Low Schmidt Number Research Articles

Resource-efficient quantum principal component analysis

Principal component analysis (PCA) is an important dimensionality reduction method in machine learning and data analysis. Recently, the quantum version of PCA has been established to diagonalize quantum states. Although these quantum algorithms promise quantum advantages, they require substantial resources beyond the reach of state-of-the-art quantum technologies. This work aims to reduce resource requirements and improve the efficiency of quantum PCA. Assuming that the quantum state is accessed through a purified quantum query model and a sampling model, we propose quantum algorithms that use minimal resource requirements for ancillary qubits to reveal properties of eigenvectors and eigenvalues of a state. In particular, we show that estimating eigenvalue λ with error ε and success probability larger than λ(1−η) requests a query complexity O~(ϵ−1) and a sample complexity O~(ϵ−2η−1) , respectively. To our knowledge, our result is the first quantum speedup that achieves asymptotic linear scaling in 1/ϵ for quantum PCA. As applications, we discuss estimating the minimum relative entropy of entanglement of bipartite pure-states and performing quantum state discrimination tasks. We show that quantum speedups are maintained when the pure state has a low Schmidt number and states of discrimination have a low rank. This study opens up a new quantum PCA method for high-dimensional quantum data analysis and discusses its application in quantum information processing tasks.

Hydrodynamic and transport behavior of solid nanoparticles simulated with dissipative particle dynamics

Inertial migration of micro- and nanoparticles flowing through microchannels is commonly used for particle separation, sorting, and focusing on many lab-on-a-chip devices. Computer simulations of inertial migration of nanoparticles by mesoscale simulation methods, such as Dissipative Particle Dynamics (DPD) would be helpful to future experimental development of these lab-on-a-chip devices. However, the conventional DPD approach has a low Schmidt number and its ability to model inertial migration is questioned. In this work, we examine the ability of DPD simulations to investigate the inertial migration of rigid nanoparticles flowing through a slit channel. By varying the exponent and cutoff distance in the weight function of the random and dissipative forces, DPD models with Schmidt number varying between 1 and 370 were examined. We show that solvent penetration into nanoparticles and solvent-induced attraction between nanoparticles can be controlled by choosing appropriate interaction coefficients of the DPD conservative force and that these properties are not influenced by the Schmidt number of the DPD model. On the other hand, hydrodynamic properties and transport behaviour of rigid nanoparticles are influenced by the Schmidt number. With the conventional DPD model, nanoparticles tend to be evenly distributed across the channel and do not remain in steady-state positions during flow. At high Schmidt numbers, the particles migrate to long-lasting steady-state positions located between the channel center and walls, in agreement with known experimental observations. We conclude that to properly simulate inertial migration, modifications to the conventional DPD model that yield a high Schmidt number are required.

Thermophoresis and Brownian Effect for Chemically Reacting Magneto-Hydrodynamic Nanofluid Flow across an Exponentially Stretching Sheet

This comparative research investigates the influence of a flexible magnetic flux and a chemical change on the freely fluid motion of a (MHD) magneto hydrodynamic boundary layer incompressible nanofluid across an exponentially expanding sheet. Water and ethanol are used for this analysis. The temperature transmission improvement of fluids is described using the Buongiorno model, which includes Brownian movement and thermophoretic distribution. The nonlinear partial differential equalities governing the boundary layer were changed to a set of standard nonlinear differential equalities utilizing certain appropriate similarity transformations. The bvp4c algorithm is then used to tackle the transformed equations numerically. Fluid motion is slowed by the magnetic field, but it is sped up by thermal and mass buoyancy forces and thermophoretic distribution increases non-dimensional fluid temperature resulting in higher temperature and thicker boundary layers. Temperature and concentration, on the other hand, have the same trend in terms of the concentration exponent, Brownian motion constraint, and chemical reaction constraint. Furthermore, The occurrence of a magnetic field, which is aided by thermal and mass buoyancies, assists in the enhancement of heat transmission and wall shear stress, whereas a smaller concentration boundary layer is produced by a first-order chemical reaction and a lower Schmidt number.

