Transportation and deposition of spherical and irregularly shaped particles flowing through a porous network into a narrow slot

Experimental Thermal and Fluid Science 109 (2019) 109894

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Transportation and deposition of spherical and irregularly shaped particles flowing through a porous network into a narrow slot

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Lisa K. Kinsalea, Mohammad A. Kazemia,b, Janet A.W. Elliottb, David S. Nobesa,

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a b

Department of Mechanical Engineering, University of Alberta, T6G 1H9 Canada Department of Chemical and Materials Engineering, University of Alberta, T6G 1H9 Canada

ARTICLE INFO

ABSTRACT

Keywords: Particle shape Particle rotation Particle deposition Particle shadowgraph velocimetry Porous media

In studies of the transportation and deposition of solid particles within a flow, the shape of particles has been a challenging factor to include in mathematical models. In many studies in the literature, irregularly shaped particles have been modelled essentially as perfect spheres to reduce the complexity in modelling the behavior of such particles. This paper seeks to illustrate, at the microscale, important features of particle transport that should be considered in any modelling effort. An experimental study was performed using particle shadowgraph velocimetry (PSV) in conjunction with several image processing techniques to analyze the behavior of solid particles that flow through a porous medium into a narrow slot. Three configurations were considered including the flow into a single straight slot and the flow into a slot with an inlet condition aimed to simulate porous media using cylindrical or diamond shaped pillars at different Reynolds numbers (Re = 0.1, 1 and 10) matched at the entrance of the slot. The measurement and image processing techniques used for determination of the particle rotation, particle shape, and velocity calculations are described. The velocity field was calculated and analyzed to identify the potential locations for particle deposition. While in general the characteristics of the continuous phase flow were unaffected by Re, local differences in geometry affected particle rotation and build-up as a function of particle shape. Also, particle rotation was observed in regions of irrotational flow as a function of particle position in the flow and particle shape. These results highlight that the flow geometry, particle shape and particle–fluid density difference can have a significant effect on particle rotation and deposition.

1. Introduction Understanding the transportation and deposition of solid particles within a fluid flow is useful in a number of applications in science and engineering. In medical research, the deposition of inhaled particles is analyzed so that the performance of drug delivery can be determined [1,2]. Some studies have examined solid particles in laminar boundary layers on a flat plate to investigate the impact of particle adhesive properties on deposition [3]. Researchers have investigated particle transport and deposition during abrasion to understand the history of sedimentary deposits [4]. This study was particularly motivated by the behavior and deposition of solid particles transported in steam-assisted gravity drainage (SAGD) operations that can affect the flow characteristics and general productivity of the well. SAGD is an in-situ enhanced oil recovery process used to produce oil from deep deposits of oil sand [5] whereby two horizontal wells are drilled into the reservoir. Steam is injected through the upper well to reduce the viscosity allowing the oil to

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become mobile at reservoir conditions which is then drained into the lower well to be produced to the surface [6]. Oil sand is a complex composition of sand, clay, water and bitumen and one of the goals of SAGD operations is to extract the bitumen with minimal sand production. A slotted liner, a sand control device used in SAGD operations, is a pipe with multiple narrow slots throughout its length and circumference, which limits the migration of sand particles into the production well [7]. After the slotted liner is placed within the reservoir and production is initiated, the multi-component flow moves from a porous network into narrow slots. Due to the presence of the slots, the flow transitions from uniform conditions further upstream [8,9] into a converging flow [10]. This region of flow convergence is referred to in this study as the near-slot region. One of the failure mechanisms of the slotted liner is due to deposition and build-up of the ‘fines’, which are clay particles and sand grains < 44 µm [11] that can lead to plugging of the slot. In a previous study [9], the particle build-up potential was shown to be impacted by the location of the pores with respect to the slot entrance. Also, from the

Corresponding author. E-mail address: [email protected] (D.S. Nobes).

https://doi.org/10.1016/j.expthermflusci.2019.109894 Received 20 March 2019; Received in revised form 11 July 2019; Accepted 9 August 2019 Available online 10 August 2019 0894-1777/ Crown Copyright © 2019 Published by Elsevier Inc. All rights reserved.

Experimental Thermal and Fluid Science 109 (2019) 109894

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analysis of the streamlines within the converging zone, it was observed that the potential locations for particle build-up are in the regions of low velocity and stagnation points. This phenomenon was also confirmed in a visualization study using dissolved asphaltene where particle build-up occurred at the leading face of the pores [12]. In review of previous studies [1–4] that investigated the transport and deposition of solid particles, it is noted that particle shape influences the behavior of particles immersed in the flow. Shape parameters have been developed to characterize irregular shapes such as the dynamic shape factor (DSF) or the equivalent diameter [2]. The DSF is the ratio of the drag force experienced by a particle to the drag force experienced by a spherical particle with the same volume [2,13]. The equivalent diameter is the diameter of a sphere which has an equivalent volume to the particle [2]. In studies that measure the equivalent diameter using 2D imaging systems, the projected area of the silhouette of the particle is equated to the projected area of an equivalent diameter sphere [14]. Other works have attempted to include the effect of shape by modelling particles as spheres, ellipsoids, cubes and cylinders in computational fluid dynamics (CFD) applications and computer graphics [15–17]. This approach is based on super-ellipsoids and uses a combination of shape parameters in order to define particle shape [15]. Super-ellipsoids are three-dimensional shapes based on ellipse-like curves which are known as Lamé curves or super-ellipses, in which the quadratic exponent in the ellipse equation is replaced with a variable exponent > 2. [16,17]. Another approach for characterizing particle shape is to use shape parameters that indicate the degree to which the particle shape deviates from a perfect circle or a known shape [18–26]. Three of the most commonly used shape parameters are equivalent diameter [2,14,20], aspect ratio [18–20] and roundness [24–26]. Modelling the behavior of irregularly shaped particles is challenging since it first requires the determination of the volume or area of an irregularly shaped particle [14]. For this reason, instead of simply ignoring the effect of shape, some studies have distinctly acknowledged that modelling the exact shape of irregularly shaped particles is indeed a limitation and modelled the particles essentially as spheres [3]. However, some recent studies are now developing methods to include the exact shape of particles within models for specific applications such as the study of the dispersion of volcanic ash [27] and the study of the motion of micro-sized biomass particles in turbulent flow [28]. In addition to particle shape, there are other particle properties [29–40] which influence whether particles will follow fluid flow streamlines and be carried from the inlet to the outlet or will deviate from streamlines and be deposited along the surface of the material which contains the fluid flow [41–43]. Two important phenomena are inertial deviation of particles from streamlines and particle–fluid density difference driven gravitational settling. The Stokes number, Stk [38,39], and the gravitational settling velocity [31,38] can be determined to assess the likelihood of each of these, respectively. There are several flow measurement techniques such as particle image velocimetry (PIV) [31,38–40], laser Doppler velocimetry (LDV) [38–40,44] and particle shadowgraph velocimetry (PSV) [32,38,39], whereby the motion of particles is used to infer the motion of fluids by assuming that the particles will follow the flow. Analysis of the dynamics of the particles [31,32,38–40] used to seed the flow can indicate if this assumption is valid. This is assumed true for conditions where the particle Stokes number < 1 and the gravitational settling velocity of the particles is much less than the local fluid flow velocity [38–40]. In other applications such as aerosol science and medical research, studies [1,29,30,33–37] have examined the transport of particles < 10 µm [1] within the human respiratory tract. These studies show that particle deposition can be influenced by inertial impaction [30,33,34,36,37], gravitational settling [34–36], diffusion [34,36], particle size [29,30], inhalation flowrates [29,33], constrictions within the flow, local changes in flow direction [30] and morphological geometry [30,33]. The objective of this study is to identify important features of particle transport that need to be included in any modelling effort. To provide a

