A B S T R A C T
The microscale simulation of colloidal **particle** **transport** **and** **deposition** in porous media was achieved with a novel colloidal **particle** tracking model, called 3D-PTPO (Three-Dimensional **Particle** Tracking model by Python ® **and** OpenFOAM ® ), using a Lagrangian method. Simulations were performed by considering the elementary pore structure as a capillary tube with converging/diverging geometries (tapered pipe **and** venturi tube). The particles are considered as a mass point during **transport** in the ﬂow **and** their volume is reconstructed when they are deposited. The main feature of this novel model is to renew the ﬂow ﬁeld by reconstructing the pore structure by taking the volume of the deposited particles into account. The inﬂuence of the **particle** Péclet number (Pe) **and** the pore shape on the **particle** **deposition** therein is investigated. The results are analyzed in terms of **deposition** probability **and** dimensionless surface coverage as a function of the number of injected particles for a vast range of Péclet numbers thus allowing distinguishing the behavior in di ﬀusion dominant **and** advection dominant regimes. Finally, the maximum dimensionless surface coverage Γ ﬁnal / Γ RSA is studied as a function of Pe. The declining trend observed for high Pe is in good agreement with experimental **and** simulation results found in the literature.

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Moreover, **particle** **transport** **and** **deposition** processes in porous media are of great technological **and** industrial interest since they are useful in many engineering applications **and** fundamentals [11-13] including contaminant dissemination, filtration, chromatographic separation **and** remediation processes [14-19]. To characterize these processes, numerical simulations have become increasingly attractive due to growing computer capacity **and** calculation facilities offering an interesting alternative, especially to complex in situ experiments [20-22]. Basically, there are two types of simulation methods, namely macro-scale simulations **and** micro-scale (pore scale) simulations. Macro-scale simulations describe the overall behavior of the **transport** **and** **deposition** process by solving a set of differential equations that gives spatial **and** temporal variation of particles concentration in the porous sample without providing any information regarding the nature or mechanism of the retention process [17]. Micro-scale (pore scale) numerical simulations directly solve the Navier-Stokes or Stokes equation to compute the flow **and** model **particle** diffusion processes by random walk for example [23].

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ρ c = 1012 kg/m 3 is initially confined in a hollow cylinder at the centre of a large
tank filled with fresh water. Cylinders with two different cross-sectional shapes, but equal cross-sectional areas, are examined: a circle **and** a rounded rectangle in which the sharp corners are smoothened. The time evolution of the front is recorded as well as the spatial distribution of the thickness of the final deposit via the use of a laser triangulation technique. The dynamics of the front **and** final deposits are significantly influenced by the initial geometry, displaying substantial azimuthal variation especially for the rectangular case where the current extends farther **and** deposits more particles along the initial minor axis of the rectangular cross section. Several parameters are varied to assess the dependence on the settling velocity, initial height aspect ratio, **and** volume fraction. Even though resuspension is not taken into account in our simulations, good agreement with experiments indicates that it does not play an important role in the front dynamics, in terms of velocity **and** extent of the current. However, wall shear stress measurements show that incipient motion of particles **and** **particle** **transport** along the bed are likely to occur in the body of the current **and** should be accounted to properly capture the final **deposition** profile of particles.