Simulation of high Schmidt number fluids with dissipative particle dynamics: Parameter identification and robust viscosity evaluation

Dissipative particle dynamics (DPD) is a widely used coarse-grained technique for the simulation of complex fluids. Although the method is capable of describing the hydrodynamics of any fluid, the common choice of DPD parameters, such as friction coefficient γ, dissipative cutoff radius rcD, coarse-graining factor Nm and weighting function exponent s, unrealistically leads to the simulation of liquid water with a low Schmidt number Sc at standard pressure and temperature. In this work we explored the influence of these parameters, finding the set of parameters needed to properly simulate liquid water. Particular attention was devoted to the numerical techniques to calculate the transport properties from equilibrium simulations, especially in the calculation of the viscosity, comparing the most commonly adopted techniques and formulating a recipe that can be used for further investigations.

Using helicity to investigate scalar transport in wall turbulence

Since flow regions of high helicity are associated with low dissipation of kinetic energy, helicity can be used to mark the flow structures that are major contributors to turbulent scalar dispersion. Employing a Lagrangian approach to compare the helicity between scalar tracers and fluid particles in the same flow field shows that flow structures that contribute to the transport of low Schmidt number markers are different than those for fluid particles. This is quite important in anisotropic wall turbulence, where the interplay between molecular and turbulent transport is critical.

Analysis of one-dimensional models for exchange flows under strong stratification

One-dimensional models of exchange flows driven by horizontal density gradients are well known for performing poorly in situations with weak turbulent mixing. The main issue with these models is that the horizontal density gradient is usually imposed as a constant, leading to non-physically high stratification known as runaway stratification. Here, we propose two new parametrizations of the horizontal density gradient leading to one-dimensional models able to tackle strongly stratified exchange flows at high and low Schmidt number values. The models are extensively tested against results from laminar two-dimensional simulations and are shown to outperform the models using the classical constant parametrization for the horizontal density gradients. Four different flow regimes are found by exploring the parameter space defined by the gravitational Reynolds number Reg, the Schmidt number Sc, and the aspect ratio of the channel Γ. For small values of RegΓ, when diffusion dominates, all models perform well. However, as RegΓ increases, two clearly distinct regimes emerge depending on the Sc value, with an equally clear distinction of the performance of the one-dimensional models.

A unified single-field Volume-of-Fluid-based formulation for multi-component interfacial transfer with local volume changes

This paper presents a novel unified single-field formulation for Volume-Of-Fluid simulation of interfacial mass transfer with local volume changes. By comparison with the previous models referred as Continuous Species Transfer in the literature, our improved model uses a single-field formulation of the local mass transfer across the interface, enabling us to take into account local volume changes induced by non-dilute species transfer. The numerical model, implemented in our in-house OpenFOAM-based simulator, is validated by comparison with analytical solutions in 1D and 2D, and a semi-analytical solution in 3D. The implemented approach is first applied to investigate competing mass transfer in an infinite cylinder. We then simulate the shrinking of a single-component rising bubble at low Schmidt number. The numerical model is shown to be well adapted to investigate Sherwood numbers and existing correlation for mass transfer at fluid interfaces.

Performance evaluation of a multiscale modelling system applied to particulate matter dispersion in a real traffic hot spot in Madrid (Spain)

Urban air pollution is one of the most important environmental problems nowadays. Understanding urban pollution is rather challenging due to different factors that produce a strongly heterogeneous pollutant distribution within streets. Observed concentrations depend on processes occurring at a wide range of spatial and temporal scales, complex wind flow and turbulence patterns induced by urban obstacles and irregular traffic emissions. The main objective of this paper is to model particulate matter dispersion at microscale while considering the effects of mesoscale processes. Computational Fluid Dynamic (CFD) PM10 simulations were performed taking into account high spatial resolution traffic emissions from a microscale traffic model and inlet vertical profiles of meteorological variables from Weather Research and Forecasting (WRF) model. This modelling system is evaluated by using meteorological and PM10 concentration data from intensive experimental campaigns carried out on 25th February and 6th July, 2015 in a real urban traffic hot-spot in Madrid. The effect of uncertainties in the inlet profiles from mesoscale input data on microscale results is assessed. Additionally, the importance of the sensible surface heat fluxes (SHF) provided by WRF and the selection of an appropriate turbulent Schmidt number in the dispersion equation are investigated. The main conclusion is that the modelling system accurately reproduces PM10 dispersion imposing appropriate inputs (meteorological variables and SHF) and a suitable turbulent Schmidt number. Better agreement is found for simulation with a low turbulent Schmidt number. This approach improves the standard microscale modelling alone because more realistic boundary conditions and mesoscale processes are considered.

