Sheath vaporization of a monodisperse fuel-spray jet

The group vaporization of a monodisperse fuel-spray jet discharging into a hot coflowing gaseous stream is investigated for steady flow by numerical and asymptotic methods with a two-continua formulation used for the description of the gas and liquid phases. The jet is assumed to be slender and laminar, as occurs when the Reynolds number is moderately large, so that the boundary-layer form of the conservation equations can be employed in the analysis. Two dimensionless parameters are found to control the flow structure, namely the spray dilution parameter 1, defined as the mass of liquid fuel per unit mass of gas in the spray stream, and the group vaporization parameter e, defined as the ratio of the characteristic time of spray evolution due to droplet vaporization to the characteristic diffusion time across the jet. It is observed that, for the small values of e often encountered in applications, vaporization occurs only in a thin layer separating the spray from the outer droplet-free stream. This regime of sheath vaporization, which is controlled by heat conduction, is amenable to a simplified asymptotic description, independent of ε,in which the location of the vaporization layer is determined numerically as a free boundary in a parabolic problem involving matching of the separate solutions in the external streams, with appropriate jump conditions obtained from analysis of the quasi-steady vaporization front. Separate consideration of dilute and dense sprays, corresponding, respectively, to the asymptotic limits λ<<1 and λ>>1, enables simplified descriptions to be obtained for the different flow variables, including explicit analytic expressions for the spray penetration distance.

Statistical distributions obtained from the compression of monodisperse, soft and frictionless particles

The cyclic compression of several granular systems has been simulated with a molecular dynamics code. All the samples consisted of bidimensional, soft, frictionless and equal-sized particles that were initially arranged according to a squared lattice and were compressed by randomly generated irregular walls. The compression protocols can be described by some control variables (volume or external force acting on the walls) and by some dimensionless factors, that relate stiffness, density, diameter, damping ratio and water surface tension to the external forces, displacements and periods. Each protocol, that is associated to a dynamic process, results in an arrangement with its own macroscopic features: volume (or packing ratio), coordination number, and stress; and the differences between packings can be highly significant. The statistical distribution of the force-moment state of the particles (i.e. the equivalent average stress multiplied by the volume) is analyzed. In spite of the lack of a theoretical framework based on statistical mechanics specific for these protocols, it is shown how the obtained distributions of mean and relative deviatoric force-moment are. Then it is discussed on the nature of these distributions and on their relation to specific protocols.

Dynamics of thermal ignition of spray flames in mixing layers

Conditions are identified under which analyses of laminar mixing layers can shed light on aspects of turbulent spray combustion. With this in mind, laminar spray-combustion models are formulated for both non-premixed and partially premixed systems. The laminar mixing layer separating a hot-air stream from a monodisperse spray carried by either an inert gas or air is investigated numerically and analytically in an effort to increase understanding of the ignition process leading to stabilization of high-speed spray combustion. The problem is formulated in an Eulerian framework, with the conservation equations written in the boundary-layer approximation and with a one-step Arrhenius model adopted for the chemistry description. The numerical integrations unveil two different types of ignition behaviour depending on the fuel availability in the reaction kernel, which in turn depends on the rates of droplet vaporization and fuel-vapour diffusion. When sufficient fuel is available near the hot boundary, as occurs when the thermochemical properties of heptane are employed for the fuel in the integrations, combustion is established through a precipitous temperature increase at a well-defined thermal-runaway location, a phenomenon that is amenable to a theoretical analysis based on activation-energy asymptotics, presented here, following earlier ideas developed in describing unsteady gaseous ignition in mixing layers. By way of contrast, when the amount of fuel vapour reaching the hot boundary is small, as is observed in the computations employing the thermochemical properties of methanol, the incipient chemical reaction gives rise to a slowly developing lean deflagration that consumes the available fuel as it propagates across the mixing layer towards the spray. The flame structure that develops downstream from the ignition point depends on the fuel considered and also on the spray carrier gas, with fuel sprays carried by air displaying either a lean deflagration bounding a region of distributed reaction or a distinct double-flame structure with a rich premixed flame on the spray side and a diffusion flame on the air side. Results are calculated for the distributions of mixture fraction and scalar dissipation rate across the mixing layer that reveal complexities that serve to identify differences between spray-flamelet and gaseous-flamelet problems.

Source terms for calculations of vaporizing and burning fuel sprays with non-unity Lewis numbers in gases with temperature-dependent thermal conductivities

Liquid-fueled burners are used in a number of propulsion devices ranging from internal combustion engines to gas turbines. The structure of spray flames is quite complex and involves a wide range of time and spatial scales in both premixed and non-premixed modes (Williams 1965; Luo et al. 2011). A number of spray-combustion regimes can be observed experimentally in canonical scenarios of practical relevance such as counterflow diffusion flames (Li 1997), as sketched in figure 1, and for which different microscalemodelling strategies are needed. In this study, source terms for the conservation equations are calculated for heating, vaporizing and burning sprays in the single-droplet combustion regime. The present analysis provides extended formulation for source terms, which include non-unity Lewis numbers and variable thermal conductivities.

Flamelet structures in spray ignition

In typical liquid-fueled burners the fuel is injected as a high-velocity liquid jet that breaks up to form the spray. The initial heating and vaporization of the liquid fuel rely on the relatively large temperatures of the sourrounding gas, which may include hot combustion products and preheated air. The heat exchange between the liquid and the gas phases is enhanced by droplet dispersion arising from the turbulent motion. Chemical reaction takes place once molecular mixing between the fuel vapor and the oxidizer has occurred in mixing layers separating the spray flow from the hot air stream. Since in most applications the injection velocities are much larger than the premixed-flame propagation velocity, combustion stabilization relies on autoignition of the fuel-oxygen mixture, with the combustion stand-off distance being controlled by the interaction of turbulent transport, droplet heating and vaporization, and gas-phase chemical reactions. In this study, conditions are identified under which analyses of laminar flamelets canshed light on aspects of turbulent spray ignition. This study extends earlier fundamental work by Liñan & Crespo (1976) on ignition in gaseous mixing layers to ignition of sprays. Studies of laminar mixing layers have been found to be instrumental in developing un-derstanding of turbulent combustion (Peters 2000), including the ignition of turbulent gaseous diffusion flames (Mastorakos 2009). For the spray problem at hand, the configuration selected, shown in Figure 1, involves a coflow mixing layer formed between a stream of hot air moving at velocity UA and a monodisperse spray moving at velocity USUA. The boundary-layer approximation will be used below to describe the resulting sl ender flow, which exhibits different igniting behaviors depending on the characteristics of t he fuel. In this approximation, consideration of the case U A = U S enables laminar ignition distances to be related to ignition times of unstrained spray flamelets, thereby pro viding quantitative information of direct applicability in regions of low scala r dissipation-rate in turbulent reactive flows (see the discussion in pp. 181–186 of Peters (2000)) . This report is organized as follows. Effects of droplet dispersion dynamics on ignition of sprays in turbulent mixing layers are discussed in Section 2. The formulation f or ignition in laminar mixing layers is outlined in Sections 3 and 4. The results are presented in Section 5. In Section 6, the mixture-fraction field and associated scalar dissipat ion rates for spray ignition are discussed. Finally, some brief conclusions are drawn in Section 7.