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5.2.3 Radiography **and** field measurements with laser-driven ions beams
The use of ion beams, **and** particularly proton beams, for radiographic applications was first proposed in 1960s [ 147 ]. Quasi-monochromatic beams of ions from conventional accelerators have been used for detecting areal density variations in samples via modifications of the proton beam density cross- section, caused by differential stopping of the ions, or by scattering. Radiography with very high energy protons ( ∼ 1 − 10 GeV) is being developed as a tool for weapon testing [ 141 ]. The use in laser-plasma experiments of ion beams produced with standard accelerators is limited by the relative long duration of the produced ion pulses **and** the difficulties **and** high cost involved in coupling externally produced **particle** beams of sufficiently high energy to laser-plasma experiments. The unique properties of protons from high intensity laser-matter interactions, particularly in terms of spatial quality **and** temporal duration, have opened up a totally new area of application of proton probing or radiography with laser-driven ion beams. As seen in Sec. 5.2.1 , the protons emitted from a laser-irradiated foil by TNSA can be described as emitted from a virtual, point-like source located in front of the target [ 33 ]. A point-projection magnifying imaging scheme is therefore automat- ically achieved **and** set by the geometrical distances at play. The proton beam as a backlighter yields a spatial resolution of a few µm. Moreover, a special arrangement of a multilayer detector, employing RCFs ( Sec. 18 ) for example, offer the possibility of energy-resolved measurements, despite the broad spectrum, by energy discrimination consequent to the localized energy **deposition** (Bragg peak) characteristics of the ions in matter ( Sec. 18.1 ). More precisely, as the detector performs spectral selection, each RCF layer contains, in a first approximation, information pertaining to a particular time, so that a "movie" of the interaction made up of discrete frames can be taken in a single shot (as shown in Sec. 11.1.1 ). Depending on the experimental conditions, 2D proton deflection map frames spanning up to 100 ps can be obtained. The ultimate limit of the temporal resolution is given by the duration of the proton burst at the source, which is of the order of the laser pulse duration. Proton radiography, as a density diagnostic, has been successfully used to study the various stages of the compression of empty CH shells under multi-beam isotropic irradiation at the moderate intensity of 10 13 W/cm 2 [ 171 ]. Also, radiographs of cylindrically compressed matter [ 286 ] **and** of shock wave

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Abstract—The objective of this study is to simulate the **transport** **and** **deposition** of colloidal particles at the pore scale by means of computational fluid dynamics simulations (CFD). This consists in the three-dimensional numerical modeling of the process of **transport** **and** **deposition** of colloidal particles in a porous medium idealized as a bundle of capillaries of circular cross section. The velocity field obtained by solving the Stokes **and** continuity equations is superimposed to particles diffusion **and** particles are let to adsorb when they closely approach the solid wall. Once a **particle** is adsorbed the flow velocity field is updated before a new **particle** is injected. Our results show that both adsorption probability **and** surface coverage are decreasing functions of the particle’s Péclet number. At low Péclet number values when diffusion is dominant the surface coverage is shown to approach the Random Sequential Adsorption value while it drops noticeably for high Péclet number values. Obtained data were also used to calculate the loss of porosity **and** permeability. Index Terms —Porous media, **particle** **transport**, **deposition**, pore scale numerical simulation.

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Physical clogging caused by solid particles is considered as the most common source of emitter plugging (Pitts et al. 2003). To reduce **particle** **deposition**, filtration is essential in drip-irrigation, **and** it is often coupled with the initial removal of large particles, **and** with screen filters for finer materials (Lamm **and** Camp 2007). Depending on filter mesh size, small particles, such as sand (>50µm), silt (>2µm) or clay (<2µm), can still enter the emitter, **and** may cause physical clogging due to different phenomena such as aggregation, cementation **and** **transport**. Numerical studies of Wei et al. (2009) **and** Liu et al. 2010 showed that velocity of suspended particles, **particle** diameters **and** sediment concentrations are the main factors responsible for physical clogging. The likelihood of emitter clogging is significantly increased when **particle** diameter exceeds 50µm (Wei et al. 2009). The average size of the labyrinth channel width is approximately 1mm (Zhang et al. 2010). Niu et al. (2013) observed that large **particle** **deposition** is usually located at the inlet **and** channel corners. However, emitters can also be obstructed by the accumulation of fine particles such as silt **and** clay (Bounoua et al. 2016, Oliveira et al. 2017). The nature of clay can strongly modify clogging mechanisms (Oliveira et al. 2017). The presence of salts can also amplify the aggregation mechanisms of clays (Cuisset 1979; Stawinski et al. 1990).