SIMULATION OF THERMAL DECOMPOSITION IN AN OPEN CAVITY: ENTROPY ANALYSIS

ABSTRACT This paper presents a numerical analysis of entropy generation in a two-dimensional rectangular channel where the inlet flow undergoes thermal decomposition resulting from a chemical reaction. The model considered viscosity and thermal conductivity to be dependent of temperature. Irreversibility due to mass transport was included in the entropy generation analysis. Relevant applications of this study are possible for the design of power generation systems and reactors. The effects of the Reynolds number, Schmidt number, and length of the heat source on thermal fluid dynamics, mass transfer, and irreversibility were also investigated. It was found that thermal decomposition increases at: a) low Reynolds numbers, b) low Schmidt numbers, and c) increased length of heat source. Additionally, overall entropy generation increased when Reynolds number and length of heat source were increased, although in all cases, overall irreversibility attains a minimum value at a specific Schmidt number.

Multi-scale phenomena of rotation-modified mode-2 internal waves

Abstract. We present high-resolution, three-dimensional simulations of rotation-modified mode-2 internal solitary waves at various rotation rates and Schmidt numbers. Rotation is seen to change the internal solitary-like waves observed in the absence of rotation into a leading Kelvin wave followed by Poincaré waves. Mass and energy is found to be advected towards the right-most side wall (for a Northern Hemisphere rotation), leading to increased amplitude of the leading Kelvin wave and the formation of Kelvin–Helmholtz (K–H) instabilities on the upper and lower edges of the deformed pycnocline. These fundamentally three-dimensional instabilities are localized within a region near the side wall and intensify in vigour with increasing rotation rate. Secondary Kelvin waves form further behind the wave from either resonance with radiating Poincaré waves or the remnants of the K–H instability. The first of these mechanisms is in accord with published work on mode-1 Kelvin waves; the second is, to the best of our knowledge, novel to the present study. Both types of secondary Kelvin waves form on the same side of the channel as the leading Kelvin wave. Comparisons of equivalent cases with different Schmidt numbers indicate that while adopting a numerically advantageous low Schmidt number results in the correct general characteristics of the Kelvin waves, excessive diffusion of the pycnocline and various density features precludes accurate representation of both the trailing Poincaré wave field and the intensity and duration of the Kelvin–Helmholtz instabilities.

CFD study about the effect of using multiple inlets on the efficiency of a micromixer. Assessment of the optimal inlet configuration working as a microreactor

This work deals with a 2D numerical study about the effect the number of inlets of a micromixer on the mixing efficiency when two fluids must be mixed at low Reynolds and high Schmidt numbers. In this study, 6 different inlet configurations (with 2, 3, 4, 5, 6 and 7 inlets) for 2 Reynolds (0.1 and 0.29) and 3 Schmidt numbers (10 × 103, 4 × 103 and 2 × 103) have been considered. Just as reference micromixer and for comparative purposes, the geometry studied in Ortega-Casanova (2017), with just 2 inlets, has been now redesigned with more inlets incorporated. Originally, the micromixer with 2 inlets, Re = 0.29 and Sc = 10 × 103 gave a mixing efficiency of ∼14%, while we show in this work that with 7 inlets and the same Reynolds number, the efficiency can be increased up to ∼80%, when Sc = 10 × 103, and up to ∼95%, when Sc = 2 ×103. Later, we show that the mixing cost of the optimal inlet configuration is one of the lowest in comparison with previous works. Additionally, when the optimal configuration is used as microreactor, the reacting efficiency also increases in comparison with the 2-inlet configuration. We also estimate the number of inlets for full and complete mixing.

