Considering the widespread presence of switching devices on the power grid (including renewable energy system inverters), network distortion is more prominent. To maximize network efficiency, our goal is to minimize these distortions. Measuring the voltage and current total harmonic distortion (THD) using power meters and other specific equipment, and assessing power factor and peak currents, represents a crucial step in creating an efficient and stable smart grid. In this paper, we propose a power meter capable for measuring both standard electrical parameters and power quality parameters such as the voltage and current total harmonic distortion factors. The resulting device is compact and DIN-rail-mountable, occupying only three modules in an electrical cabinet. It integrates both wired and wireless communication interfaces and multiple communication protocols, such as Modbus RTU/TCP and MQTT. A microSD card can be used to store the device configuration parameters and to record the measured values in case of network fault events, the device’s continuous operation being ensured by the integrated backup battery in this situations. The device was calibrated and tested against three industrial power meters: Siemens SENTRON PAC4200, Janitza UMG-96RM, and Phoenix Contact EEM-MA400, obtaining an overall average measurement error of only 1.22%.

In Paper I (Sep. Purif. Technol. 257 (2021) 117676) we showed that a semi-analytic, multi-mechanism expression for the single-fiber capture fraction, ηcap,SF, (derived using asymptotically valid approximations: Ref<0.4, Pef≫1, R≪1, R⋅Pef1/3 arbitrary and Stkp≤Stkpcrit), facilitates a deterministic-, pseudo-continuum aerosol population-balance (PB-) approach to predicting fibrous filter performance. There we explicitly considered “deep” (Lf/df,g≫1), low solidity idealized fibrous filters (FFs) challenged by polydispersed aerosols—especially single-mode log-normal (LN) ASDs of modest spread captured by a spatially uniform array of fibers of a single diameter in crossflow. However, realistic fibrous filter media often possess a LN distribution of fiber diameters, as well as a near-Gaussian orientation distribution narrowly spread about normal incidence (θ=π/2). Moreover, even if this were not so, there would be meso-scale departures from a uniform average fiber solid fraction. We show here that our tractable aerosol PBE-approach to idealized FF performance (Paper I) can be generalized to incorporate these particular structural features of commercially available fibrous filter media. But, to clarify whether these generalizations are likely to be useful, if not fully sufficient, for practical circumstances, it is also necessary to compare such methods/predictions against selected sets of well-defined experimental results. We initiate this program here, having chosen the recent experiments of Kang et al. (2019) carried out using a commercially available fiberglass filter with Lf/df,g≃300, mean solid fraction of 0.039, and df,g=2.5 μm, successively challenged by mobility-selected KCl(s) particles (with diameters between ca. 20 and 600nm) at the carrier gas velocities of 15 and 10 cm/s—capture conditions dominated by the transport mechanism of Brownian diffusion and convection, with “interception” (associated with non-negligible dp/df) becoming important above ca. dp=100nm. We conclude from these data that the effective interception diameter, dp,icpt,eff, of the particles studied is systematically larger than their stated mobility diameters—a situation which will deserve further attention in future studies. Encouraged by these preliminary but instructive comparisons, we expect that, for many current and future design purposes, our present class of semi-analytic/non-stochastic/multi-mechanism methods will provide a welcome complement, if not alternative, to much more computationally-intensive simulation methods for realistic fibrous media that have been described and implemented in the recent aerosol filtration literature. The consequences of including these structural features of fibrous filters in the presence of aerosol size- and shape polydispersity will be the subject of future studies, based on the generalized Population Balance Equation developed/proposed in Section 3.3.