relevant set of conditions, our investigation explores the behavior of solid particles transported by a viscous fluid in a complex geometry. The geometry is a simulated 2D porous media with a region of converging flow into a narrow slot. To characterize particle shape and motion of the discrete, transported phase as well as the continuous phase, PSV and several image processing techniques were employed. The continuous phase was seeded with tracer particles and two types of larger particles including spherical and irregularly shaped particles of greater densities were used to represent the fines found in oil sand reservoirs. The goal is to identify the various factors that can impact particle deposition or build-up within a flow area by analyzing the velocity vector field of the continuous phase as well as the general motion of individual particles. A complete understanding of the rotation of particles is a complex task that requires calculation of the forces acting on the body and the surface of each particle, which is beyond the scope of this paper. Here however, we have simplified the problem and identified and investigated three parameters that could influence particle rotation, namely the initial particle orientation, the location of the particle in the flow relative to solid bodies, and the shape of the particle. 2. Methodology and experimental setup This experimental study includes both velocity measurements of the continuous phase using only tracer particles and build-up tests using larger spherical and irregularly shaped particles. Three geometries were used including an open slot, and two inlet conditions aimed to simulate porous media using cylindrical pillars and diamond shaped pillars as shown in Fig. 1. For every geometry, experiments were performed at three flow conditions of different Reynolds numbers (Re) 0.1, 1 and 10. These Re correspond to flow rates (Q) of 0.3, 3 and 30 ml/min. Therefore, a total of 27 experimental runs were performed in this study. The flow conditions in the experiments were determined by matching the Re at the entrance of the slot. The Re which is defined by (Re = ρUL/ µ) was calculated based on the density (ρ) and dynamic viscosity (µ) of the liquid at room temperature (≈24 °C), the width of the slot (L) and the average velocity in the slot (U = Q/A). The density and dynamic viscosity of the 70–30% glycerol–water solution were 1191.6 kg/m3 and 0.0298 Ns/m2, respectively [45]; the width of the slot (L) was 1 mm and depth 2 mm giving a cross-sectional area of the slot (A) of 2 mm2 The average fluid flow velocities in this study were: 0.0025 m/s, 0.025 m/s and 0.25 m/s for Re = 0.1, 1 and 10 respectively. The experiments were performed with three different types of particles: 20-µm diameter polystyrene spherical microbeads (Dynoseeds TS20, Microbeads AS) tracer particles to determine the continuous phase fluid velocity, and 80-µm diameter spherical glass beads and 40-µm diameter silicon carbide irregularly shaped particles (AGSCO Corp.) to mimic particle transport and to perform the build-up tests. The particles mixed in the fluid were injected from the top of the flow cell at constant flow rates using a syringe pump (70-2002 PHD 2000, Harvard Apparatus Inc.), in the same direction as gravity. Fig. 1 shows the flow cell assembly and the three different geometries used in the experiments. Each flow cell was a sandwich of a flow channel and a transparent window to allow optical access. The window, as shown in Fig. 1(a) was made of a 6.35-mm thick acrylic sheet and fabricated with a laser cutter (VLS3.50, Universal Laser). The flow channel shown in Fig. 1(a) and (b) was manufactured using an additive manufacturing process (Form 2, Formlabs Inc.) with a clear photopolymer resin. The arranged slots shown in Fig. 1(b) were included into the top section of the flow channel to allow distribution of the solid particles across the field of view. Three different configurations of the flow cell were used in this study as shown in Fig. 1(c). These include: (i) an open slot, (ii) equally spaced cylindrical pillars of 1-mm diameter and 2-mm depth, and (iii) equally spaced diamond shaped pillars circumscribed into 1 mm diameter circles and 2 mm in depth. These geometries were selected to study the phenomena that occur in the near-slot region in the SAGD oil recovery process. The open slot geometry was compared to the 2

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Fig. 1. A schematic of: (a) the exploded flow cell assembly, (b) the flow channel design highlighting the near-slot region of interest (ROI) highlighted with a red box, and (c) expanded near-slot regions of interest highlighting the three configurations of the flow channel including: (i) the open slot and inlet conditions aimed to simulate porous media using (ii) cylindrical pillars or (iii) diamond shaped pillars. The field of view (FOV) for the analyses is highlighted with the blue boxes. Note that the FOV for the build-up tests was slightly wider than the FOV for the velocity measurements of the continuous phase. Images are to scale. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

simulated porous media geometries to investigate the effect of the presence of the simulated porous media on the flow field and particle build-up. The circular pillars and diamond shaped pillars were included to evaluate whether a change in the shape of the simulated porous network would significantly impact the flow field and the deposition of particles within the near-slot region. The experimental set-up as illustrated in Fig. 2 consists of a camera imaging the flow cell in a shadowgraph configuration illuminated by a highcurrent LED light source. A high speed camera (Photron FastCam Mini WX 50) with 2048 × 2048 pixel resolution was used to capture velocity measurements of the continuous phase. The continuous phase flow velocity measurements at Q = 0.3 ml/min and 3 ml/min were performed at a frame rate of 125 fps. However, at the highest flowrate Q = 30 ml/min the images were captured at a frame rate of 750 fps in order to freeze the motion of the tracer particles added to the flow field. A second camera with the same 2048 × 2048 pixel resolution (4M180, IO Industries Inc.) was used for imaging particle build-up over longer time periods. This camera was

connected to a digital video recorder storage (DVR Express Core 2, IO Industries Inc.) and a computer. For the build-up tests, two sets of images were collected for 12 s at 36 frames per second (fps) and exposure time of 150 µs with 16 min interval between each recording. Each camera was combined with a macro lens (105 mm f/2.8, Sigma) to image the field of view illuminated by an LED light source (BX0404-520 nm; Advanced Illumination Inc.) which provided uniform back illumination. 3. Data processing Several image processing techniques were employed to detect and track the particles within the region of interest and to determine parameters such as the fluid velocity field, particle deposition, particle size distribution, and particle rotation. All image processing was performed using commercial software (DaVis 8.3.1 LaVision GmbH) and in-house post-processing scripts (Matlab, The MathWorks Inc.). The following sections describe the techniques used to process and analyze the experimental data.

Fig. 2. A schematic of the particle shadowgraph velocimetry experimental set-up. 3

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Fig. 3. Image processing steps for detecting particles to determine particle shape: (a) the raw image, (b)–(e) pre-processing steps, and (f) ellipses fitted to the detected irregularly shaped particles.

3.1. Velocity field processing–tracer particles only

particles. This was firstly achieved by establishing a reasonable intensity difference between the particles and the remaining area in the illuminated section within the field of view (FOV) [51]. Due to the transparency of the spherical glass beads and in order to establish a significant intensity difference, the light source was restricted to allow illumination mainly of the region of interest that is within approximately 10 mm, on each end, beyond the width of the FOV. This approach allowed the spherical particles to appear with darker edges to ease the detection of the particles. The intensity difference was relatively easy to achieve with the opaque irregularly shaped silicon carbide particles. An example of the image processing steps used for particle detection is shown in Fig. 3. Fig. 3(a) shows a raw image of the irregularly shaped silicon carbide particles. The raw image was inverted by applying a 2D Gaussian smoothing filter with a kernel size of 31 pixels and a standard deviation of 0.2 to reduce noise in the image as shown in Fig. 3(b). Two processing steps were performed on the image in Fig. 3(b). Firstly, the local standard deviation of the smoothed image was calculated and normalized between 0 and 1 and the scaled standard deviation was multiplied by itself 3 times as shown in Fig. 3(c). Secondly, the image in Fig. 3(b) was normalized between 0 and 1 and the scaled image was multiplied by itself as shown in Fig. 3(d). The images in Fig. 3(c) and (d) were averaged and a binary image of the resultant image was calculated and the ellipses were detected and fitted using a built-in function (regionprop, Matlab, The Mathworks) as shown in Fig. 3(e) and (f) respectively. The fitted ellipses were used to obtain the aspect ratio of the particles.

