The rate and extent of strength gain of a concrete at early ages (reaction times) are determined exclusively by the evolution of the cementitious binder’s properties. The binder itself is a mixture of a powder of cementitious minerals and water, and so the particle’s physical properties (e.g., surface area) and chemical composition are decisive in determining the behavior of a concrete at early times. Cementitious particles are predominantly calcium aluminosilicate minerals or glasses (Taylor, 1990) having a wide distribution of particle size and shape; with particle size ranging from <0.1 to ≥100 μm. At a fixed composition, the rate of reaction of particles per unit volume increases with decreasing particle size due to their increasing specific surface area (Bentz et al., 1999; Kumar et al., 2012). In addition, reports have suggested a particle size dependence of the phase composition of multi-phase cementitious particles and of fly-ash particles produced by coal combustion (Berry et al., 1989), although the exact relationships are unknown and probably vary from material to material. Determining the exact compositional dependence of reaction rates is therefore challenging because of the inherently wide distribution of particle sizes and shapes. This problem would be tractable if these kinds of powders could be separated into narrow size bins. However, existing methods for fractionation [e.g., sieving, density fractionation, field-flow fractionation, etc. (Tiessen and Stewart, 1983; Giddings, 1984)] are cumbersome, time consuming, and produce low yields making them unsuitable for such preparatory functions.

A novel inertial microfluidics (IMF) method has recently been shown to fractionate biological cells (Di Carlo et al. 2007, 2008; Di Carlo, 2009). IMF separations are performed using “on-chip” devices that generate inertial lift forces, thereby driving particles toward size-dependent equilibrium lateral positions in a fluid streamline within a high aspect-ratio microchannel (Anderson et al., 2000; Enger et al., 2004; Gijs, 2004; Wong et al., 2004; Cheng et al., 2007; Di Carlo, 2009; Wu et al., 2009; Pratt et al., 2011). As the particles converge toward these equilibrium positions, they are collected in symmetric outlets configured with tuned fluidic resistances (Di Carlo et al. 2007, 2008; Hur et al., 2010; Lee et al., 2011; Hansson et al., 2012). Inertial approaches have garnered significant interest because such separations are particle-size-dependent, continuous, and operate efficiently at high(er) flow rates as compared to other methods (Pamme, 2007; Bhagat et al., 2009; Hou et al., 2010; Hur et al., 2011). In separate studies, Zhang et al. (2014a) and Kim et al. (2014) demonstrated size-based separation of micro/nano sized particles using IMF devices with microchannels with a rectangular cross-section and serpentine and curvilinear geometries, respectively. In another study, polystyrene particles ranging in diameter from 1 to 10 μm have been separated by IMF methods according to size and shape, with a selectivity of ±2 μm and with yields up to 90% (Chen et al., 2008). Lee et al. (2014) have demonstrated successful separation of plasma cells, with yields in excess of 70% and throughputs in the order of 10¹¹ cells/min, from human blood using IMF devices equipped with contraction–expansion array (CEA) within the microchannel. Hansson et al. (2012) also demonstrated the high-throughput filtration of particles using IMF by constructing parallel arrays of up to 16 microfluidic channels for the filtration of randomly sized particles. In more recent studies, Zhang et al. (2014b) have devised a hybrid microfluidic device, integrating inertial focusing of a typical IMF device with dielectrophoresis (DEP), for feedback-controlled manipulation and separation of micron-sized particles in a size-dependent manner. Recent advancements in the field of IMF-based methods are detailed in these review articles (Martel and Toner, 2014; Tabeling, 2014).