In Paper I (Sep. Purif. Technol. 257 (2021) 117676) we showed that a semi-analytic, multi-mechanism expression for the single-fiber capture fraction, $\eta_{\mathrm {cap, SF}}$, (derived using asymptotically valid approximations: $\RE_{\mathrm {f}} < 0.4$, $\Pe_{\mathrm {f}} \gg 1$, $R \ll 1$, $R \cdot \Pe_{\mathrm {f}}^{1/3}$ arbitrary and ${\Stk_{\mathrm {p}}} \le {\Stk_{\mathrm {p}}}_{\mathrm{crit}}$),facilitates a deterministic-, pseudo-continuum aerosol population-balance (PB-) approach to predicting fibrous filter performance. There we explicitly considered ``deep'' ($L_{\mathrm {f}}/d_{ {\mathrm {f}}, g} \gg 1$), low solidity idealized fibrous filters (FFs) challenged by polydispersed aerosols---especially single-mode log-normal (LN) ASDs of modest spread captured by a spatially uniform array of fibers of a single diameter in crossflow. However, realistic fibrous filter media often possess a LN distribution of fiber diameters, as well as a near-Gaussian orientation distribution narrowly spread about normal incidence ($\theta = \pi/2$). Moreover, even if this were not so, there would be meso-scale departures from a uniform average fiber solid fraction. We show here that our tractable aerosol PBE-approach to idealized FF performance (Paper I) can be generalized to incorporate these particular structural features of commercially available fibrous filter media. But, to clarify whether these generalizations are likely to be useful, if not fully sufficient, for practical circumstances, it is also necessary to compare such methods/predictions against selected sets of well-defined experimental results. We initiate this program here, having chosen the recent experiments of Kang et al. (Sep. Purif. Technol. 209 (2019) 461--469) carried out using a commercially available fiberglass filter with $L_{\mathrm {f}}/d_{ {\mathrm {f}}, g} \simeq 300$, mean solid fraction of $0.039$, and $d_{ {\mathrm {f}}, g} =2.5$ $\mu$m, successively challenged by mobility-selected KCl(s) particles (with diameters between ca. $20$ and $600$ nm) at the carrier gas velocities of $15$ and $10$ cm/s---capture conditions dominated by the transport mechanism of Brownian diffusion and convection, with ``interception'' (associated with non-negligible $d_{\mathrm {p}}/d_{\mathrm {f}}$) becoming important above ca. $d_{\mathrm {p}}=100$ nm.We conclude from these data that the effective {\em {interception}} diameter, $d_{\mathrm {p, icpt, eff}}$, of the particles studied is systematically larger than their stated {\em {mobility}} diameters---a situation which will deserve further attention in future studies.Encouraged by these preliminary but instructive comparisons, we expect that, for many current and future design purposes, our present class of semi-analytic/non-stochastic/multi-mechanism methods will provide a welcome complement, if not alternative, to much more computationally-intensive simulation methods for realistic fibrous media that have been described and implemented in the recent aerosol filtration literature. The consequences of including these structural features of fibrous filters in the presence of aerosol size- and shape polydispersity will be the subject of future studies, based on the generalized Population Balance Equation developed/proposed in Section 3.3.