The velocity vector field was calculated using particle image velocimetry (PIV) image processing using commercial software (DaVis 8.3.1, LaVision GmbH). Several pre-processing techniques were used to remove background noise and to allow the tracer particles to appear bright on a dark background. The images were first inverted and the inverted images were multiplied by themselves. An average of the product was calculated and subtracted from the multiplied images, and then the velocity field processing was performed. A single-frame time-series sum-of-correlation vector calculation was applied to the pre-processed images. A multi-pass cross-correlation, with decreasing interrogation windows sizes, was applied to sequential pre-processed images to calculate the velocity field. Initially, three passes were performed using an interrogation window size of 128 × 128 pixels with 87% window overlap to capture large changes in the velocity field. This was followed by another three passes using a 64 × 64 pixels interrogation window size with 87% window overlap between sequential correlations. The interrogation window sizes were selected to allow the particles to move at least one half of the interrogation window size between subsequent frames [46]. The average of the processed images was calculated to determine the velocity vector field. Finally, an in-house post-processing code using functions found in [47] (PIVMat Matlab, The MathWorks Inc.) was used for post-processing and plotting of the velocity vector maps. It is important to note that there is uncertainty related to the processing interrogation window size and cross-correlation that are used to find the average velocity field [48,49]. It has been found in literature that in an ideal case a symmetric correlation peak would be achieved if particles were matched perfectly during the cross-correlation of images. However, in reality a perfect match may not be achieved resulting in a non-symmetric correlation peak [49]. In this study, the uncertainty of the average velocity field was attained by:

Ux¯ =

x

N

3.3. Particle tracking Images were pre-processed using the technique shown in Fig. 3 for particle detection. From this step, the coordinates of the centroid of every individual particle were detected in each image. A built-in function (regionprop, Matlab, The Mathworks) was used to determine the coordinates of the centroid of every individual ellipse as well as the orientation of each ellipse with respect to the vertical axis. Finally, particle tracking was performed using a method developed in reference [52] which is a modified approach based on that by Baek and Lee [53]. Particles within a user defined radius are assumed to have similar displacement in direction and magnitude and based on the most probable trajectory, the velocity of an individual particle is determined. If there are no neighboring particles within the radius, then the nearest-neighbor-in-the-next-frame approach is used. The displacements of individual ellipses were obtained by identifying each particle in the subsequent frame.

(1)

where Ux¯ is the uncertainty of the average velocity, σx is the standard deviation, and N is the number of measured variables, that is the number of available vectors [50]. The uncertainty of the average velocity vector was calculated using (DaVis 8.3.1, LaVision GmbH). The maximum uncertainty was estimated to range from 1.33% of the maximum velocities for the low Re case to 5.73% of the maximum velocities at high Re.

3.4. Particle characterization: size and shape

3.2. Particle detection

The particles suspended in the flow contained a variety of particle sizes and shapes. Fig. 4 shows an image of a sample of the irregularly shaped 40-µm silicon carbide particles. To determine the general

Particle detection is an essential part of this study for the purpose of tracking the transported particles and analyzing the deposition of the 4

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Fig. 6. The distribution of the particle aspect ratio of the sample of 2213 irregularly shaped particles.

1 indicates that the particle is a perfect sphere [18,23]. The aspect ratio was calculated using a customized code developed in the study in reference [25] using reference [55]. Roundness is a parameter that indicates the degree to which the shape or outline of a particle deviates from a circle. It is an indication of the smoothness of the edges of the particle [18,25,26,56]. In some studies, roundness is referred to by different names such as circularity [19], sphericity [20], or shape factor [57]. However, the implications or mathematical definitions are similar. Traditionally, the roundness is calculated using the ratio of the projected area to the perimeter of the particle squared [18,19,54]. Alternatively, another approach to attain the roundness for two-dimensional images was developed in [24,25]. This approach was used to define the roundness of the particles used in this study. The approach calculates the roundness using the ratio of the average radius of curvature of the outline of a particle to the radius of the maximum inscribed circle. This was done using a circle fitting method to the corners of the particle [24–26]. The value of roundness ranges from 0 to 1. The value of roundness decreases from 1 as the outline of the particle deviates from a perfect circle [18]. The average roundness calculated for the 2213 particles was 0.40 as shown from the distribution in Fig. 7.

Fig. 4. Image of a sample of the irregularly shaped particles chosen randomly from the sample of 2213 particles.

particle characteristics, 2D images were taken of 2213 particles, which were placed on microscope glass slides in order to obtain an approximation of the size and shape distributions. The images used in the size and shape analysis were taken using a lens (50× microscopic lens) with a higher magnification than the macro lens used for the experimental analysis. There are several parameters in the literature which can be used to characterize particle size or shape [18–25]. For the purpose of identifying the size or degree of irregularity of the particles used in this study, some of the more commonly used parameters in the literature namely equivalent diameter, aspect ratio and roundness, are used [18–25,54]. The equivalent diameter, which is also referred to as the particle size in this study, was determined from the projected area of each particle in the 2D images by calculating the diameter of a circle having the same area [14]. The particle size distribution obtained is shown in Fig. 5 where the average particle size of the sample was 43 µm, which is comparable to the particle size of 40 µm in the manufacturer specifications (AGSCO Corporation). Among the various methods available in the literature to determine the aspect ratio [19,20,22], the method selected and used in this study is the calculation of the ratio of the minor axis to the major axis of a fitted ellipse to the particles [18,23]. The average aspect ratio obtained from the sample of 2213 particles was 0.68 as shown in Fig. 6. In some studies the aspect ratio is referred to by different names such as sphericity [25] or elongation [18]. However, the mathematical definition is similar which is:

Aspect Ratio =

d1 d2

3.5. Particle characterization: Stokes number A common parameter that is used to characterize particle dynamics in the literature is the Stokes number [31,32,38–40]. The Stokes number is an indication of whether it is necessary to consider particle inertia during the transport of the particles [58,59]. Generally for Stokes number < 1, particle inertia is negligible and the particles will follow the fluid flow streamlines [31,38]. The Stokes number is defined as the ratio of the response time of the particles to the characteristic time scale in the flow [38,39]. The response time is a measure of the ability of the particles to attain velocity equilibrium with the fluid flow and the characteristic flow time scale is the ratio between a typical length scale in the flow geometry and the fluid flow velocity [38]. The Stokes number can be calculated using:

(2)

Stk =

2 p dp U

18µd c

(3)

where d1 and d2 are the ‘width’ and ‘length’ of a particle. Since measuring d1 and d2 for each particle was difficult, the equivalent dimensions of the fitted ellipse to each particle were used to calculate the aspect ratio, where d1 and d2 were the minor and major axes of the fitted ellipses [18]. The aspect ratio varies from 0 to 1, where a value of

where p is the density of the particle, dp is the diameter of the particles, U is the average fluid velocity of the continuous phase, µ is the viscosity of the fluid and dc is the typical dimension of the geometry containing the fluid flow.

Fig. 5. The particle size (equivalent diameter) distribution of the sample of 2213 irregularly shaped particles.