In-season calcium-spray formulations improve calcium balance and fruit quality traits of peach.

Experiments to evaluate the effect of in-season calcium (Ca) sprays on late-season peach (Prunus persica L. Batsch cv. Calrico) were carried out for a 2-year period. Calcium formulations (0.5% and 1.0% in 2008 and only 0.5% tested in 2009) supplied either as CaCl2 or Ca propionate in combination with two or three adjuvants (0.05% of the nonionic surfactants Tween 20 and Break Thru, and 0.5% carboxymethylcellulose, CMC) were sprayed four to five times over the growing season. Peach mesocarp and endocarp Ca concentrations were determined on a 15-day basis from the beginning of May until the end of June. Further tissue analyses were performed at harvest. A decreasing trend in fruit Ca concentrations over the growing season was always observed regardless of the Ca treatments. Both in 2008 and 2009, significant tissue Ca increments associated with the application of Ca-containing sprays in combination with adjuvants were only observed in June, which may be coincident with the period of pit hardening. In 2008, both at harvest and after cold storage, the total soluble-solids concentration (° Brix) of fruits supplied with Ca propionate (0.5% and 1.0% Ca) was always lower as compared to the rest of treatments. The application of multiple Ca-containing sprays increased firmness at harvest and after cold storage, especially when CaCl2 was the active ingredient used. Supplying the adjuvants Tween 20 and CMC increased fruit acidity both at harvest and after cold storage. Evaluation of the development of physiological disorders after cold storage (2 weeks at 0°C) indicated a lower susceptibility of Ca-treated fruits to internal browning. Fruits treated with multiple CaCl2-, CMC-, and Break Thru®-containing sprays during the growing season were significantly less prone to the development of chilling injuries as compared to untreated peaches.

Levels, sources and seasonality of coarse particles (PM10-PM2.5) in three European capitals e implications for particulate pollution control

Coarse particles of aerodynamic diameter between 2.5 and 10 mm (PMc) are produced by a range of natural (windblown dust and sea sprays) and anthropogenic processes (non-exhaust vehicle emissions, industrial, agriculture, construction and quarrying activities). Although current ambient air quality regulations focus on PM2.5 and PM10, coarse particles are of interest from a public health point of view as they have been associated with certain mortality and morbidity outcomes. In this paper, an analysis of coarse particle levels in three European capitals (London, Madrid and Athens) is presented and discussed. For all three cities we analysed data from both traffic and urban background monitoring sites. The results showed that the levels of coarse particles present significant seasonal, weekly and daily variability. Their wind driven and non-wind driven resuspension as well as their roadside increment due to traffic were estimated. Both the local meteorological conditions and the air mass history indicating long-range atmospheric transport of particles of natural origin are significant parameters that influence the levels of coarse particles in the three cities especially during episodic events.

Resistance to malathion and lambda-cyhalothrin in Ceratitis capitata (Wiedemann) (Diptera: Tephritidae)