We exploit recent results for the multi-mechanism capture of aerosols by an isolated fiber in a steady low-Re crossflow, and analyze the consequences of aerosol polydispersity on the local particle capture rate per unit volume within a "deep" and spatially uniform fibrous filter medium. The linear first-order PDE governing evolution of the aerosol size distribution (ASD) function, n(v; z), within such an idealized medium (where v is particle volume and z the axial distance measured into the fibrous filter) is shown to admit exact solutions by a method of successive quadratures, free of restrictive assumptions about the functional form of either the inlet or internal ASD, or the local, multi-mechanism single fiber capture fraction, eta(cap)(v). This solution not only provides access to the usual measure of filter performance-i.e., fraction of the inlet mass (or volume) flow rate which is captured, but enables the accuracy of potentially attractive rational approximate methods to be studied. As examples, when the suspended local ASD is, and remains, single-mode log-normal-like, we formulate and examine the accuracy and efficiency of two tractable, mathematically closed, 3-moment methods for predicting the overall performance of 'thick' (L-F/d(f) >> 1) non-woven filters comprised of fibers of a single diameter in a uniform 'matte' of small solid-fraction, phi(f). To fix ideas, we illustrate our present theoretical-computational methods, and some of their practical implications, for the particular case of a L-F/d(f) = 300 filter comprised of 2.5 mu m diam. glass fibers challenged by an aerosol population of spherical KCl(s) particles under conditions close to those experimentally studied (and computationally simulated using Brownian-dynamics + CFD methods) in the recent literature. We first consider a 'coagulation-aged' aerosol population having an entrance volume fraction of 0.1 x 10(-6) with dp,g = 200 nm, suspended in a U-0 = 15 cm/s airstream (at p =1 atm, 300 K, Brownian diffusion dominated and interception influenced conditions). To demonstrate the expected improvement in filter efficiency near the previous maximum penetration particle size (MPPS) (ca. 500 nm diam) via the onset of sub-critical particle inertia effects, we also consider a carrier gas velocity of 200 cm/s, revealing a ca. 10-fold gain in local capture efficiency. Such improvements, while offset by the increased penetration of much smaller particles, should be attainable in many fibrous filter applications, provided the associated increase in gas pumping power remains manageable. We conclude with our current assessment of the relative advantages of each of the predictive methods developed and explored here. Tractable generalizations of our essentially deterministic, pseudo-continuum methods-e.g., to enable inclusion of the systematic effects of accessible fiber diameter and orientation distributions also appear to be feasible-as briefly outlined in Section 5.

Abstract When the particle-to-target radius ratio R and the inverse Peclet number 1/P are small, particle capture by interception and diffusion by cylinders at low Reynolds numbers may be described via Friedlander’s single similarity parameter Π ≡ R·P1/3, in the full range 0 < Π < ∞. Particle inertia may substantially enhance this capture efficiency, even at subcritical Stokes numbers S < S*∼2. We have recently shown that this inertial enhancement is the product of an ‘outer’ function E(S) accounting for inertial particle concentration enrichment along the stagnation line, and an ‘inner’ function F(Π, S) describing particle transport near the target. F(Π,S) is first computed here over its full range, (0 < Π < ∞; 0 < S < S*) by numerically solving the corresponding diffusion equation, previously analyzed only in the limits Π = 0 and Π = ∞. Two PDE solvers used (pseudo-spectral orthogonal collocation method and Mathematica’s NDSolve statement) typically agree within 0.1%, with a 0.7% maximal difference. While the previously invoked “additive capture fraction” approximation is now seen to contain errors of up to –17%, new correlations are developed here with a maximum global error of ±0.7%. We also provide a detailed numerical and asymptotic description for the universal structure of the theoretically interesting limit Π → ∞, finding an unusual algebraic decay of the small diffusive contribution to the flux in the region upstream from the critical tangency angle. We use these results to compute the substantial inertial effects reducing the penetration of toxic aerosol fumes, or improving the recovery of valuable aerosol materials (e.g., noble metals and/or semiconductors) for submicron aerosol/carrier gas cases of: Pt(s)/N2(g) and Ge(s)/He(g). Copyright © 2019 American Association for Aerosol Research

