In this review we explore the recent developments in the use of Magnetic Resonance Imaging (MRI) for studying granular flows. While MRI has been a valuable tool in this field for the past 40 years, recent advances in imaging hardware, reconstruction software and particles synthesis have significantly enhanced its capabilities. This article provides an overview of the current challenges of MRI and progress in the field of granular media, and gives a perspective of the possible future developments in the field.

Magnetic resonance imaging (MRI) experiments have been performed in conjunction with direct numerical simulations (DNS) to study neutrally buoyant particle-laden pipe flows. The flows are characterized by the suspension liquid Reynolds number (Res), based on the bulk liquid velocity and suspension viscosity obtained from Eilers' correlation, the bulk solid volume fraction (φb), and the particle-to-pipe diameter ratio (d/D). Six different cases have been studied, each with a unique combination of Res and φ, while d/D is kept constant at 0.058. The selected cases ensure that the comparison is performed across different flow regimes, each exhibiting characteristic behavior. In general, an excellent agreement is found between experiment and simulation for the average liquid velocity and solid volume fraction profiles. Root-mean-square errors as low as 1.7% and 5.3% are found for the velocity and volume fraction profiles, respectively. This study presents accurate and quantitative velocity and volume fraction profiles of semidilute up to dense suspension flows using both experimental and numerical methods. Three different flow regimes are identified, based on the experimental and numerical solid volume fraction profiles. These profiles explain observations in the drag change. For low bulk solid volume fractions a drag increase (with respect to an equal Res single-phase case) is observed. For moderate volume fraction distributions the drag is found to decrease, due to particle accumulation at the pipe center. For high volume fractions the drag is found to decrease further. For solid volume fractions of 0.4 a drag reduction higher than 25% is found. This drag reduction is linked to the strong viscosity gradient in the radial direction, where the relatively low viscosity near the pipe wall acts as a lubrication layer between the pipe wall and the dense core.

Using magnetic resonance imaging we are able to obtain average velocity and volume fraction profiles in a pipe flow with a neutrally buoyant suspension. In this experimental work, the effect of increasing Reynolds number and particle volume fraction on shear-induced migration is studied. For increasing bulk volume fraction, the initially nearly homogeneous suspension gradually changes to a strongly non-homogeneous suspension. This is observed for all studied Reynolds numbers. In contrast to the majority of previous (MRI) studies, experiments are also performed for suspension Reynolds numbers of approximately 5000 in order to study inertial effects on shear-induced migration.

Abstract: Ultrasound imaging velocimetry (UIV) refers to the technique wherein ultrasound images are analysed with 2D cross-correlation techniques developed originally in the framework of particle image velocimetry. Applying UIV to opaque, particle-laden multiphase flows have long been considered to be an attractive prospect. In this study, we demonstrate how fundamental differences in acoustical imaging, as compared to optical imaging, manifest themselves in the 2D cross-correlation analysis. A chief point of departure from conventional particle image velocimetry is the strong variation in the intensity profile of the acoustic wavefield, primarily caused by the attenuation of ultrasonic waves in particle-laden flows. Attenuation necessitates using a larger ensemble of correlation planes to obtain satisfactory time-averaged velocity profiles. For a given combination of imaging and flow conditions, attenuation sets upper limits on volume fraction, penetration depth, as well as temporal resolutions that may be accessed confidently. This behaviour is demonstrated in two experimental datasets and is also supported by a modified cross-correlation theory. The modification is brought about by incorporating a lumped model of ultrasonic backscattering in suspensions into existing spatial cross-correlation analysis. The two experimental datasets correspond to two distinct particle-laden pipe flows: (1) a neutrally buoyant non-Brownian suspension in a laboratory-scale flow facility, wherein particle sizes are comparable to the ultrasonic wavelength and (2) a non-Newtonian slurry in an industrial-scale flow facility, wherein particle sizes are much smaller than the ultrasonic wavelength. We illustrate how and to what extent correlation averaging can counteract the adversity caused by attenuation. The work herein offers a template for one to evaluate the performance of UIV in particle-laden flows. Graphical abstract: [Figure not available: see fulltext.].