Numerical Investigation of Fluid Mixing in a Micro-Channel Mixer with Two Rotating Stirrers by Using the Incompressible SPH Method

Fluid mixing is a crucial and challenging process for microfluidic systems, which are widely used in biochemical processes. Because of their fast performance, active micromixers that use stirrer blades are considered for biological applications. In the present study, by using a robust and convenient Incompressible Smoothed Particle Hydrodynamics (ISPH) method, miscible mixing within a two-blade micromixer is investigated. The problem discussed herein is represented by an active micromixer comprising two stir-bars that rotate to mix the fluids. Because of its Lagrangian nature, Smoothed Particle Hydrodynamics is an appropriate and convenient method for simulating moving boundary problems and tracking the particles in the mixing process. Previous investigations have been carried out for mixing flow for a low Schmidt number. However, a low Schmidt number is barely applicable for liquid mixing. Hence, in the present study, the Schmidt number is considered to be Sc=1000. The present results show that the two-blade micro-channel mixer considerably improves the mixing rate in comparison with the one-blade micro-channel mixer.

Tube-side mass transfer for hollow fibre membrane contactors operated in the low Graetz range

Transformation of the tube-side mass transfer coefficient derived in hollow fibre membrane contactors (HFMC) of different characteristic length scales (equivalent diameter and fibre length) has been studied when operated in the low Graetz range (Gz<10). Within the low Gz range, mass transfer is generally described by the Graetz problem (Sh=3.67) which assumes that the concentration profile comprises a constant shape over the fibre radius. In this study, it is experimentally evidenced that this assumption over predicts mass transfer within the low Graetz range. Furthermore, within the low Gz range (below 2), a proportional relationship between the experimentally determined mass transfer coefficient (Kov) and the Graetz number has been identified. For Gz numbers below 2, the experimental Sh number approached unity, which suggests that mass transfer is strongly dependent upon diffusion. However, within this diffusion controlled region of mass transfer, tube-side fluid velocity remained important. For Gz numbers above 2, Sh could be satisfactorily described by extension to the Lévêque solution, which can be ascribed to the constrained growth of the concentration boundary layer adjacent to the fibre wall. Importantly this study demonstrates that whilst mass transfer in the low Graetz range does not explicitly conform to either the Graetz problem or classical Lévêque solution, it is possible to transform the experimentally derived overall mass transfer coefficient (Kov) between characteristic length scales (dh and L). This was corroborated by comparison of the empirical relationship determined in this study (Sh=0.36Gz) with previously published studies operated in the low Gz range. This analysis provides important insight for process design when slow tube-side flows, or low Schmidt numbers (coincident with gases) constrain operation of hollow fibre membrane contactors to the low Gz range.

Infotaxis in a turbulent 3D channel flow

In this paper, the infotaxis-based search algorithm is tested in several simulated turbulent channel flows. The algorithm is adapted to detect plumes of high concentration instead of independent particles. Direct numerical simulation is used to test this adapted search algorithm by detection of high concentration levels in turbulent channel flows with a Schmidt number Sc of 1.0 and Reynolds numbers Re of 5600 and 28000.For the direct numerical simulation with the adapted algorithm, there is a positive relation between the initial distances to the source and the running time, which holds for Re=5600 but which is not observed at Re=28000. This is caused by the low Schmidt number and the high velocity, which leads the searcher to the source very fast after the first detection of a high concentration level.The search algorithm is also tested in reverse to detect whether a fluid is well-mixed. The time required for a detection of a too high or low concentration and the number of detections are used as measures for success. By applying the algorithm to some prescribed concentration distributions in two dimensions, it is found that the method is very sensitive to the threshold values for the mixing indicators.

Structure-rheology relationship in a sheared lamellar fluid.

