these regions becomes too small to prevent motion, leading to less and less particles coming to a stop. More studies of the relative importance between these mechanisms would help to understand the role of each particle/fluid/surface/deposit parameters (especially with recent measurements showing the importance of rolling even for large millimeter-size grains exposed to low Reynolds flows [331, 332])

### 7.2.2. The role of collective motion

As soon as a significant number of particles are deposited on a surface, they can form isolated clusters or even complex multilayer structures. Despite considerable progress in recent years (see for instance [3]), there are still several open issues related to particle collective motions:

* Collective motion of migrating and detached particles:

In the case of multilayer deposits, particles located on top of the deposit are the ones exposed to the flow (and to the near-wall turbulent structures [333]). Thus, these particles are more susceptible to start moving, especially if they are protruding from the average deposit (leading to higher hydrodynamic forces and more chances to interact with near-wall structures) [334, 335]. Once a particle starts moving within a complex deposit, it can collide with its neighbors, thereby inducing a collective motion of particles within a multilayer deposit. As displayed in Fig. 63, this collective motion is related to the size and shape of particles [297]: in the case of Zingg ellipsoids, their collective motion results in the propagation of some sorts of sediment waves (or dunes) that slowly migrate downstream of the flow. Such collective motions have profound consequences on resuspension. First, the inter-particle collisions can lead to much higher and sustained resuspension rates (as new particles continuously start moving as they are impacted by other moving particles). Second, during saltation or reptation, particles detach from the surface and move in the near-wall region. Depending on how far away from the surface they travel during such hopping motion, their velocity upon impacting the deposit changes. In fact, saltating particles travel much further away and tend to impact the deposit with a higher velocity, thereby leading to a large number of particles being set in motion due to splashing effects. Meanwhile, reptating or creeping particles remain (very) close to the surface. As a result, when the amount of particles moving near the surface is large (as in Fig. 63), particles constantly collide with each other. Such collective motions are key in the distinction between fluvial and aeolian transport [284, 242].

<figure><img src="image_80.png" /><figcaption>Figure 63: Instantaneous snapshot of a simulation with a complex multilayer deposit composed of Zingg ellipsoids. Ellipsoids are colored according to their wall-normal position. A contour plot of the streamwise velocity is shown on the back side of the domain, while 3D isosurfaces of the instantaneous streamwise velocity are plotted in red and blue. This shows the collective motion of ellipsoids, which form dunes that are slowly moving in the streamwise direction. Reprinted with permission from [297]. Copyright 2021, Cambridge University Press.</figcaption></figure>

Models that accurately reproduce these collective effects are being developed and represent valuable steps towards unified models. This is where building new bridges between communities dealing with granular flows, which are specialized in dealing with such dense flows of particles [326], turns out to be quite constructive.
## Cluster resuspension

Another challenge of multilayer resuspension is related to the fact that whole clusters can be re-suspended during single resuspension events instead of only individual particles. In fact, when the deposits formed are not too compact, clusters can be identified as particles tightly bonded to each other (thereby forming a more compact deposit than the surrounding deposit, as displayed in Fig. 64). Due to the high cohesion of such clusters, it becomes more probable that these clusters resuspend as whole blocs. This brings out several issues:

- Morphology of deposits:

Cluster resuspension is directly related to local fluctuations in the deposit structure. In turn, the deposit morphology is a direct consequence of how particles accumulate on a surface. For instance, compact deposits are typically formed when dealing with large/heavy particles (such as sediments or gravels). This is due to the strong gravity forces, which favor the motion of particles until reaching mechanically stable positions (i.e., with isostatic constraints, such as on flat areas or on regions with three contacts). In contrast, when dealing with colloidal particles, cohesion forces dominate over gravity forces and the resulting morphology depends on the deposition scenario [97]. In fact, the two extreme cases are either loose structures (which occur when colloids attach immediately at the point of first contact) or very compact ones (obtained when colloids move until reaching stable positions). In reality, the deposit structure can take a range of values in-between these two extremes [336], possibly due to the role of collisions, surface roughness or non-sphericity of particles (which induces intermediate stable positions with isostatic constraints). Properly capturing the deposit structure and cohesion is thus all the more important [337, 328]. In fact, particles/clusters trapped within the deposit bed can be much harder to remove than particles/clusters protruding from the bed, and this has led to the introduction of a 'burial depth' in some resuspension models (see for instance [338, 339]).

Current measurements do not provide sufficient information to fully characterize deposit structures, due to the opacity of the deposits which prevents detailed analysis of their internal structure. Nevertheless, the authors believe that recent advances in experimental techniques now open the way for detailed analysis of deposit structures. In fact, X-ray computed tomography techniques allow to see right through opaque particles [146, 147]. Recent studies have started to use this technique to monitor the motion of a 3D pack composed of 1055 particles and analyze how the critical shear stress for incipient motion changes according to various parameters (like grain protrusion). These techniques could also provide information on restructuring events during time.

