Theory Of Isotropic Turbulence Research Articles

Identification of Local Isotropic Turbulence Conditions in Various Bubble Columns Based on Several Reliable Parameters

Bubble columns (BCs) are widely used in the chemical industry. In many industrial applications, these important gas-liquid contactors operate in a churn-turbulent flow regime. In principle, it is essential to determine the operating conditions in every BC reactor, in which local isotropic turbulence is established. In this work, it was demonstrated that several different parameters (Kolmogorov entropy, correlation dimension and novel hybrid index) follow a monotonic decreasing trend. This finding could be explained by the constantly increasing coalesced bubble size, which brings more order into the gas-liquid system and thus any entropic or chaotic parameter should decrease with the increase in the superficial gas velocity Ug. The profiles of the new parameters in various gas-liquid systems were studied. They were extracted from different pressure signals (gauge or absolute). In this research, BCs of different diameter and equipped with different gas distributors were used. It was demonstrated that the studied parameters could be successfully correlated with the length scale of the micro eddies and thus the Ug range of applicability of the local isotropic turbulence theory under various operating conditions was indirectly determined. The overall gas holdup profiles were analyzed and, based on the exponent of the Ug value, it was found that in the aqueous solutions of alcohols studied, the conditions in the bubble bed (BB) are homogeneous, whereas in the air-tap water system aerated in different BCs, the conditions in the BB are heterogeneous. This result implies that the local isotropic turbulence conditions predominate mainly around the corresponding measurement positions.

Direct numerical simulation of three-dimensional isotropic turbulence with smoothed particle hydrodynamics

This study presents an investigation of the capability of smoothed particle hydrodynamics (SPH) to simulate three-dimensional isotropic turbulence. The effect of the error introduced by the particle disorder is assessed by comparing the standard Lagrangian SPH with an Eulerian adaptation. For the free decay of isotropic turbulence in a triple periodic box, the Eulerian SPH shows very good agreement with the reference solution, while the particle disorder in Lagrangian simulations yields an incorrect prediction of turbulent energy spectra. For the first time, a SPH investigation on linearly forced isotropic turbulence is also conducted with a focus on how the numerical dissipation affects the obtained solution. It is found that by using a Godunov-type SPH scheme for the continuity equation and by employing Roe's approximate solver for the Riemann problem at the interface of each neighboring particle, a stable solution is obtained, which is also in agreement with the results predicted by the theory of homogeneous isotropic turbulence. The efficacy of the particle shifting technique applied to turbulent SPH flows is studied in the end. Numerical findings indicate that corrective terms derived from the arbitrary Lagrangian–Eulerian theory are essential for a proper estimation of turbulence characteristics.

The Spatial Structure of Passively Simulated Atmospheric Boundary Layer Turbulence

Three types of turbulence fields were investigated using a research method combining wind tunnel tests and theoretical analysis to further explore the spatial structure of atmospheric boundary layer turbulence, which was passively simulated by a wind tunnel. The fundamental theory of turbulence is introduced, and some traditional theoretical coherence models based on isotropic turbulence theory are derived. The difference between the theoretical results and the passive simulation of atmospheric boundary layer turbulence was compared and discussed. The analysis results show that the passively simulated atmospheric turbulence basically conformed to the homogeneous isotropic turbulence assumption on the horizontal plane, but the interference of the nonisotropic turbulence components cannot be ignored either. Finally, some improvements were made to the traditional coherence function model based on the experimental results to apply the passively simulated atmospheric boundary layer turbulence.