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Not all possibilities of such a multiscale approach are explored for the moment. We succeeded to model speckled laser beams **and** their temporal smoothing, cross beam energy transfer (CBET) **and** hot electron generation due to the reso- nance absorption, SRS **and** TPD. Figure 8 shows two exam- ples of CHIC simulations with the nonlinear LPI package. The left panel shows the CBET effect on the implosion of a plasma cylinder with 18 laser beams smoothed with random phase plates. Each beam is modeled with 60 Gaussian beam- lets focused randomly near the focal plane. A significant azimuthal inhomogeneity of the laser energy **deposition** is introduced by statistical distribution of laser speckles **and** further enhanced by CBET between the beamlets coming from adjacent laser beams. The zones of energy exchange are shown with black points in the figure. Figure 8 (b) shows the pressure evolution in an experiment where a solid plastic sphere was irradiated with 60 OMEGA beams calculated with the CHIC multi-scale package [ 87 ]. A thin dark line shows the shock trajectory, which converges to the center at time of ∼2.5 ns. It was launched with a prepulse during the first nanosecond **and** further amplified with the main pulse during the second nanosecond. The main pulse was suffi- ciently intense to generate a large number of hot electrons due to the SRS **and** TPD instabilities, which contributed to the shock pressure by deposing their energy downstream the shock. However, the most energetic electrons penetrate upstream the shock front **and** depose their energy there (the pink zone in the time interval between 1 **and** 2 ns). Accounting for the energy **deposition** of hot electrons was necessary for explaining the observed shock collapse time **and** thus for evaluating of the shock pressure.

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Fixed volume, **particle**-laden flows are primarily investigated in one of two canonical config- urations, namely, a planar setting 11 , 17 **and** a circular axisymmetric setting. 18 – 20 These works were mostly experimental **and** theoretical. Problems such as bedload **transport** **and** **particle** resuspen- sion are often difficult to measure experimentally **and** therefore results from complementary direct numerical simulations (DNSs) are of value. **Particle**-laden currents which do not fall under these two canonical configurations remain largely unaddressed; the reason being that many natural configurations can be, to leading order, approximated as planar or axisymmetric, using geomet- rical arguments. The motivation behind the present work is to shed some light on the dynamics of **particle**-laden releases that are initially non-axisymmetric **and** non-planar **and** to highlight the importance of the details of the initial release. Such situations may occur, for example, in the dredging process where some sediment is intended to be deposited at some specific location which may depend on the initial shape of the release, or from voluntary or accidental collapse of buildings, the shape of which can influence the propagation **and** **deposition** of the debris. In the present work, we observe the short **and** long term dynamics of a non-canonical release (which is neither planar nor axisymmetric) to be dependent on the initial shape of the release.

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I want to thank all the people who shared my path during this work at SERMA. First, I am grateful to the reviewers of this thesis who gave me their feedback un- til final convergence. I thank Tony Lelièvre for the discussions we had during the thesis **and** for his final review. He brought the mathematical rigorousness that one needs to tackle AMS **and** more generally variance reduction techniques. I am grateful to Kenneth Burn, also reviewer, for the many exchanges we had on the manuscript. His remarks made me think **and** re-think on how to make this work more precise **and** more pedagogical. I finally thank Mariya Brovchenko from IRSN, who gave me relevant comments on my work. I now thank my supervisors who followed the progress of my work **and** directed it when needed. I thank Jamal Atif for giving me insights on which Machine Learning al- gorithms to use. To my advisor **and** mentor Eric Dumonteil: our history started with an internship on clustering. He maintained me aware of the context of this PhD, stressing on the industrial importance of this work. He help me build my path through research **and** made me enjoy it. To my day-to-day supervisor, Davide Mancusi, who was always present when needed. For the many things you said that brought me back on tracks. For your many skills, ranging from computation, to supervising, thank you for having played a big role in this project. I also want to thank Andrea Zoia for partnering on clustering **and** playing with equations in the bus.

