Figure₃: The folder "Figure₃" contains the data for each experiment. The file naming convention is as follows: IₐndLmixcm_. Each file includes: the distance between the acoustic sensors (Lₐcoustic), the channel width (Lchannel), the full spatial profiles (Lₚrofile), the time series associated with the mixture width (tLmix, Lmix), and the corresponding light intensity measurements at two different times (intensityₚrofileₜ1 and intensityₚrofileₜ2). The subsets of these raw profiles used to determine Lmix are provided separately. These are named: Lₚrofilefin1 and intensityₚrofilefin1 for time 1, Lₚrofilefin2 and intensityₚrofilefin2 for time 2. Figure₄: The folder "Figure₄" contains the data for each experiment. The file naming convention is as follows: UmixₐndStcm_. Each file includes: the theoretical free-fall velocity (Uₗim), the time series associated with the mixture velocity (tUmix, Umix), the time series associated with the Stokes number (tSt, St), and the shaded bands representing the uncertainty on St, provided as (xₚatch, yₚatch). Figure₅: The folder "Figure₅" contains the data for each experiment. The subfolder naming convention is as follows: cm_. Each subfolder contains the following files: AlphaₐndFreqcm_: Contains the Fast Fourier Transform (FFT) of the propagated signals (Fₐlphaₚlot), the associated attenuation coefficient (ALPHAₚlot), and the corresponding fitted data (Ffitₚlot, AMENTfitₚlot). MagmₐndFreqcm_: Contains the Fast Fourier Transform (FFT) of the propagated signals (Fₚlot) and the associated magnitude (AMPLₚlot). tₐndₚhicm_: Contains the experimental time (timeₐff), the associated particle concentration (phiₐff), the transition time (transition), and the end time of the experiment (endₑxp). tₛtarₐndAcm_: Contains the pulse propagation time (tₛtar) and the corresponding amplitude (A). Figure₆: The folder "Figure₆" contains the data for each experiment. The file naming convention is as follows: Iₐndₕcm_. Each file includes: the time series associated with the mixture intensity measurements (tI, Iₘix), the time series associated with the current intensity measurements (tI, Icurrent), the time series associated with the bed height measurements (tₕ, h), the transition time (transition), and the shaded bands representing the uncertainty on Iₘix (xₚatch, yₚatchₘix) and on Icurrent (xₚatch, yₚatchcurrent). Figure₇: The folder "Figure₇" contains the data for each experiment, including: the transition values of particle concentration (Phiₜrans) and their associated uncertainties (sdPhiₜrans), the transition values of the Stokes number (Stₜrans) and their associated uncertainties (sdStₜrans), the transition values of the volumetric flux per unit area (PhiUₜrans) and their associated uncertainties (sdPhiUₜrans), the fitted series associated with the relationship between particle concentration and Stokes number (xfit, yfit1), and the fitted series associated with the relationship between volumetric flux per unit area and Stokes number (xfit, yfit3). FigureS1: The folder "FigureS1" contains the data for each experiment. The file naming convention is as follows: Qcm_. Each file includes: the time series associated with the mass flow rate of the mixture (t, Qₘix). FigureS2: The folder "FigureS2" contains the data for each experiment. The file naming convention is as follows: Masscumcm_. Each file includes: the time series associated with the cumulative mass of the mixture (t, Masscum). FigureS3: The folder "FigureS3" contains the data for each experiment, including: the transition values of the Reynolds number (Reₜrans) and their associated uncertainties (SdReₜrans), the particle diameter (dp), the threshold value of the turbulent regime (Reₗim). FigureS4: The folder "FigureS4" contains the data for each experiment, including: the transition values of mass flow rate (Qₜrans) and their associated uncertainties (sdQₜrans), the transition values of the Stokes number (Stₜrans) and their associated uncertainties (sdStₜrans), and the fitted series associated with the relationship between mass flow rate and Stokes number (xfit, yfit2). FigureS5: The folder "FigureS5" contains the data for each experiment, including: a kymograph of grayscale intensity extracted from the experiment (Largfluxᵥar. tif). The horizontal axis corresponds to the spatial coordinate of the profile (Lₚrofile), and the vertical axis corresponds to time. the three intensity profiles corresponding to the dense regime (Iₚrofile1), the transition regime (Iₚrofile2), and the dilute regime (Iₚrofile3). the intensity threshold values used to characterize the signal. c12ₗow, c12, and c12ᵤp represent the reference thresholds for the dense and transition regimes, corresponding respectively to −5% tolerance, the nominal threshold, and +5% tolerance. Similarly, c3ₗow, c3, and c3ᵤp represent the reference thresholds for the dilute regime with the same ±5% tolerance.
Penlou et al. (Tue,) studied this question.