RESEARCH OF EXTERNAL MASS TRANSFER PROCESSES FOR ADSORPTION FROM SOLUTIONS IN A APPARATUS WITH STIRRING

A study has been mode of transport-controlled mass transfer-controlled to particles suspended in a stirred vessel. The motion of particle in a fluid was examined and a method of predicting relative velocities in terms of Kolmogoroff’s theory of local isotropic turbulence for mass transfer was outlined.
 To provide a more concrete visualization of complex wave form of turbulence, the concepts of eddies, of eddy velocity, scale (or wave number) and energy spectrum, have proved convenient.
 Large scale motions of scale contain almost all of the energy and they are directly responsible for energy diffusion throughout the stirring vessel by kinetic and pressure energies. However, almost no energy is dissipated by the large-scale energy-containing eddies. A scale of motion less than is responsible for convective energy transfer to even smaller eddy sires. At still smaller eddy scales, close to a characteristic microscale, both viscous energy dissipation and convection are the rule. The last range of eddies has been termed the universal equilibrium range. It has been further divided into a low eddy size region, the viscous dissipation subrange, and a larger eddy size region, the inertial convection subrange.
 Measurements of energy spectrum in mixing vessel are shown that there is a range, where the so called -(5/3) power law is effective. Accordingly, the theory of local isotropy of Kolmogoroff can be applied because existence of the internal subrange. As the integrated value of local energy dissipation rate agrees with the power per unit mass of liquid from the impeller, almost all energy from the impeller is viscous dissipated in eddies of microscale.
 The correlation for mass transfer to particles suspended in a stirred vessel is recommended. The results of experimental study are approximately 12 % above the predicted values.

Isotropic turbulence correlation functions modelling on the basis of Karman-Howarth equation

A closure model for the von Karman-Howarth equation is considered. The offered algebraic closure model is based on a single spatial-point third-order correlation function, unlike the widely used models based on a distance between two separated points. The model holds for homogeneous isotropic turbulence theory. Numerical solution of the von Karman-Howarth equation for the flow behind a bi-plane grid of circular cylinders in comparison to experimental data is presented.

Turbulent density and pressure fluctuations in the stratified intracluster medium

ABSTRACT Turbulent gas motions are observed in the intracluster medium (ICM). The ICM is density-stratified, with the gas density being highest at the centre of the cluster and decreasing radially outwards. As a result of this, Kolmogorov (homogeneous, isotropic) turbulence theory does not apply to the ICM. The gas motions are instead explained by anisotropic stratified turbulence, with the stratification quantified by the perpendicular Froude number (Fr⊥). These turbulent motions are associated with density and pressure fluctuations, which manifest as perturbations in X-ray surface brightness maps of the ICM and as thermal Sunyaev–Zeldovich effect (SZ) fluctuations, respectively. In order to advance our understanding of the relations between these fluctuations and the turbulent gas velocities, we have conducted 100 high-resolution hydrodynamic simulations of stratified turbulence (2562 × 384–10242 × 1536 resolution elements), in which we scan the parameter space of subsonic rms Mach number ($\mathcal {M}$), Fr⊥, and the ratio of entropy and pressure scale heights (RPS = HP/HS), relevant to the ICM. We develop a new scaling relation between the standard deviation of logarithmic density fluctuations (σs, where s = ln (ρ/$\langle$ρ$\rangle$)), $\mathcal {M}$, and Fr⊥, which covers both the strongly stratified (Fr⊥ ≪ 1) and weakly stratified (Fr⊥ ≫ 1) turbulence regimes: $\sigma _{\rm s}^2=\ln (1+b^2\mathcal {M}^4+0.10/(\mathrm{Fr}_\perp +0.25/\sqrt{\mathrm{Fr}_\perp })^2\mathcal {M}^2R_{\rm PS})$, where b ∼ 1/3 for solenoidal turbulence driving studied here. We further find that logarithmic pressure fluctuations σ(ln P/ < P >) are independent of stratification and scale according to the relation $\sigma _{(\ln {\bar{P}})}^2=\ln (1+b^2\gamma ^2\mathcal {M}^4)$, where $\bar{P}=P/\left\langle P \right\rangle $ and γ is the adiabatic index of the gas. We have tested these scaling relations to be valid over the parameter ranges $\mathcal {M} = 0.01$–0.40, Fr⊥ = 0.04–10.0, and RPS = 0.33–2.33.

Extended Slip-Weakening Model and Inference of Rupture Velocity

The slip-weakening model developed by Ohnaka and Yamashita is extended over the breakdown zone by equating the scaling relationships for the breakdown zone and the whole rupture area. For the extension, the study uses the relationship between rupture velocity and radiation efficiency, which was derived in the theory of linear elastic fracture mechanics, and the definition of fmax given in the specific barrier model proposed by Papageorgiou and Aki. The results clearly show that the extended scaling relationship is governed by the ratio of rupture velocity to S wave velocity, and the velocity ratio can be determined by the ratio of characteristic frequencies of a Fourier amplitude spectrum, which are corner frequency, fc, and source-controlled cut-off frequency, fmax, or vice versa. The derived relationship is tested by using the characteristic frequencies extracted from previous studies of more than 130 shallow crustal events (focal depth less than 25 km, MW 3.0~7.5) that occurred in Japan. Under the assumption of a dynamic similarity, the rupture velocity estimated from fmax/fc and the modified integral timescale give quite similar scale-dependence of the rupture area to that given by Kanamori and Anderson. Also, the results for large earthquakes show good agreement to the values from a kinematic inversion in previous studies. The test results also indicate the unavailability of the spectral self-similarity proposed by Aki because of the scale-dependent rupture velocity and the rupture velocity-dependent fmax/fc; however, the results do support the local similarity asserted by Ohnaka. It is also remarkable that the relationship between the rupture velocity and fmax/fc is quite similar to Kolmogorov’s hypothesis on a similarity in the theory of isotropic turbulence.