At the same total spherule volume fraction in a gaseous mainstream, we predict the significant alteration of mass deposition rate attending extensive aggregationillustrating our methods and results here not only for a mainstream of single-sized cluster aggregates, but also for coagulation-aged (near log-normal) distributions of large fractal-like aggregates (N-g = O(10(3)), D-f = 1.8 (DLCAs) or D-f = 2.1 (RLCAs)) compared to isolated spherule deposition in the same environment. Because of their drastically different sensitivities to aggregation, we consider, sequentially, the particle transport mechanisms of either: ordinary isothermal convective-diffusion, thermophoresis (to a cooled solid target) or inertial impaction (without rebound). Using a rather general formulation (which incorporates Knudsen transition effects expected at elevated pressures) but neglecting direct interception effects, we find that for, say, D-f = 2.1, N = O(10(3)), Kn(1): = mfp/R-1 = 1, if convective-diffusion (with Sc >> 1) were the dominant mechanism then mainstream aggregation would decrease expected mass deposition rates to much larger targets by somewhat more than one decade. However, for thermophoresis aggregation would increase deposition rates by approximately somewhat more than one decade, and, for, say, eddy impaction (in a fully turbulent duct flow) aggregation would increase deposition rates by as much as nearly 1.5 decades. Physically, these large aggregation enhancement-ratios for deposition by thermophoresis or particle Inertial Impaction are attributed to drag reduction (per spherule) associated with momentum shieldinganalogous to the aerodynamic advantages that birds, fish, bicyclists, runners,... experience when in formation. Using this approach, other impaction geometries and Knudsen number situations are also readily treated, as well as more compact even porous (D-f = 3) aggregate populations. These predictive methods, illustrative results, and conclusions are expected to be useful to investigators seeking to maximize (or minimize) particle deposition rates on solid targets by exploiting control over the spherule aggregation process in the mainstream.As an important corollary, our methods also enable the quantitative deconvolution of aggregated aerosol sampling data, i.e., correcting for the systematic distortion (falsification) of sampled aggregate size distributions, pdf(w)(N), brought about by the size-dependent capture coefficients associated with momentum-shielding (nearly power-law: S-mom approximate to N-k) for each of the mechanisms considered here (C-D, T-P, or E-I; Section5)). As demonstrated in Section6.3, while we expect Log-Normal-type distributions to retain their shape, we predict the systematic correction factors needed to obtain the mean and median aggregate sizes (N-g) that must have existed in the mainstream (see Equation(30)). These correction factors become quite significant for each of the mechanisms (especially thermophoresis and impaction) when the mainstream aggregate size-spread is large (e.g., sigma(g) > ca. 2) and the pressure is high enough to cause Kn(1) to drop to O(1).For completeness, the systematic consequences of the appreciable effective size of N >> 1 cluster aggregates, briefly discussed in Section6.2, will need to be included, especially for the deposition of D-f < 2 fractal-like aggregates on targets not much larger than the aggregates themselves (e.g. , depth filter fibers,...). However, for capture by sufficiently large targets a noteworthy conclusion is that, of the distinct aerosol transport mechanisms considered here, isothermal convective-diffusion stands out as the only mechanism for which isolated spherules will deposit more efficiently than large-N cluster aggregates (when compared in the same flow environment at the same mainstream spherule volume fraction).Copyright (c) 2018 American Association for Aerosol Research

Our recent work on the consequences of multispherule cluster aggregate (CA) formation and deposition-rates on much larger solid targets has emphasized the decisive role of momentum-shielding in determining aggregate mobility compared to N isolated spherules in the same gaseous environmentan effect analogous to the drag-reduction advantages experienced by birds electing to move in formation. The extent of momentum shielding is conveniently quantified via a dimensionless function: S-mom(N;Kn(1), aggregate structure), which facilitates predicting the deposition-rate consequences of aggregation in aerosol flow systems when the cluster deposition mechanism is dominated by either: (i) isothermal convective-diffusion (C-D), (ii) thermophoresis (T-P) or: (iii) inertial impaction (I-I). Significantly, isothermal C-D was found to be the only transport-mechanism leading to aggregation-induced reductions in spherule deposition rates on large targets (cf. isolated spherules present at the same mainstream spherule volume fraction). However, we demonstrate here that, for aggregate deposition on sufficiently small solid targetse.g., fibrous filter elements with diameters of O(10m)even these reductions, which exceed one decade for N = O(10(3)), can be overcome by the mechanism of direct-interception (D-I) associated with nonzero effective aggregate size, without the need to invoke either inertial impaction or thermophoresis. This is especially true for Diffusion-Limited (i.e., open) CAs (with D-f = 1.8) at gas pressures such that the constituent spherules are near the continuum (Kn(1) << 1) limit. Our present analysis and numerical illustrations exploit the fact that direct-interception is expected to play a negligible role for the capture of individual (dense) nanospherules (perhaps comparable in size to the prevailing gas molecule mean-free-path) but the underlying theory, exploited, extended, and illustrated here, was developed with the help of initial capture rate experimental data for much larger diameter (but unaggregated) aerosols on single filter fibers in low Re crossflow. With such small diameter targets, we demonstrate that this interception augmentation for large CAs can occur even for the limiting case of rcp D-f = 3 aggregates, before the expected onset of CA-inertial effects-i.e., Stk(N) << Stk(crit), where, for Re = O(1), Stk(crit) is also O(1). A simple method is also presented for predicting interception-modified spherule deposition rates in the presence of log-normal type aggregate size distributions.Copyright (c) 2018 American Association for Aerosol Research