<figure><img src="image_81.png" /><figcaption>Figure 64: Sketch of a multilayer deposit exposed to a fluid flow: darker particles constitute clusters of particles that can be resuspended altogether.</figcaption></figure>

- Consolidation/ageing effects

Cohesion forces within a cluster/deposit are not always constant in time. In the case of solid particles, aging effects (such as sintering) can lead to cohesion forces increasing with time [340].
Sintering occurs at high temperature and leads to the creation of stronger bonds between contacting particles due to the precipitation occurring preferentially near the contact area between surfaces. Such modifications of particle bond energies with time are generally referred to as ‘consolidation processes’ and have been shown to be responsible for lower resuspension rates on heated surfaces after long exposure time [340]. When they take place, these consolidation effects have thus a profound impact on long-term resuspension. For instance, in the case of alpine snow, higher temperature leads to snow melting and the resulting higher water content decreases the cohesion forces in snow: this process is responsible for wet loose-snow avalanches [341].

Reproducing accurately the resuspension of such complex deposits requires to properly take into account the morphology of the deposit formed. This can be obtained naturally with individual particle tracking approaches (provided that the adhesion/cohesion forces are properly estimated). Alternatively, statistical models can be developed by identifying clusters of particles within complex deposits (as in [342, 343]) and possibly by treating the motion of parcels. Parcels correspond to numerical particles which represent a large number of real particles. It allows to reduce the computational costs associated with individual particle tracking approaches, making such approaches tractable in realistic situations. However, in turn, such simplifications might require additional modeling. In fact, even if there exists a single cluster within a region, this does not mean that individual particles within this cluster cannot interact with each other. Hence, if such interactions have to be accounted for, new models have to be introduced to reproduce these effects (like filtering in large-eddy simulations of turbulent flows).

* Mixed deposit (or binary mixtures):

In real situations, deposits are often composed of particles with a range of sizes, shapes and possibly even composition. For instance, as displayed in Fig. 65a, beach sediments are usually formed by grains with a range of sizes (typically within a few millimeters). In river transport, the range of sizes can be even more pronounced, with the presence of both millimeter-size sand grains and centimeter-size gravels. In addition, river beds can be composed of a mixture of sand/gravels as well as plastic debris (as sketched in Fig. 65b).

<figure><img src="image_82.png" /><figcaption>Figure 65: Images of particles within mixed beds, i.e., formed by the accumulation of several types of particles in a complex multilayer system. These particles can vary according to their size, shape, density, composition, etc.</figcaption></figure>

The presence of particles with different sizes, shapes and composition can severely affect resuspension. In such cases, one of the issues is to properly define what has to be measured. One could define a resuspension rate for each type of particle present within the deposit. This allows to distinguish if
some of the particles within the mixture resuspend more easily than others. Yet, due to the collective motion of nearby particles, the resuspension rates might depend strongly on local particle velocities. If such collective phenomena are significant, one has to consider measuring individual resuspension events and correlating these events to the local fluid and particle velocities. As a result, resuspension rates averaged over all particles of the same type might be irrelevant unless conditioned on local measures of collective motion (e.g., mean particle velocity). This opens a whole new range of interesting discussions as to the information that should be contained in the measured quantities. Alternatively, one can also rely on a resuspension rate averaged for the whole mixture. In that case, the drawback is that no information is available on how exactly the different grains behave. Another difficulty is related to the motion of particles once they are detached from the surface, which depends on the particle size since small particles tend to undergo saltation while large particles are more prone to retraction (as in megaripples [102]).

In terms of modeling approaches, capturing the resuspension of complex mixtures is relatively straightforward when resorting to particle-tracking approaches (which naturally follow each individual particle with its given size and properties). New models would be required for statistical approaches (such as those relying on the tracking of parcels instead of individual particles). Nevertheless, precise simulations might prove useful to investigate the role of armoring, where some heavy and large particles prevent the resuspension of lighter and smaller particles located beneath them (thereby shielding the particles easier to resuspend). In addition, such complex deposits with multiple types of particles can display very different splashing effects, since each size of particles would have a different probability to be resuspended due to the impaction of a saltating particle [287].

### 7.3. The road ahead: a personal viewpoint on future models

Devising generic models that not only perform as the state-of-the-art ones (outlined in Section 4.3) but also accounting for the new phenomena discussed throughout the present section is likely to be pursued for some time. Following the guidelines set forth in Section 5, it is essential to keep in mind that such extended models should be realistic while remaining tractable in practical situations. To wrap up this section, we would like to share personal views on which modeling approaches appear as promising candidates for this task.