Extending the concept of machine acceleration used to model the bubble-particle detachment in flotation. Part 2 – Machine acceleration of solid particles in water

The machine acceleration introduced by H. J. Schulze has been a cornerstone of the bubble-particle (BP) detachment theory. It connects the mean dissipation rate of turbulence energy of water in a flotation machine with the BP detachment. In a recent paper, we scrutinized the theory and recommended its extension to cover both the longitudinal (centrifugation) and transverse (shear) effects of water turbulence. Since there is a significant difference in the densities of water, solid particles, and air bubbles, it is unknown if the available determination of the machine acceleration using the “water particles” is a good approximation for the bubble-particle aggregates. This paper aims to provide an answer to this fundamental question. For simplicity, this paper focuses on the acceleration of solid particles in water. Specifically, we use the Basset-Boussinesq-Oseen equation to quantify the particle acceleration. The correlation method in combination with the isotropic turbulence theory is applied to predict the particle acceleration components for the full range of turbulence length scale. Comparing with Schulze’s model, our recent model shows that the particle inertia should be considered in calculating the machine acceleration, especially for large and/or heavy particles and high energy dissipation rate. Our numerical results show that the machine acceleration decreases with increasing particle size and density and increases with increasing dissipation rate of turbulent kinetic energy and turbulence intensity.

Examining and extending the concept of machine acceleration used in modelling the bubble-particle detachment in flotation

The bubble-particle (BP) detachment is a significant factor in controlling the recovery of coarse particles in mechanical flotation cells. It has been quantified by balancing the restoring force of surface tension and the centrifugal force exerted on the particle-bubble aggregate by the turbulent flow field using a “machine acceleration”. The concept of machine acceleration is useful because it links the mean energy dissipation rate of turbulence with the condition of the BP detachment. Here we further examine the concept of machine acceleration by applying the theory of isotropic turbulence. We confirm the known results of the first approximation for the inertial subrange. We also show that the turbulence acceleration has two principal components, i.e., the longitudinal and transverse components measured relatively to the BP centre-line. Significantly, the longitudinal component corresponds to the centrifugal force of turbulence against the restoring force of surface tension. The transverse component can be significant to quantifying the BP detachment if the turbulence shear is strong. We also extend the theory to cover the full range of isotropic turbulence, from the viscous to inertial subranges. Our estimation of the transition from the viscous to inertial subrange shows that the viscous effect can critically affect the BP detachment. Finally, our assessment of the contributions of the longitudinal and transverse components to the machine acceleration reveals the importance of the transverse component which can lead to a rather poor approximation for the machine acceleration as currently used. This paper shows that the effect of turbulence on the BP detachment should be better quantified using both the longitudinal and transverse components of turbulence acceleration rather than their modulus as the first approximation being termed the machine acceleration.

On the Construction of Turbulent Transfer Spectral Models Using 3D Numerical Simulation of Taylor–Green Vortex Decay

In the present paper we recall the classical Taylor–Green vortex turbulent decay in terms of isotropic turbulence theory. In particular, we calculate the spectral turbulent kinetic energy transfer $$T(k)$$ and the spectral flux $${{\Pi }_{E}}(k)$$ basing on the longitudinal triple correlation function (the two-point third-order velocity moment). These functions can be also obtained in other way via the generalized Karman–Howarth equation for homogeneous turbulence using integral of triple modes interaction. In both cases, the spectral transfer and the flux appear to be different from the characteristics of isotropic or homogeneous turbulence due to the peculiarities of the problem statement. The results obtained outline the range of obstacles associated with the construction of spectral turbulent models in complex heat and mass transfer problems arising due to periodicity effects, closeness of integral turbulent scales to modeling box size and lack of spectral resolution.