The structure-rheology relationship in the shear alignment of a lamellar fluid is studied using a mesoscale model which provides access to the lamellar configurations and the rheology. Based on the equations and free energy functional, the complete set of dimensionless groups that characterize the system are the Reynolds number (ργL(2)/μ), the Schmidt number (μ/ρD), the Ericksen number (μγ/B), the interface sharpness parameter r, the ratio of the viscosities of the hydrophilic and hydrophobic parts μ(r), and the ratio of the system size and layer spacing (L/λ). Here, ρ and μ are the fluid density and average viscosity, γ is the applied strain rate, D is the coefficient of diffusion, B is the compression modulus, μ(r) is the maximum difference in the viscosity of the hydrophilic and hydrophobic parts divided by the average viscosity, and L is the system size in the cross-stream direction. The lattice Boltzmann method is used to solve the concentration and momentum equations for a two dimensional system of moderate size (L/λ=32) and for a low Reynolds number, and the other parameters are systematically varied to examine the qualitative features of the structure and viscosity evolution in different regimes. At low Schmidt numbers where mass diffusion is faster than momentum diffusion, there is fast local formation of randomly aligned domains with "grain boundaries," which are rotated by the shear flow to align along the extensional axis as time increases. This configuration offers a high resistance to flow, and the layers do not align in the flow direction even after 1000 strain units, resulting in a viscosity higher than that for an aligned lamellar phase. At high Schmidt numbers where momentum diffusion is fast, the shear flow disrupts layers before they are fully formed by diffusion, and alignment takes place by the breakage and reformation of layers by shear, resulting in defects (edge dislocations) embedded in a background of nearly aligned layers. At high Ericksen number where the viscous forces are large compared to the restoring forces due to layer compression and bending, shear tends to homogenize the concentration field, and the viscosity decreases significantly. At very high Ericksen number, shear even disrupts the layering of the lamellar phase. At low Ericksen number, shear results in the formation of well aligned layers with edge dislocations. However, these edge dislocations take a long time to anneal; the relatively small misalignment due to the defects results in a large increase in viscosity due to high layer stiffness and due to shear localization, because the layers between defects get pinned and move as a plug with no shear. An increase in the viscosity contrast between the hydrophilic and hydrophobic parts does not alter the structural characteristics during alignment. However, there is a significant increase in the viscosity, due to pinning of the layers between defects, which results in a plug flow between defects and a localization of the shear to a part of the domain.

Similarity Solutions of Unsteady Mixed Convective Boundary Layer Flow of Viscous Incompressible Fluid along Isothermal Horizontal Plate

Unsteady mixed convective boundary layer flow of viscous incompressible fluid along isothermal horizontal plate is analyzed through Similarity Solutions. The governing partial differential equations are transformed into ordinary differential equations using the similarity transformation and solved numerically along with shooting technique. The flow field for the fluid velocity, temperature and concentration at the plate surface are significantly influenced by the governing parameters such as unsteadiness parameter, permeability parameter, Prandtl number, Schmidt number and the other driving parameters. The results show that both fluid velocity and temperature decrease but no significant effect on concentration for the increasing values of Prandtl number. It is also exposed that velocity and concentration is higher at lower Schmidt number for low Prandtl fluid. Finally, the dependency of the Skin-friction co-efficient, Nusselt number and Sherwood number, which are of physical interest, are also illustrated in tabular form for the governing parameters.

Efficient Schmidt number scaling in dissipative particle dynamics.

Dissipative particle dynamics is a widely used mesoscale technique for the simulation of hydrodynamics (as well as immersed particles) utilizing coarse-grained molecular dynamics. While the method is capable of describing any fluid, the typical choice of the friction coefficient γ and dissipative force cutoff rc yields an unacceptably low Schmidt number Sc for the simulation of liquid water at standard temperature and pressure. There are a variety of ways to raise Sc, such as increasing γ and rc, but the relative cost of modifying each parameter (and the concomitant impact on numerical accuracy) has heretofore remained undetermined. We perform a detailed search over the parameter space, identifying the optimal strategy for the efficient and accuracy-preserving scaling of Sc, using both numerical simulations and theoretical predictions. The composite results recommend a parameter choice that leads to a speed improvement of a factor of three versus previously utilized strategies.