Aggregated particles nucleated and grown by Brownian encounters in atmospheric pressure gaseous flames, usually have primary particles (of radius R-1) smaller than the prevailing gas molecule mean-free-path, l(g). This simplifies their drift behavior in a strong temperature gradient, i.e., thermophoresis (TP), as has been exploited in the popular technique of TP/TEM soot sampling. Indeed, thermophoretic sampling has become the effective "calibration standard" because it also provides unambiguous aggregate morphology information and is independent of optical properties needed to interpret alternate "non-invasive" methods. However, we show here that at pressures of current engineering interest (e.g., 30-50 bar) the Knudsen number (Kn(1) = l(g)/R-1) is O(1) and the sensitivity of aggregate TP-behavior to pressure, morphology and, especially, aggregate size is altered considerably. While the recent gas kinetic theory results of Young reveal that the thermal force on each spherule should diminish as one leaves the free-molecule limit, large fractal-like aggregates receive the benefit of inter-particle "momentum shielding," and we predict that larger aggregates drift faster than smaller ones in the same temperature gradient. We show that aggregate TP-diffusivity approximately scales with a Kn(1)-dependent power, k, of the spherule number N, where the exponent k is as large as 0.44 for aggregates characterized by "dimension" D-f = 1.8, k(p)/k(g) = 1000 and Kn(1) below O(1). However, if the particle thermal conductivity far exceeds that of the carrier gas, the reduction in thermal force overwhelms the inter-particle momentum shielding below about Kn1 = 0.7, with the aggregate TP-diffusivity becoming inadequate for TP-sampling near Kn(1) = 0.2. Based on these results we conclude that to infer accurate high-pressure mainstream aggregate size distributions and volume fractions via TP-sampling, it is necessary to correct observed TEM-information for the expected "over-representation" of large aggregates. These appreciable corrections (up to 40% for the number-mean aggregate size and approximately one-decade for the associated spherule volume fraction, phi(infinity), at pressure near 50 bar), are shown to be straightforward to implement for sufficiently large mainstream (N) over bar and approximately log-normal aggregate populations.

We consider pharma-motivated processes in which compressed gas (here, COD is employed as an "anti-solvent" (AS), causing drug particle (re)precipitation from an injected presaturated organic solvent microdroplet assumed to be molecularly well-mixed at each instant. It is shown that conditions leading to appreciable homogeneous particle nucleation in this "expanded supersaturated liquid" environment can be sufficiently short-lived that they preclude appreciable particle growth because of encounters with solute molecules or other precipitate particles. This leads to relatively narrow predicted precipitated particle size distributions (PSDs), with a characteristic particle size determined by the typical critical nucleation size. Our mathematical techniques, which exploit the method of characteristics (MOC), make no presumption about PSD-shape and our numerical simulations employ realistic thermophysical properties for the previously studied model system: phenanthrene (surrogate "active pharmaceutical ingredient" [solute], toluene [solvent, S], and compressed CO, [AS]). We explicitly consider initial solvent droplet diameters in the micrometer range and CO, pressures of 52-64 bar and demonstrate the necessity of relaxing frequently made approximations (e.g., nucleation with constant surface energy, negligible Gibbs-Kelvin-Ostwald solubility corrections, solute diluteness,...). Our new methods/parametrizations/performance results for this mathematical model should already help select optimal GASP/SASP operating conditions, and, with suitable extensions, ultimately lead to the development of nearly equally tractable yet sufficiently complete process models.