Fig. 7. The distribution of particle roundness of the sample of 2213 irregularly shaped particles. 5

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The density and viscosity of the continuous phase were 1.192 g/cm3 and 0.0298 Pa s respectively. The particle density was 1.05 g/cm3 for the tracer particles, 2.5 g/cm3 for the spherical glass beads and 3.21 g/cm3 for the irregularly shaped particles. The Stokes number was calculated for the simulated porous media flow channel geometries. The pillar spacing of 0.5 mm was used as the typical dimension of the geometry containing the fluid. The diameter of the tracer particles was 20 µm and the diameter of the spherical glass beads was 80 µm. The average equivalent diameter of 43 µm as shown in Fig. 5 was used as the particle diameter for the irregularly shaped particles. At the maximum average fluid flow velocity of 0.25 m/s the Stokes numbers were 3.92 × 10−4 for the tracer particles, 1.49 × 10−2 for the spherical glass beads and 5.54 × 10−3 for the irregularly shaped particles. The Stokes numbers for all three particles were ≪1 at the maximum flow velocity and correspondingly at the lowest and intermediate flow velocities of 0.0025 m/s and 0.025 m/s used in this study, the Stokes numbers would be even smaller. It is also important to note that the particle Stokes numbers for the open slot geometry would be less than the Stokes numbers calculated for the simulated porous media geometries, since the slot width of 1 mm would be used to define dc . These factors indicate that particle inertial effects for the three different particles are negligible for all the flow conditions and the three flow geometries used in this study.

along the entrance of the slot as indicated by the red arrows in Fig. 8. The average local velocities (Uave) within the low velocity regions adjacent to the wall on one side of the entrance of the slot indicated by the red boxes shown in Fig. 8 were then plotted against Re for all three geometry configurations as shown in Fig. 9. Fig. 9 shows the extent to which Uave within the low velocity region changes with respect to the flow geometry. It was noted that as Re increases Uave increases for the three flow cell configurations. However, it was observed that Uave for the two flow cells with the simulated porous media at the inlet were generally higher than those for the open slot. The cylindrical pillars had a diameter of 1 mm and the diamond shaped pillars were circumscribed within 1 mm diameter circles. Comparing these two flow cells, the diamond shaped pillar flow cell had a greater open flow area. Therefore, Uave within the low velocity region was lower than that for the cylindrical pillars as shown in Fig. 9. However, due to having the largest open flow area, Uave within the low velocity region was the smallest for the open slot compared to all other geometries. By comparing the velocity distributions in different geometries at a given Re, represented by each row in Fig. 8, it was observed that the presence of the simulated porous media had a remarkable effect on the flow in the near-slot region.

3.6. Obtaining the deposited layer of particles

4.2. Rotation of particles

The thickness of the deposited layers in the vicinity of the slot was obtained by processing individual images with custom approaches (Matlab, The Mathworks). To demonstrate the variation of the layer thickness with time, two datasets of 432 images were collected. The first dataset consisted of images collected from time t = 0 s to t = 12 s and the second dataset consisted of images collected from t = 16 min to time t = 16.2 min. For each data set, the average of the 432 images was calculated to eliminate the moving particles and focus solely on the deposited layers along the entrance of the slot. The average of the images calculated for each data set was converted to a binary image where the particles appeared as white ‘blobs’ on a black background. All the white blobs except the two significantly largest ones, which represented the deposited layers at the entrance of the slot, were removed. Thereby the deposited layer could be observed.

Once the velocities were quantified using the tracer particles, a series of separate experiments were carried out at the same flow rates in the same geometries with the difference being that the larger particles were used instead of the tracer particles. Using the image processing techniques described in Sections 3.2 and 3.3, each irregularly shaped particle appearing in the images was identified by a fitted ellipse. The angles of rotation, θ, between the major axis of the fitted ellipse and the vertical axis (y) were measured for each particle in each image. Starting from the left hand side, Fig. 10 shows the experimental velocity vectors and velocity magnitude ( u2 + v 2 ) that would occur in the slot in the absence of the irregularly shaped particles (i.e., using the tracer particles only) at Re = 1. The streamlines calculated from the PIV results are also shown in the bottom left corner of the Fig. 10. The velocity vector field together with the streamlines shown here indicates that the flow field is irrotational within this region. Fig. 10 also shows the rotations of six selected particles labeled (a)–(f) as they entered the slot section in the open channel at Re = 1. The aspect ratio, roundness and the color assigned to each of the six selected particles in Fig. 10 are given in Table 1. Each particle shown in Fig. 10 is tracked as it is transported throughout the length of the slot. The six grayscale figures illustrate the sequence of the snapshots of selected particles within the flow that includes various shapes of particles. Every 4th frame is shown for each sequence to avoid overlapping images of particles. The snapshots were edited to exclude many other surrounding particles in the flow and to provide a better illustration of the motion of individual particles. The line plots below each pair of grayscale figures show the vertical locations (in every 4th frame) of the selected particles plotted against the absolute value of the difference between the angle of rotation, θ, (in every 4th frame) and the initial angle of rotation, i each of individual particles. It was observed in Fig. 10 that although the flow is irrotational, the particles displayed a number of different rotational behaviors within the slot. Particles with similar characteristics were paired in Fig. 10 that have all but one parameter in common: either the initial angle θ, the particle distance from the wall, or the particle shape. It can be seen that the particles (a) and (b), highlighted with red and blue in Fig. 10, were both located at relatively the same distance from the walls. However, particle (b), which is initially not aligned with the flow field, rotates much more than particle (a). It was observed that the initial orientation θi at which the particle enters the slot region strongly affected the particle rotation in the section. Particle (b) also has a

4. Results and discussion 4.1. Velocity field of the continuous phase The velocity field measurements were performed, using 20-µm tracer particles, for nine experimental conditions as shown in Fig. 8. The FOV used for analysis in this study represents the flow convergence zone into a confined narrow 2D slot [9,10]. Each row in Fig. 8 shows the flow field for different geometries at the same Re = 0.1, 1 or 10. Over the range of the experiments the velocity varied by two orders of magnitude. To highlight this, logarithmic colormaps are used in Fig. 8 to allow better observation of the lower velocity regions in the flow. Each column in Fig. 8 compares the flow field in a specific geometry at different Re and both the x and y axes were normalized with respect to the slot width, w of 1 mm. It can be seen in Fig. 8 that the velocity distribution for each experimental condition is almost symmetric about the centerline of the slot, x/w = 0. In general, the flow characteristics are similar for each Re but are strongly influenced by the particular flow geometry. A parabolic velocity profile was observed within the rectangular slots which is in agreement with the theoretically calculated velocities in the range of Re investigated here [60]. The velocity increased within the near-slot region due to the change in the cross-sectional area which provides a smaller open flow area at the entrance of the slot. Within the porous region, the relative maximum velocities occurred diagonally between the pore spaces, while the minimum relative velocity within the porous region occurred at the walls of the pillars and 6