A validity of phenomenological models of turbulence in experimental studies

Estimates of the velocity of the chaotic medium motion using information of "narrow" spectral intervals of stationary random signals generated by the motion of such media on the sensors located at two points along the direction of medium motion are considered. The question about the physical meaning of the minimum spectral interval required for such measurements with a given accuracy is posed and discussed based on the main relations given in the article and formulated using the theory of homogeneous isotropic turbulence. It is shown, that within suggested relations the process of filtration may be described using a turbulent term and so the results of the filtration could be seen as a virtual turbulent dissipation. The latter allowed semiquantitatively describing the results of the numeric calculations presented in the article and forming the ways of the further development of the approach suggested which after appropriate updating might be called a "full filtered correlation analysis" (FFCA). In particular, a method of turbulent dissipation rate measurement by means of two (or more) filters with different bandpasses applied to signals in two points of cross-correlation measurements and an approach to the physically clear description of the optimal number of Fourier-terms in the representation of the signal passed the filter are outlined as well as the approach to a turbulence spectral shape evaluation. Apart from that, with the relations given in the article, the well-known fact that Doppler measurements are not applicable to the remote sensing with use of wideband signals as an information carrier as well as the reason why such measurements are applicable in the case of signals with narrow spectra receive its clear physical explanation. The latter allows forming the definition of a monochromatic signal as it is from the point of view of a cross-correlation analysis.

Volumetric mass transfer coefficient, power input and gas hold-up in viscous liquid in mechanically agitated fermenters. Measurements and scale-up

Transport characteristics such as volumetric mass transfer coefficients, kLa, power input, P and gas hold-up, εG, are the key parameters in the design of mechanically agitated gas-liquid contactors. For their successful design, values of the key parameters can be estimated using empirical correlations. The goal of this work is to complete a complex study to investigate the behavior of kLa, P and εG in multiple-impeller vessels in non-coalescent viscous batch. We used the dynamic pressure method (DPM).The experiments were conducted in multiple-impeller vessels of both laboratory and pilot-plant scale, which enabled the scale-up studies. Several impeller types with different diameters and their combinations on a common shaft were used in the vessel, under various impeller tip speeds and gassing rates. For all impeller combinations, the gassed and ungassed power consumption, gas hold-up and volumetric mass transfer coefficient were measured in viscous batch.The measured transport characteristics were summarized into correlations. Several literature correlations were judged, using these extensive datasets. In addition to this, new correlation shapes were also established. The correlation given by and PgVL=K1PuVLK2vsK3 gave fairly good prediction of the impeller power. The correlation of this shape can also be employed to calculate the power dissipated in the bottom and upper stages of the multiple-impeller vessel.Correlation εG=K1PgVLK2vsK3, based on the theory of isotropic turbulence was shown to be reliable for various impeller types.For non-coalescent viscous batch, it is worth using correlation based on power dissipation kLa=K1(PTOT)K2vsK3 This correlation shape can be used to predict transport characteristics in industrial-scale vessels under a wide range of operational conditions.

Turbulence in protein folding: Vorticity, scaling and diffusion of probability flows.

Recently, when studying folding of a SH3 domain, we discovered that the flows of transitions between protein states can be surprisingly similar to turbulent fluid flows. This similarity was not restricted by a vortex pattern of the flow fields but extended to a spatial correlation of flow fluctuations, resulting, in particular, in the structure functions such as in the Kolmogorov theory of homogeneous and isotropic turbulence. Here, we undertake a detailed analysis of spatial distribution of folding flows and their similarity to turbulent fluid flows. Using molecular dynamics simulations, we study folding of another benchmark system—Trp-cage miniprotein, which has different content of secondary structure elements and mechanism of folding. Calculating the probability fluxes of transitions in a three-dimensional space of collective variables, we have found that similar to the SH3 domain, the structure functions of the second and third orders correspond to the Kolmogorov functions. The spatial distributions of the probability fluxes are self-similar with a fractal dimension, and the fractal index decreases toward the native state, indicating that the flow becomes more turbulent as the native state is approached. We also show that the process of folding can be viewed as Brownian diffusion in the space of probability fluxes. The diffusion coefficient plays a role of the key parameter that defines the structures functions, similar to the rate of dissipation of kinetic energy in hydrodynamic turbulence. The obtained results, first, show that the very complex dynamics of protein folding allows a simple characterization in terms of scaling and diffusion of probability fluxes, and, secondly, they suggest that the turbulence phenomena similar to hydrodynamic turbulence are not specific of folding of a particular protein but are common to protein folding.