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thin layer (100-150 nm) of boron on their vessel surfaces, in DIII-D the boron is quickly covered up with C in many areas, eroding in others. The boron is not covered in C-Mod **and** the only areas of B erosion are in the divertor [20,10]. The vessel **and** divertor geometries are significantly different as well. Figure 1 shows the cross-section of the two tokamaks for reference. The C-Mod divertor structure (see Fig. 1a) is a baffled, ‘vertical plate’ design which is optimized to spread the first power e-folding distance of the SOL (1-4 mm, mapped to outer midplane) over the vertical portions of the divertor plates. Primary limiter structures in the main chamber consist of a toroidally continuous inner-wall limiter, **and** principally two discrete outboard limiters far from the vessel wall. The DIII-D divertor has a horizontal plate design with less divertor structure – a more ‘open’ design. The inner limiter in DIII-D is also toroidally continuous. The divertor baffle structures at the entrance to both the upper **and** lower divertors serve as a toroidally-continuous limiters (marked ‘A’ **and** ‘B’ in Fig. 1b). Their location in the SOL is typically 5 cm from the separatrix, mapped to the midplane. Far out in the outer SOL are three, toroidally-spaced, small poloidal ‘bumper’ limiters protruding 1 cm from the wall.

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In shallow coastal areas Marenzelleria spp. are competing with the common ragworm Hediste diversicolor (Polychaeta, Nereidae). H. diversicolor inhabits muddy to sandy sediments down to ca. 15 m depth at densities ranging from 40 to 5000 ind. m − 2 ( Rasmussen, 1973 ). They are opportunistic omnivores, although their main feeding strategies are surface-deposit **and** ﬁlter feeding ( Scaps, 2002 ). H. diversicolor lives in more or less permanent U or Y-shaped burrows, creating a complex network of burrows extending down to ca. 15 cm ( Davey, 1994 ). Based on the reworking of tracer particles, H. diversicolor has been classiﬁed as a “gallery-diffusor”, which describes a combination of apparent biodiffusion in the upper sediment layer, with a non-local **transport** in deeper sediment ( Francois et al., 2002 ). They are known to actively ventilate their burrow, increasing the ﬂux of oxygen **and** nutrients over the sediment–water interface ( Kristensen **and** Hansen, 1999 ). However, there is a lack of information on their bioirrigation efﬁciency using inert solute tracers.

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Chapter 6. This chapter is devoted to the derivation of an asymptotic-preserving scheme for the electronic M 1 model in the diusive regime. In the rst part of this section, the case without electric eld **and** the homogeneous case are studied. The derivation of the scheme is based on an approximate Riemann solver where the in- termediate states are chosen consistent with the integral form of the approximate Riemann solver. This choice can be modied to enable the derivation of a numerical scheme which also satises the admissible conditions **and** is well-suited for capturing steady states. Moreover, it enjoys asymptotic-preserving properties **and** handles the diusive limit recovering the correct diusion equation. Numerical tests cases are presented, in each case, the asymptotic-preserving scheme is compared to the classi- cal HLL [ 118 ] scheme usually used for the electronic M 1 model. It is shown that the new scheme gives comparable results with respect to the HLL scheme in the classical regime. On the contrary, in the diusive regime, the asymptotic-preserving scheme coincides with the expected diusion equation, while the HLL scheme suers from a severe lack of accuracy because of its unphysical numerical viscosity. The second part of this section is devoted to the extension of the proposed numerical scheme proposed to the general case. The goal is to deal with the mixed derivatives which arise in the diusive limit leading to an anisotropic diusion. The derived numerical scheme preserves the realisibility domain **and** enjoys asymptotic-preserving proper- ties correctly handling the diusive limit recovering the relevant limit equation. In addition, the cases with electric eld **and** varying collisional parameter are naturally taken into account with the present approach. Numerical test cases validate the considered scheme in the non-collisional **and** diusive limits.