La mosca mediterránea de la fruta, Ceratitis capitata (Wiedemann, 1824) (Diptera: Tephritidae), es una de las plagas de mayor incidencia económica en cítricos y otros frutales a nivel mundial. En España las medidas de control de esta plaga en cítricos, desde mediados de los 90 hasta 2009, se basaron principalmente en el monitoreo de las poblaciones y en la aplicación de tratamientos aéreos y terrestres con malatión cebo. Sin embargo, desde la retirada en la Unión Europea en 2009 de los productos fitosanitarios que contienen malatión, los insecticidas más utilizados para el control de esta plaga han sido lambda-cihalotrina y spinosad. En 2004-2005 se detectaron poblaciones españolas de C. capitata resistentes a malatión. Esta resistencia se ha asociado a una mutación (G328A) en la acetilcolinesterasa (AChE), a una duplicación del gen de la AChE (Ccace2) (una de las copias lleva la mutación G328A) y a resistencia metabólica mediada por esterasas (posiblemente aliesterasas). Sin embargo, cuando se secuenció la aliesterasa CcE7 en individuos de una línea resistente a malatión, no se encontró ninguna de las mutaciones (G137D y/o W251L/S/G) asociadas a resistencia en otras especies, si bien se encontraron otras mutaciones al compararlos con individuos de una línea susceptible. Asimismo, mediante la selección en laboratorio de una línea resistente a malatión (W-4Km) con lambda-cihalotrina, se ha podido obtener una línea resistente a lambda-cihalotrina (W-1K). Finalmente, se ha demostrado la capacidad de esta especie para desarrollar resistencia a spinosad mediante selección en laboratorio. Los múltiples mecanismos de resistencia identificados evidencian el potencial de esta especie para desarrollar resistencia a insecticidas con diferentes modos de acción. Los objetivos de esta tesis doctoral son: 1) evaluar la susceptibilidad de poblaciones españolas de campo de C. capitata a lambda-cihalotrina y dilucidar los mecanismos de resistencia en la línea W-1Kλ; 2) comparar la herencia, el coste biológico y la estabilidad de la resistencia a malatión mediada por la mutación G328A y la duplicación del gen Ccace2 (una de las copias lleva la mutación G328A); y 3) investigar el papel de las mutaciones identificadas en la aliesterasa CcαE7 en la resistencia a malatión. Estos estudios son de utilidad para el desarrollo de estrategias de manejo de la resistencia que puedan prevenir o retrasar la aparición de resistencia y aumentar la sostenibilidad de los insecticidas disponibles para el control de esta plaga. Nuestros resultados indican que las poblaciones españolas de C. capitata analizadas han desarrollado resistencia a lambda-cihalotrina. Los valores de CL50 estimados para las poblaciones recogidas en la Comunidad Valenciana, Cataluña y Andalucía oscilaron entre 129 ppm y 287 ppm, igualando o sobrepasando la concentración recomendada para los tratamientos de campo (125 ppm). Estos resultados contrastan con los obtenidos con tres poblaciones de campo recogidas en Túnez, cuya susceptibilidad fue similar a la de la línea control (C). La línea resistente a lambda-cihalotrina W-1K se continuó seleccionando en el laboratorio alcanzándose unos niveles de resistencia de 205 veces con respecto a la línea C, siendo su CL50 (4224 ppm) más de 30 veces superior a la concentración recomendada para los tratamientos de campo. Esta línea resistente mostró altos niveles de resistencia cruzada a deltametrina (150 veces) y a etofenprox (240 veces), lo que sugiere que el desarrollo de resistencia a lambda-cihalotrina podría comprometer la eficacia de otros piretroides para el control de esta plaga. Hemos demostrado que la resistencia de la línea W-1K a lambda-cihalotrina fue casi completamente suprimida por el sinergista PBO, lo que indica que las enzimas P450 desempeñan un papel muy importante en la resistencia a este insecticida. Sin embargo, tanto las moscas de la línea susceptible C como las de la línea resistente W-1K perdieron inmediatamente la capacidad de caminar (efecto “knock-down”) al ser tratadas tópicamente con lambda-cihalotrina, lo que sugiere que la resistencia no está mediada por alteraciones en la molécula diana (resistencia tipo “kdr”). La resistencia metabólica mediada por P450 fue analizada comparando la expresión de 53 genes CYP (codifican enzimas P450) de las familias CYP4, CYP6, CYP9 y CYP12 en adultos de la línea resistente W-1K y de la línea susceptible C. Nuestros resultados muestran que el gen CYP6A51 (número de acceso GenBank XM_004534804) fue sobreexpresado (13-18 veces) en la línea W-1K. Por otra parte, la expresión del gen CYP6A51 fue inducida tanto en adultos de la línea W-1K como de la línea C al ser tratados con lambda-cihalotrina. Sin embargo, no se obtuvieron diferencias significativas entre la línea susceptible C y la línea resistente W-1K al comparar la cantidad de P450 y la actividad NADPH-citocromo c reductasa presente en fracciones microsomales obtenidas a partir de abdómenes. Asimismo, no hemos podido correlacionar el metabolismo de deltametrina, estimado in vitro mediante la incubación de este insecticida con fracciones microsomales, con el nivel de resistencia a este piretroide observado en los bioensayos con la línea W-1K. Por otro lado, no se encontró ninguna alteración en la región promotora 5'UTR del gen CYP6A51 (-500 pb desde el inicio de la traducción) que pudiera explicar su sobreexpresión en la línea W-1K. Los datos obtenidos sugieren que la resistencia a lambda-cihalotrina en la línea W-1K está mediada por P450 y que la sobreexpresión de CYP6A51 puede desempeñar un papel importante, aunque se necesitan más evidencias para establecer una asociación directa de la resistencia con este gen. Hemos estudiado la herencia, el coste biológico y la estabilidad de la resistencia a malatión mediada por la mutación G328A y la duplicación del gen Ccace2 (una de las copias lleva la mutación G328A). La línea susceptible C, donde no se encuentra la mutación G328A (genotipo S/S), se cruzó con dos isolíneas establecidas para representar genotipos únicos correspondientes a los dos mecanismos de resistencia asociados a la molécula diana: 1) la isolínea 267Y (genotipo R/R) establecida a partir de una pareja que portaba la mutación G328A en homocigosis; 2) la isolínea 306TY (genotipo RS/RS) establecida a partir de una pareja que portaba en homocigosis la duplicación del gen Ccace2. No se realizaron cruces recíprocos, ya que mediante experimentos de hibridación in situ en cromosomas politénicos se pudo comprobar que el locus de la AChE y la duplicación (probablemente en tándem) se localizan en el cromosoma autosómico 2L. La susceptibilidad al malatión de los parentales resistentes (R/R o RS/RS) y susceptibles (S/S), los cruces F1 (S/R, S/RS y R/RS) y los retrocruzamientos indican que la resistencia a malatión es semi-dominante en ambos casos. Sin embargo, nuestros resultados no fueron concluyentes con respecto a la naturaleza monogénica de la resistencia a malatión en estas isolíneas. Por lo tanto, no podemos descartar que otros genes que contribuyan a la resistencia, además de la mutación G328A (isolínea 267Y) y de la duplicación del gen Ccace2 (isolínea 306TY), puedan haber sido seleccionados durante el proceso de selección de 267Y y 306TY. Varios parámetros biológicos fueron evaluados para determinar si estos dos mecanismos de resistencia a malatión suponen un coste biológico para los genotipos resistentes. Individuos con genotipo R/R mostraron un retraso en el tiempo de desarrollo de huevo a pupa, un peso de pupa reducido y una menor longevidad de los adultos, en comparación con los individuos con genotipo S/S. Sin embargo, el peso de pupa de los individuos con genotipo RS/RS fue similar al de los individuos S/S, y su desarrollo de huevo a pupa intermedio entre S/S y R/R. Estas diferencias en el coste biológico pueden estar relacionadas con la reducción de la eficiencia catalítica de la AChE mutada en los individuos R/R, y al efecto compensatorio que la copia no mutada del gen tiene en los individuos RS/RS que portan la duplicación. La estabilidad de la resistencia a malatión mediada por la mutación G328A y la duplicación se analizó mediante el seguimiento de los caracteres de resistencia en la progenie de retrocruzamientos S/R x R/R y S/RS x RS/RS a lo largo de varias generaciones en ausencia de presión de selección con insecticidas. Nuestros resultados muestran que la frecuencia del alelo que porta la mutación G328A disminuyó desde 67,5% en la primera generación del retrocruzamiento S/R x R/R (75% esperado, asumiendo segregación mendeliana y que sólo hay dos alelos: uno mutado y otro no mutado) a 12% después de 10 generaciones. Por el contrario, la frecuencia de la duplicación sólo disminuyó desde 75% en en la primera generación del retrocruzamiento S/RS x RS/RS (75% esperado, asumiendo