The high-throughput capabilities of IMF methods potentially offer a significant advance in the fractionation of inorganic powders. But, IMF separation studies to date have been conducted using particles having a narrow particle size distribution (PSD) or at least well-defined shapes and size classes. For application to pulverized powders with wide PSDs and irregular shapes, the selectivity and yield of the IMF process have not been assessed. Moreover, the role of IMF operating parameters on the size selectivity and yield of particulates remains unclear, including: (a)

the relationship between the size of particles and hydrodynamic forces,

An improved understanding of the influences of these key parameters is required to tailor the IMF approach, and its application to powders with wide size and shape distributions. Therefore, the objective of this study is to establish the feasibility of IMF methods as a viable approach to separate mineral powder particulates, having either narrow or wide PSDs, into narrow size classes. A critical part of the study examines the effects of process/operating parameters so as to enhance particle yields (PY) and separation fidelity. The paper elucidates key details including: (i) the performance of a specific IMF device design in separating polydisperse particles, (ii) developing methods of analysis to quantify separation performance; both pre-and-post-separation and (iii) directions, and subjects of further research that are necessary to improve size-selectivity and particle enrichment before high-fidelity/throughput particle separations can be performed. It is anticipated that addressing the questions highlighted is critical to enhance the separation efficiency and performance of IMF devices.

For a straight microchannel, the channel width (W) and height (H) were fixed at 30 and 47 μm, respectively, to yield AR_channel = 0.638. This selection was made based on previous success using this design (Masaeli et al., 2012). Equations (5–7) were solved in a piece-wise manner to identify fluid properties, and suspension characteristics that would optimize particle enrichment/selectivity for inorganic powders with broad PSDs. Parameters of particular interest in the optimization process were: (a) carrier fluid density (ρ_F) and viscosity (μ), (b) fluid-flow rate (Q), and (c) volume fraction of solid in the suspension (V _f). These solutions are graphically represented in Figure 1 below. Also noted in Figure 1, is our justification for selection of L_c = 40 mm, which provides a balance of a compact device size, and suitable particle focusing.

Figure 1A shows, for suspensions flowing in a straight microchannel with a rectangular cross-section of a fixed geometry (L_C = 40 mm, H = 47 μm, W = 30 μm), that very high flow rates are required to enable small particles, with volume-equivalent spherical diameters ≤3.5 μm, to acquire their inertial equilibrium positions. High flow rates in narrow microchannels, however, are not practical because of transitions to turbulent flow when Re >2000 (Stone et al., 2004). The flow rate can be reduced somewhat by using fluids with a lower kinematic viscosity (μ/ρ), but this reduction is insufficient to enable very small particles to reach their equilibrium positions. Based on the trends in Figure 1A and the need to avoid any reaction with cementitious particles, ethanol was chosen as the carrier fluid with a flow rate between 55 and 135 μL/min.

Using ethanol as a carrier fluid, Eqs 5–7, the fluid-flow rate was chosen within a range of 55–135 μL/min, shown in Figure 1B, the high end of which would enable for particles larger than 3.0 μm (a_P) to migrate to their equilibrium positions. Again, focusing smaller particles would require longer channels or higher flow rates, and would therefore make device fabrication more challenging.

With L_c and Q selected, the focusing criterion in Eq. 7 was used to determine the optimal particle volume fraction in suspension. Generally, higher particulate concentrations are desirable to increase yield at the outlets. However, Figure 1C shows that high particle concentrations may induce steric crowding effects that hinder the migration of smaller particles. Based on this trade-off and Eq. 2c, an optimum particulate volume fraction (V _f) was identified to range between 0.1 and 0.5% by volume, for which particles ≥1.5 μm (a_P) are expected to acquire equilibrium positions. Here, it should be noted that the λ parameter, as described in Eq. 7, does not consider the length of the microchannel and the fluid-flow rate explicitly. Therefore, when we factor in the limiting particle sizes for a channel length (L_C) of 40 mm and fluid-flow rates of 55–130 μL/min, it is expected that in suspensions prepared at V _f <0.5%, particles wherein 1.5 μm < a_P < 3.5 μm will not acquire their inertial equilibrium positions, despite not being adversely affected by steric crowding effects. The λ parameters also does not consider particle packing explicitly. Therefore, as a first approximation, a high packing efficiency of ≈64%, was chosen. Based on the analysis above, for optimum values of L_c, Q, and V _f, the minimum size (a_P) of particles, which would acquire their inertial equilibrium positions, is 3.5 μm.