Turbulence Measurements from Compliant Moorings. Part II: Motion Correction

AbstractAcoustic Doppler velocimeters (ADVs) are a valuable tool for making high-precision measurements of turbulence, and moorings are a convenient and ubiquitous platform for making many kinds of measurements in the ocean. However, because of concerns that mooring motion can contaminate turbulence measurements and that acoustic Doppler profilers make middepth velocity measurements relatively easy, ADVs are not frequently deployed from moorings. This work demonstrates that inertial motion measurements can be used to reduce motion contamination from moored ADV velocity measurements. Three distinct mooring platforms were deployed in a tidal channel with inertial-motion-sensor-equipped ADVs. In each case, motion correction based on the inertial measurements reduces mooring motion contamination of velocity measurements. The spectra from these measurements are consistent with other measurements in tidal channels and have an slope at high frequencies—consistent with Kolmogorov’s theory of isotropic turbulence. Motion correction also improves estimates of cross spectra and Reynolds stresses. A comparison of turbulence dissipation with flow speed and turbulence production indicates a bottom boundary layer production–dissipation balance during ebb and flood that is consistent with the strong tidal forcing at the site. These results indicate that inertial-motion-sensor-equipped ADVs are a valuable new tool for making high-precision turbulence measurements from moorings.

A mesoscale approach for population balance modeling of bubble size distribution in bubble column reactors

Prediction of bubble size distribution is of paramount importance for the study of bubble column reactors. Current kernel functions for coalescence or breakage in CFD-PBM simulation are usually derived from the isotropic turbulence theory and overestimate bubble size distribution with increasing gas flow rate. Based on the energy-minimization multi-scale concept, we develop a new approach to calculate the coalescence rate through the so-called stability condition and the meso-scale energy dissipation relevant to bubble breakage and coalescence (Yang et al., 2010). The approach is independent of specific kernel functions, and provides a new constraint to the kernel functions of coalescence or breakage which were previously only related to the turbulence properties through isotropic turbulence theory. New correctors for coalescence rate could then be derived for various kernel models. Our simulation indicates that this new approach can adapt to different coalescence or breakage kernel function models, and can achieve better prediction for bubble size distribution.

Similarity Theory for Turbulence, Induced by Orbital Motion of Surface Water Waves

Similarity theory of isotropic turbulence induced by waves on the water with free surface is proposed. Scaling is obtained from experimental and numerical observations of dissipation rates for surface waves, and then used to estimate the turbulent viscosity of the locally-isotropic turbulence.

Noise from Isotropic Turbulence

Turbulence naturally returns to isotropy and often possesses locally isotropic regions. This paper presents a new method to predict noise from turbulence that has returned or is returning to isotropy. The Navier–Stokes equations are decomposed into anisotropic and isotropic turbulent components and corresponding radiating waves. An analytical solution is proposed for the radiating waves associated with isotropic turbulence that contains arguments involving the vector Green’s function of the Navier–Stokes equations and the multi-order two-point cross-correlation of the Navier–Stokes equations involving turbulent fluctuations. Using the theory of isotropic turbulence, the two-point cross-correlation of the Navier–Stokes equations is written as a vector-normalized, two-point cross-correlation multiplied by corresponding wave-number spectra of the structure functions. Composite structure functions of the field variables are adapted from canonical theory of isotropic turbulence. The vector-normalized two-point cross-correlation involves arguments of separation distance, wave number, and corresponding turbulent length and time scales. A solution of the vector Green’s function of the linearized Navier–Stokes equation for acoustic pressure is derived. A simple system of differential and algebraic equations is proposed to model the statistics of stationary and decaying isotropic turbulence, which are arguments of the model equation. Predictions of acoustic and turbulent statistics are compared with a wide variety of measurements and direct numerical simulations from various sources over a range of Reynolds numbers and initial scales. Predictions compare favorably with previous theories, direct numerical simulations, and measurements.