segregación Mendeliana y que la duplicación segrega como un único alelo) a 50% en el mismo período, lo que indica que la duplicación es más estable que la mutación. Asimismo, se analizó la presencia de la mutación y de la duplicación en poblaciones de campo recogidas en seis localidades en 2004-2007, cuando todavía se usaba el malatión, y se comparó con poblaciones recogidas en los mismos campos en 2010, un año después de la prohibición del malatión en la Unión Europea. La frecuencia media del genotipo susceptible (S/S) aumentó del 55,9% en el período 2004-2007 a 70,8% en 2010, mientras que la frecuencia de los genotipos portadores de la mutación en homocigosis o heterocigosis (R/R y S/R) disminuyó del 30,4 al 9,2%, los que llevan la duplicación en homocigosis o heterocigosis (RS/RS y S/RS) aumentaron levemente desde 12,8 hasta 13,3%, y los que llevan a la vez la mutación y la duplicación (R/RS) también aumentaron del 1 al 6,7%. Estos resultados son consistentes con que la duplicación del gen Ccace2 (con una copia con la mutación G328A y la otra copia no mutada) es más ventajosa que la mutación G328A por si sola, ya que la duplicación mantiene los niveles de resistencia a la vez que limita el coste biológico. Para investigar la asociación entre la resistencia a malatión y las mutaciones encontradas previamente en CcE7, hemos generado isolíneas con mutaciones específicas seleccionadas por su ubicación próxima a la entrada al centro activo de la enzima. La isolínea Sm2 (procedente de una hembra heterocigota para la mutación V96L y un macho homocigoto para el alelo no mutado) mantuvo altos niveles de resistencia a malatión, incluso después de 30 generaciones sin presión de selección. Por el contrario, la isolínea 267Y (compuesta por individuos homocigotos para la mutación L267Y) y la línea 306TY (compuesta por individuos homocigotos para la doble mutación R306T-N307Y) mostraron una reducción significativa en los niveles de resistencia. También hemos encontrado que la resistencia a malatión de la línea Sm2 fue parcialmente revertida por DEF y TPP, y que Sm2 mostró una reducción significativa en la actividad MTB, como se ha descrito en otras especies que muestran resistencia específica a malatión mediada por aliesterases. Además, fue posible asociar la presencia de la mutación V96L en individuos de la línea Sm2 con supervivencia a una concentración discriminante de malatión (5,000 ppm) y con una baja actividad MTB. Estos resultados sugieren una posible relación entre la mutación V96L en la aliesterasa CcE7 y la resistencia a malatión, aunque todavía no se puede concluir que la resistencia es causada por esta mutación, siendo necesarios más estudios para comprobar su contribución a la resistencia. En conclusión, se ha encontrado por primera vez resistencia a lambda-cihalotrina en poblaciones de campo de C. capitata, y nuestros resultados indican que las P450 son el principal mecanismo de resistencia en la línea W-1K. Esta situación se suma al caso previamente descrito de resistencia en campo a malatión asociada a la mutación G328A, a la duplicación del gen Ccace2 (una de las copias lleva la mutación G328A) y a resistencia metabólica mediada por esterasas. Nuestros resultados también indican que la alteración de la molécula diana AChE parece ser responsable de un cierto nivel de resistencia a malatión en C. capitata, que puede ser estimada como aproximadamente 25-40 veces para la mutación G328A y 40-60 veces para la duplicación; mientras que la resistencia mediada por esterasas y que ha sido asociada en este estudio con la mutación V96L en CcE7 puede conferir un efecto multiplicativo (por un factor de 5 a 10) aumentando la resistencia a malatión a 200-400 veces. Por otra parte, hemos demostrado que los insectos resistentes que llevan la duplicación tienen un coste biológico menor y muestran una estabilidad mayor que aquellos con la mutación G328A en ausencia de presión de selección con insecticidas. Esto representa un escenario en el que los genotipos con la duplicación permanecerán en el campo en frecuencias bajas a moderadas, pero podrían ser seleccionados rápidamente si se utilizan malatión u otros insecticidas que muestren resistencia cruzada. Estos resultados tienen importantes implicaciones para los programas de manejo de la resistencia, ya que el repertorio de insecticidas eficaces para el control de C. capitata es cada vez más limitado. Además, la coexistencia de múltiples mecanismos de resistencia en poblaciones de campo ofrece el potencial para desarrollar resistencia frente a otros insecticidas disponibles para el control de esta plaga. Estrategias para de manejo de la resistencia basadas en la alternancia de insecticidas con diferentes modos de acción, y su combinación con otros métodos de control, deben ser implementadas para evitar el desarrollo de resistencia en campo. ABSTRACT The Mediterranean fruit fly (Medfly), Ceratitis capitata (Wiedemann, 1824) (Diptera: Tephritidae), is one of the most economically damaging pests of citrus and other fruit crops worldwide. Control measures in citrus crops in Spain from the mid 90's to 2009 were mainly based on field monitoring of population levels and aerial and ground treatments with malathion bait sprays. However, since the withdrawal of phytosanitary products containing malathion in the European Union in 2009, lambda-cyhalothrin and spinosad have become the most widely used insecticides for the control of this pest. Resistance to malathion was found in Spanish field populations of C. capitata in 2004-2005. This resistance has been associated with a mutation G328A in the acetylcholinesterase (AChE), a duplication of the AChE gene (Ccace2) (one of the copies bearing the mutation G328A), and metabolic resistance mediated by esterases (probably aliesterases). However, when the gene of the aliesterase CcE7 was sequenced in individuals from a malathion resistant strain of C. capitata, none of the known G137D and/or W251L/S/G mutations associated to resistance in other species were found, though other mutations were detected when compared with individuals from a susceptible strain. Noteworthy, a lambda-cyhalothrin resistant strain (W-1K) was obtained by selecting a field-derived malathion resistant strain (W-4Km) with lambda-cyhalothrin. Moreover, it has also been demonstrated the capacity of this species to develop resistance to spinosad by laboratory selection. The multiple resistance mechanisms identified highlight the potential of this species to develop resistance to insecticides with different modes of action. The objectives of this PhD Thesis are: 1) to assess the susceptibility of Spanish field populations of C. capitata to lambda-cyhalothrin and to elucidate the resistance mechanisms in the W-1Kλ strain; 2) to compare the inheritance, fitness cost and stability of the malathion resistance mediated by the G328A mutation and the duplication of the Ccace2 gene (with one of the copies bearing the mutation G328A); and 3) to investigate the role of the aliesterase CcαE7 mutations in malathion resistance. All these studies will be of use for devising proactive resistance management strategies that could prevent or delay resistance development and would increase the sustainability of the insecticides available for Medfly control. Our results indicate that Spanish field populations of C. capitata have developed resistance to lambda-cyhalothrin. The LC50 values estimated for populations collected at Comunidad Valenciana, Cataluña and Andalucía ranged from 129 ppm to 287 ppm, equaling or overpassing the recommended concentration for field treatments (125 ppm). These results contrast with those obtained with three different Tunisian field populations, whose susceptibility was similar to that of the control (C) strain. The lambda-cyhalothrin resistant W-1K strain has been further selected to achieve a 205-fold resistance compared to the C strain, being its LC50 (4,224 ppm) more than 30 times higher than the recommended concentration for field applications. This resistant strain showed high levels of cross-resistance to deltamethrin (150-fold) and etofenprox (240-fold), suggesting that the development of resistance to lambda-cyhalothrin may compromise the effectiveness of other pyrethroids for the control of this species. We have shown that the resistance of the W-1K strain to lambda-cyhalothrin was almost completely suppressed by the synergist PBO, indicating that P450 enzymes play a very important role in resistance to this insecticide. However, both susceptible C and resistant W-1K flies were knocked down after topical treatment with lambda-cyhalothrin, suggesting that kdr resistance mediated by alterations of the target site is not playing a major role. Metabolic resistance mediated by P450 was further analyzed by comparing the expression of 53 