Anticipating condensation conditions at solid surfaces or within thermal boundary layers is important in many industrial applications involving condensible vapor flows in contact with cooler solid surfaces. In the case of hydrocarbon fuel/air combustion products at moderate pressures containing acid-precursor species (like NO2, SO3, HCl, etc.) surfaces that operate below the prevailing “acid dew point” (ADP) temperature (which can be significantly higher than the DP expected for H2O alone) become vulnerable to chemical attack. Surfaces cold enough to cause acid “mist” onset (AMO) in the vapor phase create potential environmental problems and become much less efficient for condensate capture. Previous methods for estimating ADP and AMO have several drawbacks, the most prominent of which are: limitation to one acid precursor species, dependence on a local curve-fit to earlier thermodynamic ADP-calculations, absence of systematic transport effects associated with the local temperature gradient, and “silence” about the resulting liquid acid composition. Our present, more fundamental, approach overcomes each of these limitations and yet, will be seen to remain tractable from an engineering viewpoint. While we illustrate our methods for the case of a prototypical ternary (N=3) acid condensate (highly non-ideal liquid mixture of H2O + HNO3 + H2SO4) produced from a high temperature ideal gas mixture containing H2O(g) and much smaller concentrations of the aqueous acid precursors: NO2, SO3 (or HNO3(g) and H2SO4(g)), our methods can be formally extended to N=4,5,… if one has access to VLE data for each of the N(N−1)/2 participating binary systems (if the resulting N-component liquid mixture does not itself phase-separate). Our present results also properly reduce from the N-component case to the N−1 case, hence even to the singular case: N=1 (i.e., the DP- and MO-conditions for pure water in the absence of any acid precursor). Because some of the vapor species of interest (e.g., H2O, HNO3, and H2SO4) have molecular weights rather different from the mean molecular weight of the flue gases, Ludwig–Soret transport effects can become non-negligible (in the presence of the temperature gradients expected for high temperature combustion products) both Tw(ADP) and Tw(AMO) will often be seen to be “transport-shifted”, although, as discussed in Appendix A Thermal “fragility” of the mainstream polyatomic components: H, Appendix B Rational upper bound to the effective acid species concentration when the mainstream initially contained its molecular precursors, in many cases these effects are complicated by the thermal instability of the largest precursor molecules. Further extensions of likely future interest (e.g., effects of homogeneous chemistry within the thermal boundary layer where molecules like HNO3 and H2SO4 may have to be assembled from their lighter precursors; the effects of nucleation kinetic barriers and/or vapor phase non-ideality) are also identified and are the subject of our ongoing research.

We illustrate the importance of environment-dependent surface energy changes in predicting the micronization of active pharmaceutical ingredients (APIs) in gas antisolvent precipitation (GASP) processes. This size-reduction scheme exploits compressed CO2(g) as antisolvent (AS) at near-ambient temperatures. Ordinary API-loaded solvents (often sprays) are contacted with dense CO2, and during CO2 uptake in an evolving expanding liquid API + solvent + CO2 solution droplet, particle nucleation (N) sets in, continuing along with growth (G) and, ultimately, coagulation. A rational method [due to Nielsen and Sohnel (J. Cryst. Growth 1971, 11, 233) and Mersmann (J. Oyst. Growth 1990, 102, 841)] is used to estimate the changing embryonic solid/ternary solution interfacial energy, gamma. We demonstrate the dramatic yield and crystal size distribution (CSD) consequences of surface energy evolution (SEE) by carrying out N/G calculations for the surrogate organic API: phenanthrene dissolved in representative well-mixed micrometer-sized toluene droplets (sprayed into 298 K CO2 for p < 60 bar). To solve the population balance partial differential equation, we exploit the method of characteristics. Our results demonstrate that assuming constant surface energy, sometimes reasonable for API precipitation via the rapid expansion of supercritical-CO2 solvent (i.e.: relatively dilute rapid expansion of a supercritical solution conditions), fails for GASP-process modeling. When the crystal growth kinetics are sufficiently rapid, SEE also modifies performance via the Gibbs Kelvin reduction of small particle growth rates. Rational yet tractable methods to incorporate both systematic effects in future design/optimization/parameter estimation calculations are suggested.