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Fig. 8. The velocity field within the region of interest for the three flow cell configurations (the open slot and inlet conditions aimed to simulate porous media using cylindrical pillars or diamond shaped pillars). The colors in the background represent the velocity magnitude ( u2 + v 2 ) and the black arrows represent the velocity vector field. Each row shows the flow field in different geometries at a constant Reynolds number (Re = 0.1, 1.0 or 10). Each column compares the flow field in a certain geometry at different Reynolds numbers (Re = 0.1, 1.0 and 10). To emphasize the differences in velocity magnitude between the rows (note the different color map scale in each row), low velocity regions are selected with red boxes and the average velocities Uave within the low velocity regions are shown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

seen that the distance of the particle from the walls is another important factor in the rotation. Both particles (c) and (d) have a similar shape and both enter the channel with similar orientation. However, particle (c) is closer to the center of the slot where the velocity variation in the cross-stream direction is lower compared to the position of particle (d). This can be confirmed with the velocity profile shown within the slot in Fig. 10. Particle (c) is located within the region closer to the peak of the parabolic velocity profile and the gradient in stream-wise velocity is lower. As a result, it moves with a relatively smaller amount of rotation as it passes through the slot towards the exit compared to particle (d) that is in a region of stronger stream-wise velocity gradient, leading to a faster rotation rate of the particle. Finally, the comparison of particles (e) and (f) (highlighted with orange and purple in Fig. 10 further confirms that the particle shape (i.e., the aspect ratio) has a significant impact on the rotation. Both particles entered the channel with a similar angle as well as a similar initial position with respect to the walls. However, particle (f) with an aspect ratio of 0.358 undergoes a higher level of rotation compared to particle (e) with an aspect ratio of 0.172, because particle (f) is more exposed to a velocity difference on its surface due to its shape. Particle (e) shows minimal deviation from its initial orientation while passing through the slot compared to particle (f). Comparing all particles (a)–(f), it can be seen in Fig. 10 that particle (d) experienced the highest rotation. This particle is relatively larger than the five other particles and also maintains the smallest distance to the solid wall where a higher gradient in the stream-wise velocity field exists. This can be seen in the velocity field shown in Fig. 10 (top left) or

Fig. 9. A plot of the average velocity Uave within the low velocity regions (represented by the red boxes in Fig. 8) versus Reynolds number (Re = 0.1, 1.0 and 10) for the three flow cell configurations (the open slot and inlet conditions aimed to simulate porous media using cylindrical pillars or diamond shaped pillars). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

higher aspect ratio than particle (a), which may have also contributed to particle (b) experiencing a higher rotation. From the comparison of the rotations of the particles (c) and (d) (highlighted with yellow and green respectively in Fig. 10) it can be 7

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Fig. 10. The rotations of six selected particles labeled (a)–(f) as they entered the slot section in the open channel at Re = 1. The colored figure in the top left represents the corresponding velocity vectors and velocity magnitudes ( u2 + v 2 ) obtained experimentally that would occur in the slot in the absence of the irregularly shaped particles (using tracer particles only). The streamlines calculated from the PIV results are also shown in the bottom left corner. The effects of three parameters on particle rotation, namely, the initial angle of the particle at the entrance, the distance of the particle from the side walls, and the shape of the particle are displayed. The six grayscale figures illustrate a sequence of snapshots of selected particles within the flow for the open channel geometry at Re = 1. Every 4th frame is shown for each sequence to avoid overlapping images of particles. In the line plots below the grayscale images, the x-axis shows the absolute value of the difference between the angle of rotation of the particles, θ, (in every 4th frame) and the initial angle of each particle, i between the major axis of the fitted ellipse to each particle and the vertical y direction. The y-axis shows the locations of the center of the fitted ellipse with respect to the origin. The origin is taken to be at the middle of the slot at the entrance section. Images displaying the initial orientation of the six particles are shown at the bottom of the figure. Note that the aspect ratios and roundness of the six particles (a) to (f) are stated in Table 1.

simulated porous region shown in Fig. 11. To better illustrate how the rotation of particles can influence the deposition of particles, a sequence of snapshots of two separate particles flowing near the slot entrance is compared in Fig. 11(a). The snapshots in Fig. 11(a) were edited to exclude other surrounding particles in the flow and to provide a better illustration of the motion of individual particles. Note that the trajectories of particles P1 and P2 in Fig. 11(a) were captured at two different times and then were overlapped onto one image. Therefore, P1 and P2 were not at any time in physical contact. The velocity vectors and streamlines shown in Fig. 11(b) and (c), were obtained from the velocity measurements of the continuous phase (using the 20-µm tracer particles only). These may differ from the velocity field and streamlines in Fig. 11(a) due to the presence of the larger 40-µm irregularly shaped particles, and/or because of the deposited layer of particles (that are not shown). However, we ignore this effect and assume that the velocities in both cases are the same. As shown in Fig. 11(a), even though both particles seemingly have similar aspect ratios, initial orientations, and initial locations in the channel, they showed completely different motions in the near slot

Table 1 The aspect ratio and roundness of the six particles (a)–(f) that were selected to identify factors that influence particle rotation. The colors assigned in Fig. 10 to each particle are included in the table. Particles

Aspect ratio

Roundness

(a)

0.140

0.801

(c)

0.444

0.588

(b) (d) (e) (f)

Color code

0.404 0.418 0.172 0.358

0.843 0.560 0.728 0.686

can be inferred from the compactness of the streamlines shown in Fig. 10. So far, we have discussed some parameters that could potentially affect the rotation of different particles in the slot section where the flow seems to be irrotational. However, particles behave differently when they enter a more complex part of the geometry such as the 8

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Fig. 11. (a) Sequence of frames illustrating the behavior of two solid irregularly shaped particles transported through a porous media made of diamond shaped pillars into a narrow slot at Re = 0.1. The snapshots in (a) were edited to exclude the other surrounding particles in the flow and to provide a better illustration of the motion of individual particles. P1 and P2 flowed at two different times in the experiments and therefore, they were not in physical contact. (b) The experimental velocity vectors in the same location obtained from a separate experiment using tracer particles and PIV algorithm. (c) The streamlines calculated from the experimental velocities. (d) Illustrates the hypothesis to be considered that P1 and P2 may be located at different z–locations. This may have led to P1 and P2 being located at different velocity regions.

region. In this region, the streamlines are not straight as can be seen in Fig. 11(c). Both particles almost followed the same streamline in the first three frames. However, particle P1 begins to cross the streamline and rotates which caused it to collide into the layer of deposited particles on the horizontal surface before the entrance to the slot. Particle P2 remained oriented along the local velocity vectors (or the streamlines) and followed the flow convergence and flowed through into the slot. From the shape of the streamlines, it appears that P2 did not rotate before entering the slot section and maintains its orientation along the fluid flow path before the slot. On entering the slot, it rotates significantly compared to the curvature of the flow. From the observation of these two particles in Fig. 11 it can be seen that the rotation of a particle during its motion is a key factor which affects whether the particle deposits or exits the porous media into the channel. One may argue that the different behaviors of P1 and P2 might be due to the fact that the flow in the channel is a three dimensional one and since P1 could be closer to either of the front or the back walls, it may be in a lower velocity region and settle more easily. This hypothesis is tested in Fig. 11(d). By comparing the sequences in Fig. 11(a), it can be inferred that this is not the case since if P1 was in a lower velocity region, it would move more slowly than P2 in the first few frames. As a result, other factors, including the difference in the shapes, which could not be seen clearly in the projected 2D images, higher weight of P1 compared to P2, or interaction with other neighboring particles that have been removed from the images might have affected the deposition of P1. This indicates that understanding the detailed behavior of particles in such flows is complex and requires more extensive study.