genes of the families CYP4, CYP6, CYP9 and CYP12 in adults flies from the resistant W-1K and the susceptible C strains. We found that the gene CYP6A51 (GenBank accession number XM_004534804) was overexpressed (13-18-fold) in the W-1K strain. Moreover, the expression of the CYP6A51 gene was induced when adults of the W-1K and C strains were treated with lambda-cyhalothrin. However, no significant differences were obtained between susceptible C and resistant W-1K strains for the quantity of P450 and for the activity of NADPH- cytochrome c reductase measured in microsomal fractions obtained from abdomens. Moreover, we failed to correlate the metabolism of deltamethrin, analyzed in vitro by incubating this insecticide with microsomal fractions, with the resistance level against this pyrethroid observed in bioassays with W-1K. The sequencing of the 5´UTR region of the CYP6A51 gene failed in finding an alteration in the promoter region (-500 bp from translation start site) that could explain overexpression in the W-1K strain. All data obtained suggest that resistance to lambda-cyhalothrin in the W- 1K strain is mediated by P450 and that overexpression of CYP6A51 may play a major role, although further evidences are needed to establish a direct association of resistance with this gene. We have studied the inheritance, fitness cost and stability of the malathion resistance mediated by the G328A mutation and the duplication of the Ccace2 gene (with one of the copies bearing the mutation G328A). The malathion-susceptible C strain where the G328A mutation is not found (S/S genotype) was crossed with two isolines established to represent unique genotypes corresponding to the two target-site resistance mechanisms: 1) the 267Y isoline (genotype R/R) was established from a couple bearing the mutation G328A in homozygosis; and 2) the 306TY isoline (genotype RS/RS) was established from a couple being homozygous for the duplication of the Ccace2 gene. Reciprocal crosses have not been performed, since in situ hybridization on polythene chromosomes showed that the AChE locus and the duplication (most probably in tandem) are placed at the autosomal chromosome 2L. Mortality responses to malathion of resistant isolines (R/R or RS/RS) and susceptible (S/S) genotypes, F1 crosses (S/R, S/RS, and R/RS), and the back-crosses indicated that resistance to malathion is inherited as a semi-dominant trait in both cases. However, our results were not conclusive about the monogenic nature of the resistance to malathion in these isolines. Thus, we can not discard that other genes contributing to resistance, in addition to the mutation G328A (isoline 267Y) and the duplication of the Ccace2 gene (isoline 306TY), may have been selected during the selection process of 267Y and 306TY. Several biological parameters were evaluated to determine if these two malathion resistance mechanisms impose a fitness cost for resistant genotypes. Individuals with genotype R/R have a reduced fitness in terms of developmental time from egg to pupa, pupal weight and adult longevity, when compared to susceptible individuals (genotype S/S). Interestingly, the fitness cost was substantially diminished in individuals with genotype RS/RS. These differences in fitness may be related to the reduction of the catalytic efficiency of mutated AChE in individuals R/R, and the compensatory effect that the non-mutated copy of the gene has on individuals RS/RS bearing the duplication. The stability of malathion reistance associated with the mutation G328A or the duplication was analyzed by following these resistant traits in the progeny of the back-crosses S/RS x RS/RS and S/R x R/R over consecutive generations in the absence of insecticide selection pressure. Our results show that the frequency of the allele bearing the mutation G328A decreased from 67.5% at the first generation of the back-cross S/R x R/R (75% expected, assuming Mendelian segregation and that there are only two alleles: one mutated and the other non-mutated) to 12% after 10 generations. By contrast, the frequency of the duplication only declined from 75% at the first generation of the back-cross S/RS x RS/RS (75% expected, assuming Mendelian segregation and that the duplication segregates as an unique allele) to 50% in the same period, indicating that the duplication is more stable than the mutation. The presence of the mutation and the duplication was analyzed in field populations collected in six localities in 2004-2007, when malathion was still used, and compared to populations collected in the same fields in 2010, one year after the prohibition of malathion in the European Union. The average frequency of the susceptible genotype (S/S) increased from 55.9% in the period 2004-2007 to 70.8% in 2010, whereas the frequency of those genotypes carrying the mutation in homozygosis or heterozygosis (R/R and S/R) declined from 30.4 to 9.2%, those carrying the duplication in homozygosis or heterozygosis (RS/RS and S/RS) increased slightly from 12.8 to 13.3%, and those carrying both the mutation and the duplication (R/RS) also increased from 1 to 6.7%. These results are consistent with the duplication of the Ccace2 gene (with one of the copies bearing the mutation G328A and the other copy non-mutated) being more advantageous than the G328A mutation alone by maintaining resistance while restoring part of the fitness. In order to investigate the association of malathion resistance with mutations previously found in the aliesterase CcE7, we have generated isolines bearing specific mutations selected by their putative location near the upper part of the active site gorge of the enzyme. The isoline Sm2 (originating from a female heterozygous for the mutation V96L and a male homozygous for the non-mutated allele) kept high levels of resistance to malathion, even after 30 generations without selection pressure. On the contrary, the isoline 267Y (composed by individuals homozygous for the mutation L267Y) and the strain 306TY (composed by homozygous for the double mutation R306T-N307Y) showed a significant reduction in the levels of resistance. We have found also that resistance to malathion in the Sm2 isoline was partially reverted by DEF and TPP, and that Sm2 showed a significant reduction in MTB activity, as reported for other species showing malathion-specific resistance mediated by aliesterases. Besides, it was possible to associate the presence of the mutation V96L in individuals from the Sm2 isoline with both survival to a discriminating concentration of malathion (5,000 ppm) and low MTB activity. Our results point out to a possible connection betwen the mutation V96L in the aliesterase CcE7 and resistance to malathion, though we can not yet conclude that the resistance is caused by the mutation, being needed further work to understand its contribution to resistance. In conclusion, resistance to lambda-cyhalothrin has been found for the first time in field populations of C. capitata, and metabolic resistance mediated by P450 appears to be the main resistance mechanism in the resistant strain W-1K. These findings add to the previously reported case of field resistance to malathion, associated to the G328A mutation and the duplication of the Ccace2 gene (with one of the copies bearing the mutation G328A) and to metabolic resistance mediated by esterases. Our results also indicate that altered target site AChE appears to be responsible for a certain level of resistance to malathion in C. capitata, that can be estimated as about 25-40-fold for the mutation G328A and 40-60-fold for the duplication; whereas metabolic resistance mediated by esterases and associated in this study with the mutation V96L in CcE7 may confer a multiplicative effect (by a factor of 5 to10) increasing malathion resistance to 200-400-fold. Moreover, we have shown that resistant insects carrying the duplication have better fitness and exhibit a higher stability than those with the mutation G328A in the absence of insecticide pressure. This represents a scenario where genotypes with the duplication will remain in the field at low to moderate frequencies, but could be rapidly selected if malathion or other insecticides showing cross-resistance are used. These findings have important implications for resistance management programs, as the repertoire of effective insecticides for C. capitata control is becoming very limited. Besides, multiple resistance mechanisms coexisting in field populations provide the potential to develop resistance to other available insecticides for the control of this pest. Appropriate resistance management strategies based on the alternation of insecticides with different modes of action, and their combination with other control methods, must then be implemented to avoid the evolution of resistance in the field.