Exploiting a molecular "collision-theory" viewpoint, we reformulate and correct for systematic effects of fluid-phase solute diffusion, reported growth-rate data for {001} naphthalene single crystal surfaces under supercritical CO2-conditions at low supersaturations, S. By considering dimensionless incorporation probabilities, epsilon(S, T, ...; {hkl}) for this prototypical organic crystal, we initiate the process of quantifying the environment-dependence of epsilon as a rational route to crystal growth rate predictions at molecular volume fractions, phi, ranging all the way from ideal vapors (phi << 1) to liquid-like densities (phi similar or equal to 0.64). Our rational "ansatz" for predicting growth species collision fluxes enables a two-stage data-reduction process. First we infer "apparent" incorporation probabilities, epsilon(app), ignoring fluid-phase solute diffusion effects. Second, we recover their intrinsic counterparts, using E-app and invoking rational transport estimates for the prevailing crystal size/flow conditions. Treating available data near 318 K at 77-91 bar (Tai, C. Y.; Cheng, C.-S. AIChE J. 1995, 41, 2227-2236) and 150-200 bar (Uchida et al. Cryst. Growth Des. 2004, 4, 937-942), we conclude that E decreases significantly with (CO2-) pressure-with important mechanistic and anti-solvent precipitation (ASP) process modeling implications.

The availability of acid dew-point correlations (for flue gases containing the precursors of sulfuric-, nitric-, hydrochloric acids, etc.) that directly relate T w , dp to the participating species partial pressures (e.g., Banchero and Verhoff, 1975 , Verhoff and Banchero, 1974 ) without the explicit need for liquid phase thermodynamic properties has led to their popularity for preliminary design estimates of onset surface temperatures for corrosive deposits. Despite the fact that these correlations cannot be used when either or both precursor partial pressures become too small, when they are invoked within their intended domains of validity, we show here that they can be conveniently used to not only quickly estimate acid dew-point temperatures in the presence of unavoidable gas phase precursor species Soret separation effects, but also to provide preliminary estimates of the surface temperatures, T w , AMO , associated with the local onset of acid mists in the vicinity of cooled surfaces. Our present simple theoretical/numerical methods are illustrated for the most familiar case of sulfuric acid deposits. While we indicate that increased accuracy and generality will require a more fundamental approach in which condensate thermodynamic non-ideality is explicitly introduced, we show here that prudent use of these earlier engineering correlations can lead to immediately useful preliminary estimates of both transport-shifted T w , dp - and T w , AMO - values .