Our device incorporates a straight microchannel with cross-sectional dimensions of H = 47 μm, W  = 30 μm, and L_c = 40 mm. The inlet of the IMF device is where the suspension is injected (see Figure 2). Following the inlet and long inertial focusing channel, there is a gradual expanding outlet region, with a radius of curvature (R_curvature) of 3 mm, which allows the particles to maintain their streamline positions without Dean flow effects (Masaeli et al., 2012) (see Figure 2). Previous studies (Masaeli et al., 2012) have indicated that the gradual expansion in the channels increases the spacing between equilibrium positions of particles of different sizes, so that each outlet can collect particles from any given equilibrium position with less interference from nearby positions.

Of the seven outlets shown in Figure 2, outlets O5, O6, and O7 are identical by symmetry to outlets O3, O2, and O1, respectively. Therefore, the remainder of this section will focus on the characteristics of outlets O1 through O4. When comparing the outlets, the resistance ratio, α_ij, of outlet i to outlet j is defined as the ratio of the fluid-flow rates Q_i/Q_j. For the design shown in Figure 2, α₁₂ = 3/4, α₁₃ = 1/2, and α₁₄ = 1/4. The outlets have serpentine geometries to increase fluidic resistance and limit flow-rate distortions (Masaeli et al., 2012). In the discussion that follows, particle collections in different outlets are described in the terms of the resistances of the outlets in which they are collected. It should be noted that outlets of higher resistances (i.e., O1, O7, O2, and O6) could alternately also be referred to “outer” channels, on account of their siphoning fluid closer to the inertial focusing channel walls, and outlets of lower resistance (i.e., O3, O4, and O5) as the “inner” channels, as they follow fluid trajectories closer to the microchannel centerline. This IMF device is thus optimized to permit separation of cementitious particles into four different size classes.

Four powders were evaluated: (i) ordinary portland cement (OPC), (ii) finely ground limestone, a common filler material used in concrete binders (Lothenbach et al., 2008; Oey et al., 2013), (iii) coal fly ash (FA), a post-combustion residue that is often used as a pozzolanic additive in concrete (Lothenbach et al., 2011), and (iv) three size-classified silica microsphere powders with median diameters of 1.5, 4.0, or 8.0 μm.

The OPC was an ASTM C150 compliant Type I/II formulation with an estimated phase mass composition of 58.5% C₃S, 18.4% C₂S, 5.6% C₃A, 9.2% C₄AF, 4.2% CaCO₃, 1.3% MgO, and an Na₂O equivalent of 0.40%². The ground limestone (CaCO₃) is a commercially available powder of >95% purity produced by OMYA A.G. The oxide composition of the FA powder, estimated using X-ray fluorescence, is 57.98% SiO₂, 27.71% Al₂O₃, and 6.23% Fe₂O₃, with minor quantities of CaO, MgO, Na₂O, K₂O, P₂O₅, TiO₂ also measured. The silica microsphere powders were used to test the selectivity and yield of the device for powders with uniform shape and narrow size range.

The PSDs of each powder were measured by static light scattering (SLS) using ultrasonically agitated isopropanol as a carrier fluid to prevent reaction or agglomeration during the measurement. The measured size distributions are shown in Figure 3. The density of OPC, FA, limestone, and silica microspheres was assumed to be 3250, 2700, 2600, and 2650 kg/m³, respectively. The specific surface areas of the OPC, FA, and limestone powders, inferred from their PSDs by assuming spherical particles (Bullard and Garboczi, 2004), are 418, 495, and 401 m²/kg, respectively. Similarly, the specific surface area of the silica microsphere powders with median diameter of 1.5, 4.0, and 8.0 μm are calculated as being: 1791, 508, and 270 m²/g, respectively.