Higher-order dissipation in the theory of homogeneous isotropic turbulence

The two-point theory of homogeneous isotropic turbulence is extended to source terms appearing in the equations for higher-order structure functions. For this, transport equations for these source terms are derived. We focus on the trace of the resulting equations, which is of particular interest because it is invariant and therefore independent of the coordinate system. In the trace of the even-order source term equation, we discover the higher-order moments of the dissipation distribution, and the individual even-order source term equations contain the higher-order moments of the longitudinal, transverse and mixed dissipation distribution functions. This shows for the first time that dissipation fluctuations, on which most of the phenomenological intermittency models are based, are contained in the Navier–Stokes equations. Noticeably, we also find the volume-averaged dissipation $\unicode[STIX]{x1D700}_{r}$ used by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82–85) in the resulting system of equations, because it is related to dissipation correlations.

Hyperuniformity and its generalizations.

Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystal and liquid: They are like perfect crystals in the way they suppress large-scale density fluctuations and yet are like liquids or glasses in that they are statistically isotropic with no Bragg peaks. These exotic states of matter play a vital role in a number of problems across the physical, mathematical as well as biological sciences and, because they are endowed with novel physical properties, have technological importance. Given the fundamental as well as practical importance of disordered hyperuniform systems elucidated thus far, it is natural to explore the generalizations of the hyperuniformity notion and its consequences. In this paper, we substantially broaden the hyperuniformity concept along four different directions. This includes generalizations to treat fluctuations in the interfacial area (one of the Minkowski functionals) in heterogeneous media and surface-area driven evolving microstructures, random scalar fields, divergence-free random vector fields, and statistically anisotropic many-particle systems and two-phase media. In all cases, the relevant mathematical underpinnings are formulated and illustrative calculations are provided. Interfacial-area fluctuations play a major role in characterizing the microstructure of two-phase systems (e.g., fluid-saturated porous media), physical properties that intimately depend on the geometry of the interface, and evolving two-phase microstructures that depend on interfacial energies (e.g., spinodal decomposition). In the instances of random vector fields and statistically anisotropic structures, we show that the standard definition of hyperuniformity must be generalized such that it accounts for the dependence of the relevant spectral functions on the direction in which the origin in Fourier space is approached (nonanalyticities at the origin). Using this analysis, we place some well-known energy spectra from the theory of isotropic turbulence in the context of this generalization of hyperuniformity. Among other results, we show that there exist many-particle ground-state configurations in which directional hyperuniformity imparts exotic anisotropic physical properties (e.g., elastic, optical, and acoustic characteristics) to these states of matter. Such tunability could have technological relevance for manipulating light and sound waves in ways heretofore not thought possible. We show that disordered many-particle systems that respond to external fields (e.g., magnetic and electric fields) are a natural class of materials to look for directional hyperuniformity. The generalizations of hyperuniformity introduced here provide theoreticians and experimentalists new avenues to understand a very broad range of phenomena across a variety of fields through the hyperuniformity "lens."

A review of stochastic description of the turbulence effect on bubble-particle interactions in flotation

Flotation in mechanically agitated cells has been the workhorse of the mining industry, but our quantitative understanding of the effect of microturbulence generated by agitation on flotation is still very limited. This paper aims to review the literature on quantifying the microturbulence effects on bubble-particle interactions in flotation. The particular focus is on the stochastic description of bubble-particle interactions in the turbulent flow which is a random field. We briefly review the stochastic description of microturbulence and motions of particles of micrometre sizes and bubbles of millimetre sizes in the isotropic turbulence of mechanical flotation cells. The key starting point is the generic equation of motion, which can be decomposed into the mean turbulent variables and fluctuating turbulent variables. The turbulent flow of the carrying liquid is characterised using isotropic turbulence theory. The next focus is on reviewing bubble-particle turbulent collision and detachment interactions. Bubble-particle turbulent collision is poorly quantified; no quantitative models of the bubble-particle turbulent collision efficiency relevant for flotation are available. Current theories on bubble-particle turbulent detachment face some deficiencies. In assessing the microturbulence effect on bubble-particle detachment, the majority of studies only considers the particle acceleration in the centrifugal direction but ignore the transverse acceleration of particles, which is due to turbulent shear flow. Critically, contact angle required in quantifying the detachment is not constant, single-valued as considered in the theories, but can vary from receding to advancing value during the relaxation of the triple contact line on the particle surface. The latest experiments show that multiple-valued contact angle can significantly affect stability and detachment of floating particles. Finally, quantifying the microturbulence effect on flotation requires further research.