From plant surface to plant metabolism: the uncertain fate of foliar-applied nutrients

The application of agrochemical sprays to the aerial parts of crop plants is an important agricultural practice world-wide. While variable effectiveness is often seen in response to foliar treatments, there is abundant evidence showing the beneficial effect of foliar fertilizers in terms of improving the metabolism, quality, and yields of crops. This mini-review is focused on the major bottlenecks associated with the uptake and translocation of foliar-applied nutrient solutions. A better understanding of the complex scenario surrounding the ultimate delivery of foliar-applied nutrients to sink cells and organs is essential for improving the effectiveness and performance of foliar fertilizers.

Análisis y simulación numérica de problemas electrohidrodinámicos relacionados con el electrospray

La presente tesis es un estudio analítico y numérico del electrospray. En la configuración más sencilla, un caudal constante del líquido a atomizar, que debe tener una cierta conductividad eléctrica, se inyecta en un medio dieléctrico (un gas u otro líquido inmiscible con el primero) a través de un tubo capilar metálico. Entre este tubo y un electrodo lejano se aplica un voltaje continuo que origina un campo eléctrico en el líquido conductor y en el espacio que lo rodea. El campo eléctrico induce una corriente eléctrica en el líquido, que acumula carga en su superficie, y da lugar a un esfuerzo eléctrico sobre la superficie, que tiende a alargarla en la dirección del campo eléctrico. El líquido forma un menisco en el extremo del tubo capilar cuando el campo eléctrico es suficientemente intenso y el caudal suficientemente pequeño. Las variaciones de presión y los esfuerzos viscosos asociados al movimiento del líquido son despreciables en la mayor parte de este menisco, siendo dominantes los esfuerzos eléctrico y de tensión superficial que actúan sobre la superficie del líquido. En el modo de funcionamiento llamado de conochorro, el balance de estos esfuerzos hace que el menisco adopte una forma cónica (el cono de Taylor) en una región intermedia entre el extremo del tubo y la punta del menisco. La velocidad del líquido aumenta al acercarse al vértice del cono, lo cual propicia que las variaciones de la presión en el líquido generadas por la inercia o por la viscosidad entren en juego, desequilibrando el balance de esfuerzos mencionado antes. Como consecuencia, del vértice del cono sale un delgado chorro de líquido, que transporta la carga eléctrica que se acumula en la superficie. La acción del campo eléctrico tangente a la superficie sobre esta carga origina una tracción eléctrica que tiende a alargar el chorro. Esta tracción no es relevante en el menisco, donde el campo eléctrico tangente a la superficie es muy pequeño, pero se hace importante en el chorro, donde es la causa del movimiento del líquido. Lejos del cono, el chorro puede o bien desarrollar una inestabilidad asimétrica que lo transforma en una espiral (whipping) o bien romperse en un spray de gotas prácticamente monodispersas cargadas eléctricamente. La corriente eléctrica transportada por el líquido es la suma de la corriente de conducción en el interior del líquido y la corriente debida a la convección de la carga acumulada en su superficie. La primera domina en el menisco y la segunda en el chorro lejano, mientras que las dos son comparables en una región intermedia de transferencia de corriente situada al comienzo del chorro aunque aguas abajo de la región de transición cono-chorro, en la que el menisco deja de ser un cono de Taylor. Para un campo exterior dado, la acumulación de carga eléctrica en la superficie del líquido reduce el campo eléctrico en el interior del mismo, que llega a anularse cuando la carga alcanza un estado final de equilibrio. El tiempo característico de este proceso es el tiempo de relajación dieléctrica, que es una propiedad del líquido. Cuando el tiempo de residencia del líquido en la región de transición cono-chorro (o en otra región del campo fluido) es grande frente al tiempo de relajación dieléctrica, la carga superficial sigue una sucesión de estados de equilibrio y apantalla al líquido del campo exterior. Cuando esta condición deja de cumplirse, aparecen efectos de relajación de carga, que se traducen en que el campo exterior penetra en el líquido, a no ser que su constante dieléctrica sea muy alta, en cuyo caso el campo inducido por la carga de polarización evita la entrada del campo exterior en el menisco y en una cierta región del chorro. La carga eléctrica en equilibrio en la superficie de un menisco cónico intensifica el campo eléctrico y determina su variación espacial hasta distancias aguas abajo del menisco del orden de su tamaño. Este campo, calculado por Taylor, es independiente del voltaje aplicado, por lo que las condiciones locales del flujo y el valor de la corriente eléctrica son también independientes del voltaje en tanto los tamaños de las regiones que determinan estas propiedades sean pequeños frente al tamaño del menisco. Los resultados experimentales publicados en la literatura muestran que existe un caudal mínimo para el que el modo cono-chorro que acabamos de describir deja de existir. El valor medio y la desviación típica de la distribución de tamaños de las gotas generadas por un electrospray son mínimos cuando se opera cerca del caudal mínimo. A pesar de que los mecanismos responsables del caudal mínimo han sido muy estudiados, no hay aún una teoría completa del mismo, si bien su existencia parece estar ligada a la aparición de efectos de relajación de carga en la región de transición cono-chorro. En esta tesis, se presentan estimaciones de orden de magnitud, algunas existentes y otras nuevas, que muestran los balances dominantes responsables de las distintas regiones de la estructura asintótica de la solución en varios casos de interés. Cuando la inercia del líquido juega un papel en la transición cono-chorro, los resultados muestran que la región de transferencia de corriente, donde la mayor parte de la corriente pasa a la superficie, está en el chorro aguas abajo de la región de transición cono-chorro. Los efectos de relajación de carga aparecen de forma simultánea en el chorro y la región de transición cuando el caudal se disminuye hasta valores de un cierto orden. Para caudales aún menores, los efectos de relajación de carga se notan en el menisco, en una región grande comparada con la de transición cono-chorro. Cuando el efecto de las fuerzas de viscosidad es dominante en la región de transición, la región de transferencia de corriente está en el chorro pero muy próxima a la región de transición cono-chorro. Al ir disminuyendo el caudal, los efectos de relajación de carga aparecen progresivamente en el chorro, en la región de transición y por último en el menisco. Cuando el caudal es mucho mayor que el mínimo del modo cono-chorro, el menisco deja de ser cónico. El campo eléctrico debido al voltaje aplicado domina en la región de transferencia de corriente, y tanto la corriente eléctrica como el tamaño de las diferentes regiones del problema pasan a depender del voltaje aplicado. Como resultado de esta dependencia, el plano caudal-voltaje se divide en diferentes regiones que se analizan separadamente. Para caudales suficientemente grandes, la inercia del líquido termina dominando frente a las fuerzas de la viscosidad. Estos resultados teóricos se han validado con simulaciones numéricas. Para ello se ha formulado un modelo simplificado del flujo, el campo eléctrico y el transporte de carga en el menisco y el chorro del electrospray. El movimiento del líquido se supone casi unidireccional y se describe usando la aproximación de Cosserat para un chorro esbelto. Esta aproximación, ampliamente usada en la literatura, permite simular con relativa facilidad múltiples casos y cubrir amplios rangos de valores de los parámetros reteniendo los efectos de la viscosidad y la inercia del líquido. Los campos eléctricos dentro y fuera del liquido están acoplados y se calculan sin simplificación alguna usando un método de elementos de contorno. La solución estacionaria del problema se calcula mediante un método iterativo. Para explorar el espacio de los parámetros, se comienza calculando una solución para valores fijos de las propiedades del líquido, el voltaje aplicado y el caudal. A continuación, se usa un método de continuación que permite delinear la frontera del dominio de existencia del modo cono-chorro, donde el método iterativo deja de converger. Cuando el efecto de la inercia del líquido domina en la región de transición cono-chorro, el caudal mínimo para el cual el método iterativo deja de converger es del orden del valor estimado del caudal para el que comienza a haber efectos de relajación de carga en el chorro y el cono. Aunque las simulaciones no convergen por debajo de dicho caudal, el valor de la corriente eléctrica para valores del caudal ligeramente mayores parece ajustarse a las estimaciones para caudales menores, reflejando un posible cambio en los balances aplicables. Por el contrario, cuando las fuerzas viscosas dominan en la región de transición, se pueden obtener soluciones estacionarias para caudales bastante menores que aquel para el que aparecen efectos de relajación de carga en la región de transición cono-chorro. Los resultados numéricos obtenidos para estos pequeños caudales se ajustan perfectamente a las estimaciones de orden de magnitud que se describen en la memoria. Por último, se incluyen como anexos dos estudios teóricos que han surgido de forma natural durante el desarrollo de la tesis. El primero hace referencia a la singularidad en el campo eléctrico que aparece en la línea de contacto entre el líquido y el tubo capilar en la mayoría de las simulaciones. Primero se estudia en qué situaciones el campo eléctrico tiende