Representative scanning electron micrographs of the powder particles, in secondary electron mode, are shown in Figure 4. Both the OPC and limestone have non-spherical particles (AR_particle > 1) in a wide range of sizes, while the silica particles are nearly spherical (AR_particle ≈ 1) and possess a narrower size distribution. The FA particles are present in a wide range of shapes, with a wide range of inhomogeneity in the surface morphology of the larger particles, although the majority of the small particles appear to be nearly spherical. The influence of particle shape distribution on the separation selectivity will be discussed in a later section.

Optical microscopy-based image capture and analysis (ICA) was applied to characterize the particle size-selectivity and particle enrichment in the different outlets. Particles collected in a given outlet are dispersed onto a glass slide, and an optical microscope fitted with a 20× objective was used to image the particles. To characterize particle separations in a statistically consistent manner, at least eight images, with a field of view (FoV) of 420 μm × 420 μm, are captured for particles exhausted at each outlet. Illumination, brightness, and contrast are each adjusted to achieve the best distinction between the particle boundaries and the background. The images are processed using a custom algorithm embedded within ImageJ (Schneider et al., 2012).

The image-processing algorithm applies the following routines to improve image features: (a) a Gaussian filter to remove background noise, (b) intensity thresholding to distinguish the particle boundaries from the background and (c) a watershed algorithm to subtract the residual image from the particles and their boundaries. The macro then performs a pixel count within the particle boundaries, and an image scale of 0.3225 μm/pixel edge is used to generate a PSD for the image. The sizes of the particles are related to both their cumulative volume percentages and the corresponding particle numbers. The results obtained from all the images for a given outlet are averaged to present a single PSD for that outlet. The outlet PSDs are used to evaluate PYs according to: (8a)Particle yield (silica microspheres)PYa=NaoutletiNainlet (8b)Particle yield (cementitious powders)PY=NoutletiNinlet where, N is the particle number, i refers to a specific outlet, and “a” refers to specific size.

The calculation of PY is accomplished using two methods for particulates with narrow or broad size distributions. For silica microspheres, PY is assessed for each outlet while accounting for the size of the particle (Eq. 8a). Therefore, PY for the silica microspheres includes particle enrichment and particle size-selectivity. For cementitious powders, which have a very broad range of particle sizes, PY is calculated by simply counting the number of particles collected in a given outlet and dividing this value by the total number of particles counted at the inlet without accounting for particle size (Eq. 8b). This provides indications of particle enrichment but not of size-selectivity. Therefore, for particle size-selectivity, the median particle diameter (i.e., the d₅₀) and SD of the distribution are presented in addition to PY. This procedure was applied because cementitious powders have numerous size-classes and imposing arbitrary size-classes is difficult.

To quantitatively analyze the particle separation metrics, the PSDs obtained from the ICA routine were fitted to Rayleigh, Gamma, and Rosin–Rammler distributions using a Nelder–Mead simplex optimization method (Nelder and Mead, 1965; Olsson and Nelson, 1975). The Rosin–Rammler distribution (Eq. 9a, RRD) was found to best fit the measured PSDs, in terms of the coefficient of determination and residuals analysis (Eq. 9b), so only the analysis of the RR distributions is discussed further. The RR distribution is given by: (9a)RRx=100 1−eln0.2xd80m (9b)Residuals ErrorResiduals=∑i=1i=NRRsimxi−RRmesxiRRmesxi (9c)SDσ=1B∑i=1i=BRRxixi−μ2 where (9d)Mean particle diamter μ=1B∑i=1i=BRRixi where, RR(x) is the cumulative percentile of particles with sizes less than or equal to x, x (μm) is the particle size, d₈₀ (μm) is the 80th percentile of the distribution, B (unitless) is the number of bins that represent the size-classes as obtained from the ICA routine, μ (μm) is the mean particle size, and m is a dimensionless exponent that influences the curvature of the RR function. The SD (σ) of the fitted distributions (Eq. 9c) can be used to define a size dispersion ratio (DR, Eq. 10), in the particle sizes of any given device outlet in relation to the dispersion in the particle sizes of the inlet. Values of DR >1 imply a larger scatter in outlet particle sizes and hence reduced size refinement, while DR <1 implies a narrower distribution and thus enhanced particle size refinement. When DR ≈ 0, this corresponds to monosized (on average) particles in the outlet. In the following sections, DR will be used as a measure of the particle size refinement produced (i.e., the purity of particle separation) at any given IMF device outlet. (10)Dispersion rationDR=σoutletσinlet

