). Judging by the charge density, the viscosity of alkaline-earth fluorides should increase from molten \(\hbox {BaF}_{2}\) to \(\hbox {MgF}_{2}\). However, the results indicate a different tendency, which may be explained by a Coulomb force that is very strong. The low viscosity of \(\hbox {MgF}_{2}\) can be attributed to a decreased cohesive force, due to a partial loss of the Coulomb force caused by a higher charge density of the material. The viscosities were also compared to those of molten alkali fluorides and alkaline-earth chlorides. The viscosities of molten alkaline-earth fluorides were higher than those of molten alkali fluorides and alkaline-earth chlorides. The \(\hbox {CaF}_{2 }\) viscosity determined in this study was compared to literature values and showed a reasonable value in the relatively low-viscosity region.

TIDAL HEATING IN MULTILAYERED TERRESTRIAL EXOPLANETS

The internal pattern and overall magnitude of tidal heating for spin-synchronous terrestrial exoplanets from 1 to 2.5 R(sub E) is investigated using a propagator matrix method for a variety of layer structures. Particular attention is paid to ice-silicate hybrid super-Earths, where a significant ice mantle is modeled to rest atop an iron-silicate core, and may or may not contain a liquid water ocean. We find multilayer modeling often increases tidal dissipation relative to a homogeneous model, across multiple orbital periods, due to the ability to include smaller volume low viscosity regions, and the added flexure allowed by liquid layers. Gradations in parameters with depth are explored, such as allowed by the Preliminary Earth Reference Model. For ice-silicate hybrid worlds, dramatically greater dissipation is possible beyond the case of a silicate mantle only, allowing non-negligible tidal activity to extend to greater orbital periods than previously predicted. Surface patterns of tidal heating are found to potentially be useful for distinguishing internal structure. The influence of ice mantle depth and water ocean size and position are shown for a range of forcing frequencies. Rates of orbital circularization are found to be 10-100 times faster than standard predictions for Earth-analog planets when interiors are moderately warmer than the modern Earth, as well as for a diverse range of ice-silicate hybrid super-Earths. Circularization rates are shown to be significantly longer for planets with layers equivalent to an ocean-free modern Earth, as well as for planets with high fractions of either ice or silicate melting.

Analytical Modeling of Slip Flow in Parallel-plate Microchannels

This paper presents analytical modeling of slip liquid flow in parallel-plate microchannels, and can be divided in two parts. In the first part, classical relationships describing velocity, flow rate, pressure gradient, and shear stress are extended to the more general cases where there exist two different values of the yet-unknown slip lengths at the top and bottom walls of the channel. These formulations can be used to experimentally determine the values of slip length on the channels fabricated from two different hydrophobic walls. In the second part, the emphasis is on the quantification of the slip length analytically. Generating mechanism of slip is attributed to the existence of a low-viscosity region between the liquid and the solid surface. By extending the previous works, the analytical values of slip length are determined using exact, rather than empirical, values of air gap thickness at different ranges of air flow Knudsen number. In addition to the exact expressions of air gap thickness, the corresponding ranges of the channel height where slip flow can be induced are also found analytically. It is found that when the channel height is larger than 700 孬 air flow is in continuum regime and no-slip boundary condition can be used. For the case where the channels height is smaller than 700 孠and larger than 7.5 孬 slip boundary condition should be used to model the air flow in the channel. Finally, for the channel with the height smaller than 7.5 孬 the Navier-Stokes equation cannot be used to model the air flow, and instead molecular-based approaches should be used. The results of this paper can be used as a guideline for both experimentalists and theoreticians to study the slip flow in parallel-plate microchannels.

The viscosity distribution around a rising bubble in shear-thinning non-newtonian fluids

The viscosity distribution of the liquid around a rising bubble in carboxymethyl cellulose (CMC) aqueous solutions was measured experimentally by particle image velocimetry (PIV). The effect of the concentration of CMC solutions on the viscosity distribution around a bubble and the coupling relations between the viscosity field, flow field and shear stress field were also studied. Results indicated that the specific viscosity (non-dimensionalized by η0) decreases with the increase in CMC solution concentration due to a shear thinning effect. Within the experimental range, similar viscosity distributions of liquids around a rising bubble were found: a hollow cylindrical low viscosity region around the bubble wake and a high viscosity region in the central bubble wake.

Dependency of slab geometry on absolute velocities and conditions for cyclicity: insights from numerical modelling

SUMMARY The aim of this study is to quantify the relationship between the kinematics of subduction, deformation in the overriding plate and the evolution of slab geometry. A 2-D finite element numerical code is used, and a first objective consists in benchmarking previously published analogue models. Far-field plate velocities are applied, and once the subducting plate reaches the 660 km discontinuity, modelled as a rigid base, we obtain two different forms or styles of subductionthatdependontheoverridingplatevelocity vop:ifvop >0,theslabliesforwardson the 660km discontinuity (style 1), and if vop ≤ 0, the slab lies backwards on the discontinuity (style 2). We also obtain a cyclic pattern with the slab folding on itself repeatedly when vsp > 0 and 2vop + vsp > 0 (where vsp is the subducting plate velocity). These conditions result from the analysis of several simulations in which the subduction velocities and plate viscosities are varied. When the slab periodically folds on the 660km discontinuity, periods of shallow slab dip and compression in the overriding plate are followed by periods of slab steepening and relative extension in the overriding plate. Folding periodicity is controlled by the slab viscosity and subduction velocity. When a low-viscosity zone is included in the overriding plate, the trench motion is effectively decoupled from the overriding plate velocity, therefore allowing it to be directly controlled by the deep dynamics of the slab. For the cyclic style 2 corresponding to forward folding of the slab, the low-viscosity region in the overriding plate increases the stress amplitudes oscillations, the trench motion and the folding periodicity with time. Therefore the strength of the entire overriding plate is shown to directly control the dynamics of subduction. Using the Nazca and South American plate velocities we produce models of cyclic folding with a period of ca. 22Ma and a minimal dip angle of ca. 10 ◦ . Episodic folding of the slab on the 660km discontinuity would produce the necessary changes in slab dip and overriding plate deformation that explain episodes of volcanic quiescence alternating with greater rates of shortening along the Andes.