Abstract: We discuss empirical techniques to extract quantitative particle volume fraction profiles in particle-laden flows using an ultrasound transducer. A key step involves probing several uniform suspensions with varying bulk volume fractions from which two key volume fraction dependent calibration parameters are identified: the peak backscatter amplitude (acoustic energy backscattered by the initial layer of the suspension) and the amplitude attenuation rate (rate at which the acoustic energy decays with depth owing to scattering losses). These properties can then be used to reconstruct spatially varying particle volume fraction profiles. Such an empirical approach allows circumventing detailed theoretical models which characterize the interaction between ultrasound and suspensions, which are not universally applicable. We assess the reconstruction techniques via synthetic volume fraction profiles and a known particle-laden suspension immobilized in a gel. While qualitative trends can be easily picked up, the following factors compromise the quantitative accuracy: (1) initial reconstruction errors made in the near-wall regions can propagate and grow along the reconstruction direction, (2) multiple scattering can create artefacts which may affect the reconstruction, and (3) the accuracy of the reconstruction is very sensitive to the goodness of the calibration. Despite these issues, application of the technique to particle-laden pipe flows shows the presence of a core with reduced particle volume fractions in laminar flows, whose prominence reduces as the flow becomes turbulent. This observation is associated with inertia-induced radial migration of particles away from the pipe axis and is observed in flows with bulk volume fractions as high as 0.08. Even transitional flows with low levels of intermittency are not devoid of this depleted core. In conclusion, ultrasonic particle volume fraction profiling can play a key complementary role to ultrasound-based velocimetry in studying the internal features of particle-laden flows. Graphic abstract: [Figure not available: see fulltext.]

Particle-laden pipe flows exhibit a gradual laminar-turbulent transition, beyond a critical volume fraction (φ). While classical transition behavior is characterized by the presence of turbulent puffs, this intermittent nature is absent for particle-induced transition. For small pipe-to-particle diameter ratios (D/d) even dilute systems exhibit this particle-induced transition behavior. In this study we use neutrally buoyant particles with a D/d of 5.7, which represents a "sweet spot,"allowing the use of particle image velocimetry to study this particular phenomenon. The average velocity profile gradually changes from a parabola (laminar flow) to a blunted velocity profile for increasing Reynolds number. The instantaneous velocity profiles fluctuate around this profile. These velocity fluctuations, described by ux-rms and ur-rms, gradually increase for increasing Reynolds number, as do the Reynolds stresses. For low Res, the velocity fluctuations increase proportional to the bulk velocity, which can be explained by a simple model based on the finite size of the particles. The velocity fields show the presence of elongated streamwise structures. The largest length scales are found in the transition region, where average integral length scales up to 5D are found. The structures decrease in length when the flow has fully transitioned to a turbulent state.

Partial cavitation dynamics in an axisymmetric converging-diverging nozzle are investigated experimentally. Shadowgraphy is used to visualize and analyze different cavitation regimes. These regimes are generated by changing the global static pressure and flow velocity independently. Cloud cavitation is the most interesting and complex regime, because the shedding of vapor clouds is caused by two different mechanisms: the re-entrant jet mechanism and the bubbly shock mechanism. The dynamics are investigated using a position-time diagram. Using such a diagram we show that for cavitation number σ > 0.95 the cavity shedding is caused by the re-entrant jet mechanism, and for σ < 0.75 the mechanism responsible for periodic cavity shedding is the bubbly shock mechanism. Both mechanisms are observed in the transition region, 0.75 < σ < 0.95. The shedding frequencies, expressed as Strouhal numbers, collapse on a single curve when plotted against the cavitation number, except for the transition region. The re-entrant jet mechanism is a pressure gradient driven phenomenon, which is caused by a temporary stagnation point at the cavity front. This leads to stick-slip behavior of the cavity. In the bubbly shock regime, a shock wave is induced by a collapse of the previously shedded vapor bubbles downstream of the venturi, which triggers the initiation of the detachment of the growing cavity. The propagation velocity of the shock wave is quantified both in the liquid and the mixture phase by means of the position-time diagram.