a infinito en la línea de contacto. Después, se comprueba que dicha singularidad no supone un fallo en la descripción del problema y que además no afecta a la solución lejos de la línea de contacto. También se analiza si los esfuerzos eléctricos infinitamente grandes a los que da lugar dicha singularidad pueden ser compensados por el resto de esfuerzos que actúan en la superficie del líquido. El segundo estudio busca determinar el tamaño de la región de apantallamiento en un chorro de líquido dieléctrico sin carga superficial. En esta región, el campo exterior es compensado parcialmente por el campo que induce la carga de polarización en la superficie del líquido, de forma que en el interior del líquido el campo eléctrico es mucho menor que en el exterior. Una región como ésta aparece en las estimaciones cuando los efectos de relajación de carga son importantes en la región de transferencia de corriente en el chorro. ABSTRACT This aim of this dissertation is a theoretical and numerical analysis of an electrospray. In its most simple configuration, a constant flow rate of the liquid to be atomized, which has to be an electrical conductor, is injected into a dielectric medium (a gas or another inmiscible fluid) through a metallic capillary tube. A constant voltage is applied between this tube and a distant electrode that produces an electric field in the liquid and the surrounding medium. This electric field induces an electric current in the liquid that accumulates charge at its surface and leads to electric stresses that stretch the surface in the direction of the electric field. A meniscus appears on the end of the capillary tube when the electric field is sufficiently high and the flow rate is small. Pressure variations and viscous stresses due to the motion of the liquid are negligible in most of the meniscus, where normal electric and surface tension stresses acting on the surface are dominant. In the so-called cone-jet mode, the balance of these stresses forces the surface to adopt a conical shape -Taylor cone- in a intermediate region between the end of the tube and the tip of the meniscus. When approaching the cone apex, the velocity of the liquid increases and leads to pressure variations that eventually disturb the balance of surfaces tension and electric stresses. A thin jet emerges then from the tip of the meniscus that transports the charge accumulated at its surface. The electric field tangent to the surface of the jet acts on this charge and continuously stretches the jet. This electric force is negligible in the meniscus, where the component of the electric field tangent to the surface is small, but becomes very important in the jet. Far from the cone, the jet can either develop an asymmetrical instability named “whipping”, whereby the jet winds into a spiral, or break into a spray of small, nearly monodisperse, charged droplets. The electric current transported by the liquid has two components, the conduction current in the bulk of the liquid and the convection current due to the transport of the surface charge by the flow. The first component dominates in the meniscus, the second one in the far jet, and both are comparable in a current transfer region located in the jet downstream of the cone-jet transition region where the meniscus ceases to be a Taylor cone. Given an external electric field, the charge that accumulates at the surface of the liquid reduces the electric field inside the liquid, until an equilibrium is reached in which the electric field induced by the surface charge counters the external electric field and shields the liquid from this field. The characteristic time of this process is the electric relaxation time, which is a property of the liquid. When the residence time of the liquid in the cone-jet transition region (or in other region of the flow) is greater than the electric relaxation time, the surface charge follows a succession of equilibrium states and continuously shield the liquid from the external field. When this condition is not satisfied, charge relaxation effects appear and the external field penetrates into the liquid unless the liquid permittivity is large. For very polar liquids, the field due to the polarization charge at the surface prevents the external field from entering the liquid in the cone and in certain region of the jet. The charge at the surface of a conical meniscus intensifies the electric field around the cone, determining its spatial variation up to distances downstream of the apex of the order of the size of the meniscus. This electric field, first computed by Taylor, is independent of the applied voltage. Therefore local flow characteristics and the electric current carried by the jet are also independent of the applied voltage provided the size of the regions that determine these magnitudes are small compared with the size of the meniscus. Many experiments in the literature show the existence of a minimum flow rate below which the cone-jet mode cannot be established. The mean value and the standard deviation of the electrospray droplet size distribution are minimum when the device is operated near the minimum flow rate. There is no complete explanation of the minimum flow rate, even though possible mechanisms have been extensively studied. The existence of a minimum flow rate seems to be connected with the appearance of charge relaxation effects in the transition region. In this dissertation, order of magnitude estimations are worked out that show the dominant balances in the different regions of the asymptotic structure of the solution for different conditions of interest. When the inertia of the liquid plays a role in the cone-jet transition region, the region where most of the electric current is transfered to the surface lies in the jet downstream the cone-jet transition region. When the flow rate decreases to a certain value, charge relaxation effects appear simultaneously in the jet and in the transition region. For smaller values of the flow rate, charge relaxation effects are important in a region of the meniscus larger than the transition region. When viscous forces dominate in the flow in the cone-jet transition region, the current transfer region is located in the jet immediately after the transition region. When flow rate is decreased, charge relaxation effects appears gradually, first in the jet, then in the transition region, and finally in the meniscus. When flow rate is much larger than the cone-jet mode minimum, the meniscus ceases to be a cone. The electric current and the structure of the solution begin to depend on the applied voltage. The flow rate-voltage plane splits into different regions that are analyzed separately. For sufficiently large flow rates, the effect of the inertia of the liquid always becomes greater than the effect of the viscous forces. A set of numerical simulations have been carried out in order to validate the theoretical results. A simplified model of the problem has been devised to compute the flow, the electric field and the surface charge in the meniscus and the jet of an electrospray. The motion of the liquid is assumed to be quasi-unidirectional and described by Cosserat’s approximation for a slender jet. This widely used approximation allows to easily compute multiple configurations and to explore wide ranges of values of the governing parameters, retaining the effects of the viscosity and the inertia of the liquid. Electric fields inside and outside the liquid are coupled and are computed without any simplification using a boundary elements method. The stationary solution of the problem is obtained by means of an iterative method. To explore the parameter space, a solution is first computed for a set of values of the liquid properties, the flow rate and the applied voltage, an then a continuation method is used to find the boundaries of the cone-jet mode domain of existence, where the iterative method ceases to converge. When the inertia of the liquid dominates in the cone-jet transition region, the iterative method ceases to converge for values of the flow rate for which order-of-magnitude estimates first predict charge relaxation effects to be important in the cone and the jet. The electric current computed for values of the flow rate slightly above the minimum for which convergence is obtained seems to agree with estimates worked out for lower flow rates. When viscous forces dominate in the transition region, stationary solutions can be obtained for flow rates significantly smaller than the one for which charge relaxation effects first appear in the transition region. Numerical results obtained for those small values of the flow rate agree with our order of magnitude estimates. Theoretical analyses of two issues that have arisen naturally during the thesis are summarized in two appendices. The first appendix contains a study of the singularity of the electric field that most of the simulations show at the contact line between the liquid and the capillary tube. The electric field near the contact line is analyzed to determine the ranges of geometrical configurations and liquid permittivity where a singularity appears. Further estimates show that this singularity does not entail a failure in the description of the problem and does not affect the solution far from the contact line. The infinite electric stresses that appear at the contact line can be effectively balanced by surface tension. The second appendix contains an analysis of the size and slenderness of the shielded region of a dielectric liquid in the absence of free surface charge. In this region, the external electric field is partially offset by the polarization charge so that the inner electric field is much lower than the outer one. A similar region appears in the estimates when charge relaxation effects are important in the current transfer region.