4.3. Particle deposition In this section, the particle deposition which was observed during the particle build-up tests is evaluated. The Stokes numbers obtained in Section 3.5 suggest that particle deposition is unlikely to be caused by inertial deviation from the streamlines. However, further analysis of the particle dynamics was performed to determine which physical phenomena contributed to particle deposition in this study. This was done using the particle–fluid density difference driven gravitational settling velocity, U [32,38,39], defined by:

U =

gdp2 (

p

18µ

f

) (4)

where g is the acceleration due to gravity, dp is the diameter of the particles, p is the density of the particle, f is the density of the continuous phase and µ is the viscosity of the fluid [31,38]. Table 2 gives the diameter, density, particle–fluid density difference and the gravitational settling velocity of each of the three particles used in this study. The results in Table 2 show that the density of the tracer particles was very close to the density of the continuous phase (negligible particle–fluid density difference). Additionally, it can be seen that the U of the tracer particles is −1.04 × 10−6 m/s, which is negligible compared to the U of the irregularly shaped and spherical particles. The U of the tracer particles is also significantly less than the three average fluid velocities used in this study. These observations illustrate that the tracer particles are neutrally buoyant and gravitational effects are negligible. 9

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Table 2 Diameter, density, particle–fluid density difference and settling velocity of the three particles used in this study, namely, tracer particles (polystyrene spherical microbeads), spherical particles (glass beads) and irregularly shaped (silicon carbide). Note the equivalent diameter was used as the length scale to characterize the irregularly shaped particles. PARTICLES

dp (µm)

Tracer particles (polystyrene spherical microbeads)

20

1.05

80

2.5

43

3.21

Spherical particles (glass beads)

Irregularly shaped (silicon carbide) using the equivalent diameter

Therefore, the tracer particles followed the flow faithfully and could be used to calculate the velocity field of the continuous phase. However, the particle–fluid density differences were greater for the particles that were used to represent the ‘fines’ in SAGD operations (i.e., the spherical glass beads and the irregularly shaped silicon carbide) as shown in Table 2. This indicates that these particles were influenced by gravitational effects, which could lead to the sedimentation of the particles. The gravitational influence on particle deposition for the spherical and irregularly shaped particles can be observed in Fig. 12 which shows the build-up of both spherical and irregularly shaped particles for the three flow cell configurations at Re = 0.1, 1 and 10. The left panels in Fig. 12 show the build-up of the spherical particles and the right panels show the build-up of the irregularly shaped particles. Initially at the beginning of each test, a deposited layer was observed due to the gravitational settling of the particles during filling of the flow channel and preparation for the test as shown in Fig. 12. It is important to note that the particle concentration at the inlet was not uniform so that there was some variation of the initial build-up. The results from the build-up tests were analyzed based on any observed changes of the initial layer of particles after 16 min. From the results, it was observed that at the lowest flowrate (Re = 0.1), the thickness of the deposited layer in all geometries increased after 16 min for both types of particles. This can be related to the plot in Fig. 9, whereby at Re = 0.1, Uave within the low velocity region was approximately zero for all the geometries. The actual values of Uave stated in Fig. 8 at Re = 0.1 were 0.000126 m/s, 0.00112 m/s and 0.00111 m/s for the open slot, cylindrical pillars, and diamond shaped pillars respectively. Thereby the velocities at Re = 0.1 were inadequate to wash the particles into the slot and the build-up increased. At the intermediate flow rate (Re = 1), the presence of the porous medium affected particle deposition. That is, the thickness of the deposited layer in the open channel increased after 16 min but the initially deposited layer decreased in the channels with simulated porous media. This can be confirmed with the velocity calculations in Section 4.1 whereby at Re = 1, the Uave within the low velocity regions were calculated to be 0.00124 m/s, 0.0131 m/s and 0.0107 m/s for the open slot, cylindrical pillars, and diamond shaped pillars, respectively as shown in Fig. 8. The average velocity in that region increased by an order of magnitude for the simulated porous media. Thereby particle build-up was observed for the open slot at Re = 1 whereas for the cylindrical and diamond shaped pillars the initial particle build-up was washed away with the flow. At the highest flowrate (Re = 10), the deposition of particles was difficult to capture as the high velocity of the liquid in the near slot region would wash out most of the particles almost immediately and carried them through the slot. However, to be able to demonstrate this phenomenon, at Re = 10 the experiments were started with a lower flowrate which allowed the particles to form a large deposited layer. The flowrate was then increased rapidly to Q = 30 ml/min and Re = 10 and the initially deposited layer in all three channels shrank significantly because the higher flow rate of the liquid washed out the particles in the vicinity of the entrance of the slot. Additionally, as described in Section 3.6 the images from the build-up test were processed by finding the average of 432 images taken at time t = 0 s and

3 p (g/cm )

|

p

0.142 1.308 2.018

f

|(g/cm3)

U (m/s)

1. 04 × 10 1. 53 × 10

4

1. 09 × 10

4

6

t = 16 min. However, at Re = 10 the averages of approximately 35 images within the first dataset for all the geometries were obtained, since the flow rate washed away the particles so quickly, that the average of the 432 images would not adequately portray how quickly the particles washed away at the highest flowrate. At Re = 10 the Uave within the low velocity regions were 0.0254 m/ s, 0.127 m/s and 0.114 m/s for the open slot, cylindrical pillars, and diamond shaped pillars, respectively. Uave was also the highest for the cylindrical pillars, so it was observed in Fig. 12 that both the spherical and irregularly shaped particles were completely carried away into the slot after 16 min. However, the whole layer was not washed away completely for the diamond shaped pillars. Particle build-up was present further from the slot and away from the region of converging flow of the continuous phase. The value of Uave for the diamond shaped pillars varied very little from that for the cylindrical pillars; therefore, the tortuosity of the flow path probably hindered the particles from being completely washed away in the case of the diamond shaped pillars. Finally, the open slot is the case with the lowest Uave and the highest open flow area, so that at Re = 10 the particles were not completely washed away after 16 min as shown in Fig. 12. This shows that despite the presence of gravitational effects, at the highest Re the shear stresses in the fluid contributed to a decrease in particle build-up after 16 min. 5. Limitations of the study One of the challenges of this study was the inability to obtain spherical and irregularly shaped microparticles of the same material. The analysis included two types of particles including 80-µm spherical glass beads and 40-µm irregularly shaped silicon carbide particles. Although the sizes of the particles were within the same order of magnitude, there is a density difference between the particles used in this study. The silicon carbide particles have a density of 3.21 g/cm3 whereas the spherical glass beads have a density of 2.5 g/cm3. Thereby, the difference in the density of the particles could have possibly contributed to the fact that there was very little difference observed between the deposition of the large spherical glass beads compared to that of the small irregularly shaped silicon carbide particles. Another limitation in this study was that uniform and consistent particle dispersion at the inlet was not achieved. A quantitative analysis of particle deposition with respect to time requires a controlled continuous particle feed at the inlet. For these reasons, it was difficult to quantitatively compare the particle deposition with respect to time. Therefore, this study is focused on the observation of the factors that influence particle build-up within the near-slot region 6. Conclusion This paper strictly focuses on the observations made from an experimental study to illustrate the importance of considering the actual shape of particles when modeling particle transport within a fluid. The behavior of solid particles that flow through a porous medium into a narrow slot has been explored using PSV measurements and image processing techniques. Irregularly shaped particles have been traditionally modelled as spheres to reduce the complexity of the 10

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Fig. 12. Particle deposition (after 16 min) for both spherical and irregularly shaped particles in three flow cell configurations: open slot, cylindrical pillars, and diamond shaped pillars, at Re of 0.1, 1 and 10.

at lower flow rates, the build-up of fine particles in the near-slot region can potentially plug the pore throats and change the local permeability. Cylindrical pillars appear to be slightly more resistant to the formation of a layer of particles near the slot opening. Their geometry generated slightly higher flow rates due to their larger size compared to the diamond shape. However, the presence of the simulated porous media influenced the flow field within the near-slot region. Uave within the low velocity regions for the cylindrical pillars and diamond shaped pillars were generally greater than that of the open slot. As a result, particle build-up within the near-slot region of the open slot after 16 min was greater than the build-up within the simulated porous media geometries.