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We denote by XY transposition the transposition operating on the first **and** second directions in which the data are contiguous. Similarly, XZ transposition operates on the first **and** third directions.
The XY transposition follows [ 27 ] except that, in 3D, it is performed on every slices along Z direction. Figure 11a illustrates this transformation. Each work-group loads a tile (grey square) into local memory (red). Each work-item transposes its own subset of data by writing data to their correct positions (green). Contiguous access in global memory is ensured by use of the tile **and** the bus width is filled up by wrapping elements into OpenCL vector types. Memory camping is avoided by roaming the global memory arrays diagonally – in dashed lines in the Figure. Finally a one row padding is used in tiles to avoid bank conflicts. Similarly, XZ transpositions are performed along slices in Y direction. The work of [ 27 ] is extended to deal with 3D data. Using same conventions as previously, Figure 11b sketches this transformation. To avoid memory camping, the global memory is roamed in XZ planes. Because of the larger strides when going along Z direction than in Y, we used a cubic tile to reduce the number of large strides.

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4.1. Gleason et al.
Gleason’s research group has published many relevant article on the subject of CVD, focusing namely on **particle** encapsulation **and** electrically-conductive thin coatings. [12, 16, 31, 32, 33, 34]. Gleason et al. have developed their own terminology. Their nomenclature philosophy is based on adding a lower case acronym, describing the nature of the technique, contained between parentheses as a prefix to CVD. More precisely, (i)CVD **and** (o)CVD stand for initiated **and** oxidative CVD, respectively. PECVD is an exception to this rule **and** is considered as a category by itself. Furthermore, they use the term VDP to describe a CVD that does not require additional heating nor any other form of intiation, while usually other reseach groups consider CVD **and** VDP as synonyms. (pi)CVD, which stands for photo-initiated CVD, is included in (i)CVD, but (i)CVD refers to thermally-activated CVD most of the time, more specifically using heating filament that is refered elsewhere by hot wire chemical vapour **deposition** (HWCVD) [19, 13]. Based on the inclusion of (pi)CVD, PECVD could also have been categorized as a type of (i)CVD, but it is not, for unknown reasons. It is important to not confuse the term initiated from (i)CVD with photo-initiator, which will be detailed later in this paper.

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6.2.2 Simulation results
Complexity **and** computer time
Before addressing the simulation results for the ensemble-averaged physical observables, we briefly analyse the computational cost of the performed calculations as a function of the complexity of the underlying stochastic tessellations. Eigenvalue calculations have been run on a the same computer cluster as the one adopted for the previous benchmarks. The average number of polyhedra hN p i pertaining to each random geometry increases with decreasing Λ c , i.e., with increasing fragmentation. The scaling law is fairly independent of the mixing statistics m, **and** roughly goes as hN p i ∼ 1/Λ 3 c for any m. The exponent of the scaling law stems from the dimension d = 3. The number n of fragmented fuel pins does not affect these results, as expected. The corresponding (ensemble-averaged) computer times for each assembly configuration are reported in Tab. 6.2. Dispersions σ[t] are also given. The simulation time increases when increasing the portion of the assembly that is subject to fragmentation. While a decreasing trend for hti as a function of Λ c is clearly apparent, subtle effects due to correlation lengths **and** volume fractions for the material compositions come also into play, **and** strongly influence the average computer time. For some configurations, the dispersion σ[t] may become very large, **and** even be comparable to the average hti. The chosen tessellation model visibly affects the computer time. Atomic mix simulations are based on a single homogenized realization.