It should be noted that the ICA routine was first validated against experiments performed on the near monosized silica microspheres. In general, at least three images for each of the three silica powders were captured and processed using the ICA macro. As seen in Figure 5, the results obtained from the macro agree well with the PSDs measured by SLS. In addition, RRD fits to the measured silica microsphere PSDs were obtained (see Figure S2 in Supplementary Material) and excellent agreement is noted between the PSDs and the median diameters (d₅₀) derived from ICA methods and Rosin–Rammler fittings. The SDs calculated using Eq. 9c increased with increasing particle size suggesting larger dispersions in particle size with increasing d₅₀ (Figure S2C in Supplementary Material). This is expected due to errors that result from both shadowing and centered-weighted optical focusing, which gain increasing the significance with increasing particle size.

The results obtained on all the powder separations are in excellent agreement with those reported by Yamada and Seki (2005) and by Zhou et al. (2013). For example, Yamada and Seki conducted experiments using a 40:3 mass ratio mixture of 1.0 and 2.1 μm polymer microspheres in a suspension with 0.002% mass loading. In their study, small amounts of liquid were repeatedly removed from the microchannel through side branch channels to align and concentrate particles close to the channel walls as they continued to move downstream. They reported preferential accumulation of the 1.0 μm particles in higher-resistance (outer channels) outlets, as they rapidly migrated close to the channel walls and of 2.1 μm particles in lower-resistance (inner channels) outlets, as they took longer to migrate close to the channel walls (Yamada and Seki, 2005; Zhou et al., 2013). This behavior is similar to that observed in our study, wherein smaller particles migrated rapidly to the channel walls and collected in outer channels (higher resistance) whereas larger particles remained close to the channel centerline until collected in the inner channels (lower resistance). However, it should be noted that in the work of Yamada and Seki and Zhou et al. (Yamada and Seki, 2005), the collection of particles was employed in the non-inertial regime and, as such, particle collections were merely based on their migration with respect to the channel walls (or centerline) before they acquired their equilibrium positions. Contrastingly, in our work, the IMF devices are designed with microchannel lengths tuned to allow particles to acquire their inertial equilibrium positions before collection.

Zhou et al. (2013) used a combination of microchannels with different aspect ratios to study the inertial focusing behavior of 9.94 and 20 μm particles suspended in a liquid with 0.025% mass loading. They reported that for a fluid-flow rate of 100 μL/min, the 20 μm particles were found predominantly in lower-resistance outlets and 9.94 μm particles in higher-resistance outlets. These results were explained in terms of the influence of particle size on the magnitude of the inertial lift forces. It was suggested that smaller particles are subjected to smaller wall-induced lift, so they equilibrate closer to the channel walls than larger particles (Zhou et al., 2013). Even though this explanation ignores the effect of shear-gradient lift forces, Eqs 1c,d indeed suggest that for a given channel aspect ratio, the magnitude of wall-induced lift forces is proportional to particle size. Zhou et al. (2013) also suggested that larger particles experience a greater rotation-induced lift that causes them to migrate away from smaller particles and toward the channel centerline within the IMF device.