mathematical models. This study observed that the differences in the shapes and the sizes of the particles influence their dynamic behaviors in the flow, including their rotation, which in turn affect their tendencies to be deposited on the solid walls. The results give a visual understanding of the significance of particle shape and rotation on particle deposition even at a microscale. The rotation of particles depends on several factors including their shape, initial orientations, and relative locations in the flow field. These factors can join together and influence particle deposition near the slot entrance. Results showed that micro-sized particles can exhibit rotational behavior within an irrotational velocity flow field region. This work also highlights that the particle–fluid density difference driven gravitational settling velocity can have a significant impact on particle deposition. It was observed that particle inertial effects were negligible in the flow regimes investigated. In general, the velocity of the continuous phase has a significant impact on the build-up of the particles. Particle build-up was most likely to occur in regions of lower continuous phase velocity. It was observed that

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 paper. 11

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Acknowledgements

0078-x. [24] H. Wadell, Volume, shape, and roundness of quartz particles, Geology. 43 (1935) 250–280, https://doi.org/10.1086/624298. [25] J. Zheng, R.D. Hryciw, Traditional soil particle sphericity, roundness and surface roughness by computational geometry, Géotechnique 65 (2015) 494–506, https:// doi.org/10.1680/geot.14.P.192. [26] J.C. Santamarina, G. Tech, Advances in Geotechnical Engineering: The Skempton Conference, Thomas Telford Ltd, 2004, , https://doi.org/10.1680/aigev1.32644. [27] J. Saxby, F. Beckett, K. Cashman, A. Rust, E. Tennant, The impact of particle shape on fall velocity: implications for volcanic ash dispersion modelling, Volcanol. Geotherm. Res. 362 (2018) 32–48, https://doi.org/10.1016/j.jvolgeores.2018.08. 006. [28] A. Elfasakhany, X.S. Bai, Numerical and experimental studies of irregular-shape biomass particle motions in turbulent flows, Eng. Sci. Technol. 22 (2019) 249–265, https://doi.org/10.1016/j.jestch.2018.10.005. [29] C.A. Ruzycki, A.R. Martin, R. Vehring, W.H. Finlay, An in vitro examination of the effects of altitude on dry powder inhaler performance, Aero. Med. Pulm. Drug Deliv. 31 (2017) 221–236, https://doi.org/10.1089/jamp.2017.1417. [30] B. Grgic, W.H. Finlay, P.K.P. Burnell, A.F. Heenan, In vitro intersubject and intrasubject deposition measurements in realistic mouth-throat geometries, Aero. Sci. 35 (2004) 1025–1040, https://doi.org/10.1016/j.jaerosci.2004.03.003. [31] A.K. Prasad, Particle image velocimetry, Curr. Sci. 79 (2000) 51–60. [32] Y. Çengel, J.M. Cimbala, Fluid mechanics: fundamentals and applications, McGrawHill (2006), https://doi.org/10.1088/1751-8113/44/8/085201. [33] Z. Zhang, C. Kleinstreuer, C.S. Kim, Micro-particle transport and deposition in a human oral airway model, J. Aero. Sci. 33 (2002) 1635–1652, https://doi.org/10. 1016/S0021-8502(02)00122-2. [34] C. Kleinstreuer, Z. Zhang, J.F. Donohue, Targeted drug-aerosol delivery in the human respiratory system, Annu. Rev. Biomed. Eng. 10 (2008) 195–220, https:// doi.org/10.1146/annurev.bioeng.10.061807.160544. [35] J. Heyder, J. Gebhart, Gravitational deposition of particles from laminar aerosol flow through inclined circular tubes, Aero. Sci. 8 (1977) 289–295, https://doi.org/ 10.1016/0021-8502(77)90048-9. [36] I. Balásházy, T.B. Martonen, W. Hofmann, Inertial impaction and gravitational deposition of aerosols in curved tubes and airway bifurcations, Aero. Sci. Technol. 13 (1990) 308–321, https://doi.org/10.1080/02786829008959447. [37] Y. Zhang, W.H. Finlay, E.A. Matida, Particle deposition measurements and numerical simulation in a highly idealized mouth-throat, Aero. Sci. 35 (2004) 789–803, https://doi.org/10.1016/j.jaerosci.2003.12.006. [38] M. Raffel, C.E. Willert, F. Scarano, C.J. Kähler, S.T. Wereley, J. Kompenhans, Particle Image Velocimetry, Springer International Publishing AG, part of Springer Nature, 2018, , https://doi.org/10.1007/978-3-319-68852-7. [39] C. Tropea, A.L. Yarin, J.F. Foss, Springer Handbook of Experimental Fluid Mechanics, Springer, Berlin Heidelberg, 2007, , https://doi.org/10.1007/978-3540-30299-5. [40] A. Melling, Tracer particles and seeding for particle image velocimetry, Meas. Sci. Technol. 8 (1997) 1406–1416. [41] A.R. Lambert, P.T. O’shaughnessy, M.H. Tawhai, E.A. Hoffman, C. Lin, regional deposition of particles in an image-based airway model: large-eddy simulation and left-right lung ventilation asymmetry, Aero. Sci. Technol. 45 (2011) 11–25, https:// doi.org/10.1080/02786826.2010.517578. [42] C. Darquenne, Aerosol deposition in health and disease, Aero. Med. Pulm. Drug Deliv. 25 (2012) 140–147, https://doi.org/10.1089/jamp.2011.0916. [43] J. Fan, Numerical Study of Particle Transport and Deposition in Porous Media, (Ph.D. Thesis), Université Bretagne Loire, 2018. [44] H.-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques, Springer, Berlin Heidelberg, 2003, , https://doi. org/10.1007/978-3-662-05165-8. [45] J.B. Segur, H.E. Oberstar, Viscosity of glycerol and its aqueous solutions, Ind. Eng. Chem. 43 (1951) 2117–2120, https://doi.org/10.1021/ie50501a040. [46] C.E. Willert, M. Gharib, Digital particle image velocimetry, Exp. Fluids. 10 (1991) 181–193, https://doi.org/10.1007/BF00190388. [47] F. Moisy, PIVMat, 2017, https://www.mathworks.com/matlabcentral/ fileexchange/10902-pivmat-4-10, accessed December 1, 2018. [48] S. Ansari, Newtonian and Non-Newtonian Flows Through Mini-Channels and MicroScale Orifices for SAGD Applications, (Master’s Thesis), University of Alberta, 2016, , https://doi.org/10.7939/R3J09WC3C. [49] B. Wieneke, PIV uncertainty quantification from correlation statistics, Meas. Sci. Technol. 26 (2015), https://doi.org/10.1088/0957-0233/26/7/074002. [50] A. Sciacchitano, B. Wieneke, PIV uncertainty propagation, Meas. Sci. Technol. 27 (2016), https://doi.org/10.1088/0957-0233/27/8/084006. [51] L. Kinsale, D.S. Nobes, Development of an Online System to Measure sand Production Through Mini-Slots in SAGD Operations Using PSV, Okanagan Fluid Dyn. Meet., Kelowna, Br. Columbia, Canada, 2017. [52] D. Homeniuk, Development and testing of macro and micro three-dimensional particle tracking systems, (master’s thesis) Thesis, University of Alberta, 2009. [53] S.J. Baek, S.J. Lee, A new two-frame particle tracking algorithm using match probability, Exp. Fluids. 22 (1996) 23–32, https://doi.org/10.1007/BF01893303. [54] E.P. Cox, A method of assigning numerical and percentage values to the degree of roundness of sand grains, Paleontology 1 (1927) 179–183. [55] J. Zheng, Wadell_roundness.m Particle roundness and sphericity computation, 2014, https://www.mathworks.com/matlabcentral/fileexchange/60651-particleroundness-and-sphericity-computation, accessed November 1, 2018. [56] P.P. Lewicki, G. Pawlak, Effect of mode of drying on microstructure of potato, Dry. Technol. 23 (2005) 847–869, https://doi.org/10.1081/DRT-200054233. [57] J.R. Hernandez-Aguilar, R.G. Coleman, C.O. Gomez, J.A. Finch, A comparison