Schmidt number effects on Rayleigh-Taylor instability in a thin channel

The classical gravitational instability of a layer of denser fluid overlying a layer of less dense fluid, commonly known as the Rayleigh-Taylor instability, has been studied for well over a hundred years. In this article, we present the results of numerical simulations of a variant of this instability in which a plug of dense fluid is released from rest in a thin channel between two flat, vertical walls, causing a downward acceleration of the entire fluid column and formation of boundary layers near the walls. The plug of dense fluid undergoes distinctly different evolution near the walls and in the fluid interior. The instability in the interior, which we label the “hammerhead” instability based on its shape, is robust over a range of physical parameters, but disappears below a threshold Schmidt number. Fluid near the wall is slowed, and thin tendrils that link the near wall fluid to the main body of the fluid plug form, and in some cases undergo their own instability. We characterize the fully three-dimensionalized state, finding that while bulk measures of kinetic energy three-dimensionalization do not discriminate between low and high Schmidt number cases, the geometric distributions of the dynamical parameters Q and R from the turbulence literature are profoundly different in the high Schmidt number case. Finally, we consider the role of shear in situations in which the two plates are not exactly vertical, demonstrating that shear diminishes the importance of three-dimensionalization, while the hammerhead instability remains relevant.

Large Eddy Simulation of the Mixing of a Passive Scalar in a High-Schmidt Turbulent Jet

Accurate subgrid-scale (SGS) scalar flux models are essential when large eddy simulation (LES) is used to represent flow, mixing and transport of passive and active scalars in engineering, and environmental applications in turbulent regime. Many SGS scalar flux models have been developed for flows with low Schmidt numbers (Sc), but their application to high Sc flows has important limitations. In high Sc flows, the behavior of the scalar field becomes anisotropic because of intermittency effects, phenomenon that must be accounted for by SGS scalar flux models. The objective of this paper is to evaluate the ability of three SGS scalar flux models to predict the scalar behavior of a high Sc-number flow configuration, namely the anisotropy-resolved SGS scalar flux model: (1) appropriate for high Sc-number flow configurations, and two additional SGS models (linear eddy diffusivity based SGS models) with (2) constant, and (3) dynamically calculated turbulent Schmidt number. The LES simulation results accomplished by these models are compared to each other and to experimental data of a turbulent round jet discharging a diluted scalar into a low-velocity coflowing water stream. The comparison of simulation results and experimental observations shows that, in general, all SGS models reproduce the mean filtered concentration distribution in radial direction. The dynamic eddy diffusivity and anisotropy models reproduce the rms of the concentration and SGS scalar fluxes distribution. In particular, the anisotropy model improves the prediction reliability of LES. However, the three models evaluated in this study cannot accurately predict the scalar behavior at the superviscous layer. Finally, this work demonstrates that complex models can achieve reliable predictions on reasonable grids using less computational effort, while simple models require fine grids with increased computational costs.

Lattice Boltzmann simulation of dissolution and precipitation in porous media

In this paper, we simulate numerically the dissolution and precipitation in porous media by using the lattice Boltzmann method (LBM). The fluid flow in porous media is simulated by using a multiple-relaxation-time (MRT) LBM, while a D2Q9 lattice BGK model is used for reactive solute transport. Frst, the code of LBM is tested by simulating the diffusion and reaction at a boundary in an open rectangular domain, and comparing the results with the analytic solution. Then, the effects of the Reynolds number (Re), the Schmidt number (Sc) and the Damkohler number (Da) on the variations of the geometry of the porous media and the concentration field are carefully studied. It can be found that for the dissolution (precipitation), as Re is increased, the porosity of the porous media will be increased (decreased), and the average concentration will be decreased (increased). Besides, at low Damkohler numbers or Schmidt numbers, the dissolution and precipitation will be reaction-controlled and are highly uniform. However, as Da or Sc is high, the dissolution and precipitation will be diffution-controlled, and mainly occur in the upstream and large pore space.