We present a bivariate population balance-based formulation of the performance of well-mixed adiabatic combustors fed by ethanol (EtOH)-containing sprays of prescribed droplet size distribution (DSD) and composition. Our historically interesting example is the fuel-cooled V-2 chemical rocket-using 75 wt % EtOH + H(2)O solution, and oxidizer O(2)(L). Of special interest are the predicted combustion "intensity'' (GW/m(3)) and efficiency (EtOH fraction vaporized) at each ratio of combustor mean residence time to feed-droplet characteristic vaporization time. Our formulation exploits a quasi-steady, gas-diffusion-controlled individual droplet evaporation rate law, and the method-of-characteristics to solve the associated first-order population balance partial differential equation governing the joint distribution function n(m(1), m(2)) of the fuel spray exiting such a chamber, where m(1) - EtOH mass/droplet, and m(2) - H(2)O mass/droplet. Besides the combustor efficiency and intensity, this bivariate distribution function enables predictions of corresponding unconditional DSD, and the joint distribution function(diam., droplet temperature)-perhaps measurable. Our numerically exact formulation/results also provide valuable test cases for convenient approximate methods (bivariate moment and spectral/weighted residual) to predict these "correlated'' bivariate distribution functions in more complex situations. (C) 2011 American Institute of Chemical Engineers AIChE J, 57: 3534-3554, 2011

AIChE JournalVolume 57, Issue 11 p. 3244-3244 Book Review Combustion By I. Glassman and R. A. Yetter Daniel E Rosner, Corresponding Author Daniel E Rosner daniel.rosner@yale.edu Yale University, 319 Mason Laboratory, P.O. Box 208286, New Haven, CT 06520Yale University, 319 Mason Laboratory, P.O. Box 208286, New Haven, CT 06520Search for more papers by this author Daniel E Rosner, Corresponding Author Daniel E Rosner daniel.rosner@yale.edu Yale University, 319 Mason Laboratory, P.O. Box 208286, New Haven, CT 06520Yale University, 319 Mason Laboratory, P.O. Box 208286, New Haven, CT 06520Search for more papers by this author First published: 24 March 2011 https://doi.org/10.1002/aic.12633Citations: 1Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article.Citing Literature Volume57, Issue11November 2011Pages 3244-3244 RelatedInformation

A theory of aerosol coagulation rates resulting from continuum-regime Brownian coagulation in the presence of size-dependent particle thermophoresis is developed and explored here. We are motivated by a wide variety of applications in which particle Brownian coagulation occurs in a nonisothermal gas where differential thermophoretic drift contributes to, but does not dominate, the encounter frequency between suspended spherical particles (e.g., mist droplets) of different sizes. We employ a Smoluchowski-like population-balance to demonstrate the relative roles of Brownian diffusion and thermophoresis in shaping the short and long time (asymptotic or ``coagulation-aged'') mist-droplet size distribution (DSD) function. To carry out these combined-mechanism DSD-evolution calculations we developed a rational ``coupled'' coagulation rate constant (allowing for simultaneous Brownian diffusion and relative thermophoretic drift) rather than simply adding the relevant individual coagulation ``kernels.'' Dimensionless criteria are provided to facilitate precluding other coagulation mechanisms not considered here (such as simultaneous sedimentation or Marangoni-flow-induced mist-droplet phoresis) and potential complications not included in the present model [as finite-rate coalescence, initial departures from the continuum (Stokes drag-) limit, and even dense (nonideal) vapor effects].

P. Curie's principle applied to an isotropic medium of arbitrary EOS does not preclude coupling between homogeneous (chemical,...) rate processes and local fluid dilation rate. Yet, practical examples of this coupling have largely remained unexplored. Using recently studied supercritical "antisolvent" (SAS) examples for precipitating high-value particles (e.g., pharmaceuticals), we suggest that the characteristic dilation time t(V) of the swelling solvent can be small enough to noticeably reduce the operative coagulation rate "constant," beta. Moreover, we expect that this coupling can occur under conditions in which postnucleation Brownian coagulation must be accounted for in predicting the efficacy of such micron-sized powder production methods. Accordingly, a rational approximate theory for this rate constant "correction factor," beta/beta(0), is proposed here, emphasizing the applicable limit of continuum Brownian diffusion control. We also present a preliminary assessment of the particle size distribution (PSD) consequences of these "corrections," implying strategies to reduce both mean particle size and PSD spread. Possible generalizations are indicated. (C) 2010 American Institute of Chemical Engineers AIChE J, 57: 307-318, 2011