Regimes of spray vaporization and combustion in counterflow configurations

This article addresses the problem of spray vaporization and combustion in axisymmetric opposed-jet configurations involving a stream of hot air counterflowing against a stream of nitrogen carrying a spray of fuel droplets. The Reynolds numbers of the jets are assumed to be large, so that mixing of the two streams is restricted to a thin mixing layer that separates the counterflowing streams. The evolution of the droplets in their feed stream from the injection location is seen to depend fundamentally on the value of the droplet Stokes number, St, defined as the ratio of the droplet acceleration time to the mixing layer strain time close to the stagnation point. Two different regimes of spray vaporization and combustion can be identified depending on the value of St. For values of St below a critical value, equal to 1/4 for dilute sprays with small values of the spray liquid mass loading ratio, the droplets decelerate to approach the gas stagnation plane with a vanishing axial velocity. In this case, the droplets located initially near the axis reach the mixing layer, where they can vaporize due to the heat received from the hot air, producing fuel vapor that can burn with the oxygen in a diffusion flame located on the air side of the mixing layer. The character of the spray combustion is different for values of St of order unity, because the droplets cross the stagnation plane and move into the opposing air stream, reaching distances that are much larger than the mixing layer thickness before they turn around. The vaporization of these crossing droplets, and also the combustion of the fuel vapor generated by them, occur in the hot air stream, without significant effects of molecular diffusion, generating a vaporization-assisted nonpremixed flame that stands on the air side outside the mixing layer. Separate formulations will be given below for these two regimes of combustion, with attention restricted to the near-stagnation-point region, where the solution is self-similar and all variables are only dependent on the distance to the stagnation plane. The resulting formulations display a reduced number of controlling parameters that effectively embody dependences of the structure of the spray flame on spray dilution, droplet inertia, and fuel preferential diffusion. Sample solutions are given for the limiting cases of pure vaporization and of infinitely fast chemistry, with the latter limit formulated in terms of chemistry-free coupling functions that allow for general nonunity Lewis numbers of the fuel vapor.