As described in Section 7.1, more realistic models are expected to account for local variations both in particle (e.g., shape, size, density) and surface properties (e.g., contaminated or inhomogeneous surfaces). This is where particle tracking approaches could shine, since they allow to treat in a rather straightforward manner any distribution of particle properties (size, shape, etc.). However, the drawback of these approaches is that they contain a high level of information. Hence, to remain tractable in practical situations, work is still needed to come up with accurate but reduced descriptions of the key phenomena (such as using dumbbells/trumbbells for elongated flexible fibers). In contrast, customized models would require more extensive adaptations to be applicable to complex particles. In particular, empirical models would require to have a set of data for the resuspension of each type of particles.

In addition, as discussed in Section 7.2, unified models can be developed provided that all the mechanisms are properly included (including inter-particle collisions and the collective motion that results from continuous and sustained collisions). In the authors' opinion, such unified models are now within reach, thanks to numerous developments for both monolayer and multilayer resuspension that could be gathered in a generic model spanning the range of deposits encountered in real applications. One issue is, however, to develop models that remain flexible enough so that additional mechanisms/forces can be introduced/changed depending on the application which is aimed for. Such a flexibility is needed to apply the same model to predict resuspension induced by various mechanisms or even a combination of them, as is the case for walking-induced resuspension (which is triggered by the airflow, by vibrations due to the foot tapping on the nearby surface and by electrostatic forces [346]). Here also, we believe that particle-tracking approaches are more adapted to treat such complex issues while remaining flexible enough to easily add/remove/change some of the mechanisms/phenomena/forces at play. In our view, the key challenge is related to the amount of information that should be resolved by such models. In fact, tractable models cannot realistically track
the motion of each individual particle while solving exactly the hydrodynamic forces and adhesion forces
for each particle (as in [215]). Consequently, simplifications are in order and careful considerations about
the consistency between the various levels of description entering each sub-model are needed. This is where
dynamic PDF approaches appear as particularly interesting candidates. Indeed, we are of the opinion
that dynamic PDF models allow to treat with a high-enough accuracy some of the key phenomena (like
transport, polydisperse and/or multimodal particle properties) while still remaining tractable in realistic
situations thanks to adequate models that capture the phenomena that are not explicitly solved.

8. Conclusions and perspectives

Particle resuspension is a process in which a set of discrete elements, or particles, adhering to a wall surface are set in motion and eventually carried away from that surface by a fluid flow. As such, a cursory look at this problem might give the impression that the physics is already well understood and that what remains to be done is to work out simple rules for more engineering concerns. This is not so and this review has been written with two main objectives in mind.

The first main objective was to reveal the rich complexity of this phenomena and shed new light on the
key physical processes involved. To fulfill that purpose, the approach chosen in this work has consisted in
bringing out the key mechanisms through which particles deposited on a surface are resuspended and, then,
in analyzing the physical forces involved in terms of fundamental interactions (particle-fluid, particle-particle
and particle-surface). Central to this endeavor is the issue of coming up with universal descriptions. This
leads to revisiting not just the formulation but the very essence of a model of particle resuspension. What
makes up a model and what is the nature of the information to be resolved are questions worth pondering
on. Once a consistent modeling framework was set up, it appeared, however, that the present picture needs
to be extended. A specific section was therefore dedicated to proposing new areas of developments, in which
two directions where significant progress is expected were suggested. The first direction is at the level of each
particle and consists in accounting for more complex individual objects in order to go beyond the current
assumption of small spherical particles. By complex, it is meant here particles with more complex shapes but
also potentially deformable or flexible. Once a mechanical description of these particles is chosen in terms
of a selected number of variables attached to each particle and whose evolution in time characterizes the
dynamics of that particle, a satisfactory resuspension model should be able to accommodate such particle
properties. The second direction of progress is at the level of description of the collective behavior, in
particular to reproduce key aspects of multilayer resuspension. These two directions operate at two different
levels but it is interesting to note that we need to capture at the same time more complex dynamics of
individual particles as well as more complex collective phenomena. In other words, the quest for a truly
unified picture continues and it is hoped that the present review is helpful to point out potential new roads.

This corresponds to the second main objective of this work which is basically a call for new contributions
since addressing these challenging tasks would greatly benefit from physicists with a keen eye for both
particle dynamics and collective behavior. While trying to encourage colleagues to work at the nanoscale (in
fact, decades before nanotechnology actually picked up), Richard P. Feynman once formulated his invitation
by "there is plenty of room at the bottom". It is believed that the same is true even at more macroscopic
levels and that resuspension is an example that "there is also plenty of room at the top".

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that
could have appeared to influence the work reported in this review.

Acknowledgement

CH acknowledges Grégory Lécrivain (HZDR, Germany) for useful and constructive discussions, especially
on collision-induced resuspension from dense monolayer deposits.
SB. Research presented in this article was supported by the Laboratory Directed Research and Development program of Los Alamos National Laboratory under project number 20210204DR.

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