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roughness exponent hydraulic head different arrangements of reaction partners light intensity initial light intensity hydraulic gradient hydraulic conductivity effective hydraulic conduc[r]

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Importance sampling is a well-known reduction variance method, which has been applied to **transport** problems in many situations. We refer for instance to the textbooks [10] [14] for a general presentation. The key-point in such a method is the way one computes the importance function. If it is solution to the adjoint problem, then one achieves a zero-variance method. However, solving the adjoint problem is at least as difficult as solving the direct problem at hand. Therefore, many methods using approximations of the adjoint solution have been developped. This is the spirit of the exponential transform (see [6] **and** [10]). In some situations, a diffusion approximation is used for this calculation, as for instance in [17]. In other situations, discrete ordinates approximation is preferred [15]. The method which is the closest to the one presented here is probably [2], in which the adjoint equation is formulated as an integral equation, **and** solved using a space discretization. An importance difference is, however, that when solving the adjoint problem, the scattering is neglected in [2]. Here, we use the same kind of method, but taking advantage of the radially symmetric geometry, we are able to take scattering effects into account.

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velocity fluctuations normalized by their standard deviation. Using this normalisation we can compare PDF for set of events with different experimental configurations (flow velocity, confinement). For each configuration {h, d} one pressure drop is represented. The corresponding computed position PDF of the beads are plotted on figure 11. First, the two experiments in nanoslits of depth h = 3390 nm – where β is lower than 1 – reveal a shape of the velocity PDF similar to the one observed on figure 8 for high ∆P . The corresponding position PDF shows a large depletion for z/h > 0.3 (close to the center). This confirms for this case that the gap between experimental **and** predicted velocities is also due to an inhomogeneous distribution of beads in the nanoslit depth, not compensated by Brownian diffusion. On the contrary, in the case h = 1650 nm with beads of diameter d = 490 nm, we find a velocity PDF shape similar to the ones observed in figure 8 in the “homogeneous” regime. This is confirmed by the position PDF which reveals a flat distribution up to z/h = 0.4. In the last case (purple curve), a very confined configuration (r = 0.77), the velocity PDF has a quite different shape. It is due to the narrowness of the accessible velocity range for the beads. The accessible range of position for the beads is also very thin (see figure 11). Even if beads are weakly Brownian in this case, the confinement is high enough to allow a homogeneous distribution of the beads in the nanoslits. The existence of two regimes (“homogeneous”,

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After having graduated from my Master’s degree, in July 2013, I did two promising job interviews **and** nothing seemed to lead me to extending my university studies further. What I had not taken into account were the persuasive skills of Patrizio Antici who had been my thesis supervisor for the previous six months. He had made me familiar with the topic of proton acceleration via laser- plasma interaction **and** collaborating with him had given very good results. During a lunch break at the department of Applied Science for Engineering of the university of Rome “La Sapienza” we had the conversation that would have determined the following three **and** a half years of my life, at least from the scientific point of view. He told me about the interesting prospects of continuing the work that we had started together **and** suggested me to apply for a doctoral student position at “La Sapienza”. My journey through diverging electron beams **and** unreliable proton sources, too high emittances **and** unwieldy beam lines, unclear manuscripts **and** fussy referees, had just begun. The collaboration with Patrizio became even stronger about one year later, as he accepted to become my thesis supervisor at the Institut National de la Recherche Scientifique, when I signed an agreement for an Italian-Canadian joint doctorate.

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The necessary changes to the actual tallying subroutines that are used during **particle** tracking follow directly from the discussion in section 2 . As a summary, Algorithm 1 shows a pseudocode outlining the salient points of the tally server algorithm as implemented in OpenMC. There are a few important points to note regarding this algorithm. Firstly, the array of scores created when a scoring event occurs contains the scores for all specified scoring functions. This means that the receiving server will increment multiple tally scores from a single message. Also note that the servers must be informed of when a batch of particles (or the simulation) has been completed as the servers are now responsible for computing sums **and** sums of squares of the tally score bins in order to calculate variances. At the end of the simulation, the servers must collectively write the tally results to disk. This can be done efficiently using parallel I/O techniques such as MPI-IO or parallel HDF5.

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