The authors gratefully acknowledge financial support from the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Alberta Ingenuity Fund, and the Canadian Foundation for Innovation (CFI). J.A.W. Elliott holds a Canada Research Chair in Thermodynamics. The authors also thank RGL Reservoir Management Inc. for their financial support. References [1] J. Heyder, Deposition of inhaled particles in the human respiratory tract and consequences for regional targeting in respiratory drug delivery, Proc. Am. Thorac. Soc. 1 (2004) 315–320, https://doi.org/10.1513/pats.200409-046TA. [2] A. Tsuda, F.S. Henry, J.P. Butler, Particle transport and deposition: basic physics of particle kinetics, Compr. Physiol. 3 (2013) 1437–1471, https://doi.org/10.1002/ cphy.c100085. [3] A.I. Kartushinsky, I.A. Krupensky, S.V. Tisler, M.T. Hussainov, I.N. Shcheglov, Deposition of solid particles in laminar boundary layer on a flat plate, High Temp. 47 (2009) 892–901, https://doi.org/10.1134/S0018151X09060170. [4] W.C. Krumbein, Measurement and geological significance of shape and roundness of sedimentary particles, Sedim. Res. 11 (1941) 64–72, https://doi.org/10.1306/ D42690F3-2B26-11D7-8648000102C1865D. [5] J.G. Speight, Nonthermal methods of recovery, Enhanc. Recover. Methods Heavy Oil Tar Sands, first ed., Elsevier, 2009, pp. 185–220, , https://doi.org/10.1016/ B978-1-933762-25-8.50011-0. [6] J.R. Etherington, I.R. McDonald, Is bitumen a petroleum reserve? Society of Petroleum Engineers, SPE Annu. Tech. Conf. Exhib., Houston, Texas, U.S.A., 2004, pp. 1–7, , https://doi.org/10.2118/90242-MS. [7] J. Xie, S.W. Jones, C.M. Matthews, B.T. Wagg, P. Parker, R. Ducharme, Slotted liner design for SAGD wells, World Oil 228 (2007) 67–75. [8] A.M. Al-Bahlani, T. Babadagli, SAGD laboratory experimental and numerical simulation studies: a review of current status and future issues, Pet. Sci. Eng. 68 (2009) 135–150, https://doi.org/10.1016/j.petrol.2009.06.011. [9] S. Ansari, Y. Yusuf, L. Kinsale, R. Sabbagh, D.S. Nobes, Visualization of fines migration in the flow entering apertures through the near-wellbore porous media, SPE Therm. Well Integr. Des. Symp. Society of Petroleum Engineers, 2018, , https://doi. org/10.2118/193358-MS. [10] Y. Yusuf, S. Ansari, M. Bayans, R. Sabbagh, Study of flow convergence in rectangular slots using particle shadowgraph velocimetry, 5th Int Conf. Exp. Fluid Mech. Munich, Ger. (2018) 579–584. [11] M. Mahmoudi, V. Fattahpour, A. Nouri, T. Yao, B.A. Baudet, M. Leitch, Oil sand characterization for standalone screen design and large-scale laboratory testing for thermal operations, SPE Therm. Well Integr. Des. Symp. 2015, https://doi.org/10. 2118/178470-MS. [12] Y.J. Lin, P. He, M. Tavakkoli, N.T. Mathew, Y.Y. Fatt, J.C. Chai, A. Goharzadeh, F.M. Vargas, S.L. Biswal, Examining asphaltene solubility on deposition in model porous media, Langmuir 32 (2016) 8729–8734, https://doi.org/10.1021/acs. langmuir.6b02376. [13] R. Lau, H.K.L. Chuah, Dynamic shape factor for particles of various shapes in the intermediate settling regime, Adv. Powder Technol. 24 (2013) 306–310, https:// doi.org/10.1016/j.apt.2012.08.001. [14] W.C. Hinds, Aerosol Technology–Properties, Behavior, and Measurement of Airborne Particles, John Wiley & Sons, Linc, second ed., 1999. [15] L. Rosendahl, Using a multi-parameter particle shape description to predict the motion of non-spherical particle shapes in swirling flow, Appl. Math. Model. 24 (2000) 11–25, https://doi.org/10.1016/S0307-904X(99)00023-2. [16] T. Wriedt, Using the T-matrix method for light scattering computations by nonaxisymmetric particles: superellipsoids and realistically shaped particles, Part. Part. Syst. Charact. 19 (2002) 256–268, https://doi.org/10.1002/1521-4117(200208) 19:4<256::AID-PPSC256>3.0.CO;2-8. [17] B.Y. Ni, I. Elishakoff, C. Jiang, C.M. Fu, X. Han, Generalization of the super ellipsoid concept and its application in mechanics, Appl. Math. Model. 40 (2016) 9427–9444, https://doi.org/10.1016/j.apm.2016.06.011. [18] S. Ghaemi, P. Rahimi, D.S. Nobes, Assessment of parameters for distinguishing droplet shape in a spray field using image-based techniques, At. Sprays. 19 (2009) 809–831, https://doi.org/10.1615/AtomizSpr.v19.i9.10. [19] F. Podczeck, S. Rahman, J. Newton, Evaluation of a standardised procedure to assess the shape of pellets using image analysis, Pharmaceutics 192 (1999) 123–138, https://doi.org/10.1016/S0378-5173(99)00302-6. [20] K. Patchigolla, D. Wilkinson, M. Li, Measuring size distribution of organic crystals of different shapes using different technologies, Part. Part. Syst. Charact. 23 (2006) 138–144, https://doi.org/10.1002/ppsc.200601022. [21] L. Mayor, J. Pissarra, A.M. Sereno, Microstructural changes during osmotic dehydration of parenchymatic pumpkin tissue, Food Eng. 85 (2008) 326–339, https:// doi.org/10.1016/j.jfoodeng.2007.06.038. [22] H.J. Hwang, S.W. Kim, C.P. Xu, J.W. Choi, J.W. Yun, Morphological and rheological properties of the three different species of basidiomycetes phellinus in submerged cultures, Appl. Microbiol. 96 (2004) 1296–1305, https://doi.org/10.1111/j.13652672.2004.02271.x. [23] Y. Takashimizu, M. Iiyoshi, New parameter of roundness R: circularity corrected by aspect ratio, Prog. Earth Plan. Sci. 3 (2016), https://doi.org/10.1186/s40645-015-

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Experimental Thermal and Fluid Science 109 (2019) 109894

L.K. Kinsale, et al. between capillary and imaging techniques for sizing bubbles in flotation systems, Miner. Eng. 17 (2004) 53–61, https://doi.org/10.1016/j.mineng.2003.09.011. [58] R. Israel, D.E. Rosner, Use of a generalized stokes number to determine the aerodynamic capture efficiency of non-stokesian particles from a compressible gas flow, Aero. Sci. Technol. 2 (1983) 45–51, https://doi.org/10.1080/ 02786828308958612.

[59] S.K. Jha, Effect of particle inertia on the transport of particle-laden open channel flow, Eur. J. Mech. B/Fluids. 62 (2017) 32–41, https://doi.org/10.1016/j. euromechflu.2016.10.012. [60] H.A. Stone, C. Duprat, Chapter 2: low-reynolds-number flows, Fluid-Structure Interact. Low-Reynolds-Number Flows, Royal Society of Chemistry, 2016, pp. 25–77, , https://doi.org/10.1039/9781782628491-00025.

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