Particle shape is likely to be an important factor in determining IMF lift forces and focusing behavior, although its influences have received less attention than those of particle size. Masaeli et al. (2012) recently showed that particles suspended in fluids acquired different inertial equilibrium positions depending on their aspect ratios (AR). Specifically, particles having larger aspect ratio have a greater angular momentum than spheres under the influence of hydrodynamic forces. In addition, the wall-induced lift force on an irregularly shaped particle depends on orientation; the wall-induced lift force is larger when a long edge is perpendicular to the channel walls than when it is parallel to the walls. When these effects are averaged over many rotations, particles with high aspect ratio focus close to the channel centerline and therefore collect in inner-more outlets than would be expected for spheres (Masaeli et al., 2012). These shape effects are broadly consistent with the results of the present study, in which larger particles accumulate in higher-resistance outlets when they are spherical (e.g., for silica microspheres, as shown in Figure 6), but do tend to accumulate in lower-resistance outlets when they have irregular shapes (e.g., for limestone, FA, and OPC, as shown in Figures 7–10). Furthermore, it can be speculated that the outer channels (e.g., O1, O2, O6, and O7) pull fluid closer to the channel walls allowing particles to migrate close to the channel walls. Particles with small rotational diameters are capable of occupying these positions and, therefore, collect in outer channels. Particles with large rotational diameters, on the other hand, are not able to occupy positions close to the channel walls and, as such, remain close to channel centerline until collected in the inner outlets (O3, O4, and O5).

However, the irregular shape distribution of the cementing powder particles is not enough to explain the focusing behavior observed in this study. This can be said in light of the observed migration behavior of coal fly-ash particles (Figures 7–9), which despite being nearly spherical (Figure 4) exhibit migration behavior similar to that of non-spherical OPC and limestone particles and in contrast to that of silica microspheres. While coal fly-ash particles are broadly spherical, they contain plerospheres and pores on their surfaces (Fisher et al., 1978) which may affect hydrodynamic forces at a micro-scale – further investigation is warranted to study these effects in detail. It is expected that another factor must be responsible for the inverse relation between particle size and outlet collection location observed for the limestone, fly ash, and cement powders. We suggest that the wide PSD, resulting in large particle numbers, of these powders is at least partially responsible. When particles having a very broad size range are introduced into a fluid streamline, they attempt to migrate to equilibrium positions as a function of their size and shape. Particle collisions, either with other particles or with the channel walls, could frustrate the ability of some particles to achieve equilibrium positions. The effect of collisions should be negligible in dilute suspensions, but may become important or even decisive at higher solid concentrations. In general, the number density of smaller particles is much greater in these cementitious powders than that of larger particles, so collisions between two large particles would be less probable than collisions involving small particles. The collision of two small particles could potentially perturb the migration of both particles significantly, but momentum conservation implies that a collision between one large and one small particle would significantly perturb the path of only the small particle. Therefore, in general, collisions would more likely inhibit smaller particles to focus at equilibrium positions than larger particles. If the smaller particles remain unfocused by collisions, they would accumulate more evenly in all the outlets and thereby resulting in wider dispersions especially in the lower-resistance outlets where only larger particles are expected. This reasoning is in good agreement with the observations of this study. Furthermore, the notion that particle crowding and collisions would degrade the IMF separations is supported by the observation that higher suspension concentrations correspond to wider size distributions in the outlets (Figure 11B). Again, higher solid concentrations increase the likelihood of collisions among the particles and would tend to impede the migration of the smaller particles more than larger particles toward their equilibrium positions within the channel.

This work has explored the feasibility of IMF-based methods for size fractionation of mineral particulates having irregular shapes and size distributions spanning several orders of magnitude. When operated at high flow rates, IMF devices are able to separate particulates according to size into overlapping classes, each of which has a narrower size distribution than the parent (i.e., the input) particle system. For some size classes, the spread of the size distribution was reduced by about 75%. Optical ICA methods have been developed to measure the quality of the separations in terms of a DR of the SDs of the output to the input size distributions. Particle shape, the width of the input size distribution, and the solids concentration in suspension all influence the separation quality at a given flow rate. Suspension properties and flow conditions that increase the frequency of interparticle collisions, or that produce multiple equilibrium positions for particles of equivalent size, will degrade the quality of separations by keeping the smaller particles unfocused. These aspects, especially those of particle shape effects, remain worthy of further research and attention.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The Supplementary Material for this article can be found online at http://journal.frontiersin.org/article/10.3389/fmats.2015.00048