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Purpose: Ultrasound imaging is commonly used in decompression research to assess venous gas emboli (VGE) post-dive, with higher loads associated with increased decompression sickness risk. This work examines, for the first time in humans, the performance of a novel electrical impedance spectroscopy technology (I-VED), on possible detection of post-dive bubbles presence and arterial endothelial dysfunction that may be used as markers of decompression stress. Methods: I-VED signals were recorded in scuba divers who performed standardized pool dives before and at set time points after their dives at 35-minute intervals for about two hours. Two distinct frequency components of the obtained signals, Low-Pass Frequency-LPF: 0-0.5 Hz and Band-Pass Frequency-BPF: 0.5-10 Hz, are extracted and respectively compared to VGE presence and known flow-mediated dilation trends for the same dive profile for endothelial dysfunction. Results: Subjects with VGE counts above the median for all subjects were found to have an elevated average LPF compared to subjects with lower VGE counts, although this was not statistically significant (p=0.06), as well as significantly decreased BPF standard deviation post-dive compared to pre-dive (p=0.008). Conclusions: I-VED was used for the first time in humans and operated to provide qualitative in-vivo electrical impedance measurements that may contribute to the assessment of decompression stress. Compared to ultrasound imaging, the proposed method is less expensive, not operator-dependent and compatible with continuous monitoring and application of multiple probes. This study provided preliminary insights; further calibration and validation are necessary to determine I-VED sensitivity and specificity.
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Embolia Aérea , Enfermedades Vasculares , Humanos , Impedancia Eléctrica , Embolia Aérea/diagnóstico por imagen , Embolia Aérea/etiología , Arterias , DescompresiónRESUMEN
Microbial adhesion and spreading on surfaces are crucial aspects in environmental and industrial settings being also the early stage of complex surface-attached microbial communities known as biofilms. In this work, Pseudomonas fluorescens-laden droplets on hydrophilic substrates (glass coupons) are allowed to partially evaporate before running wetting measurements, to study the effect of evaporation on their interfacial behavior during spillover or splashing. Forced wetting is investigated by imposing controlled centrifugal forces, using a novel rotatory device (Kerberos). At a defined evaporation time, results for the critical tangential force required for the inception of sliding are presented. Microbe-laden droplets exhibit different wetting/spreading properties as a function of the imposed evaporation times. It is found that evaporation is slowed down in bacterial droplets with respect to nutrient medium ones. After sufficient drying times, bacteria accumulate at droplet edges, affecting the droplet shape and thus depinning during forced wetting tests. Droplet rear part does not pin during the rotation test, while only the front part advances and spreads along the force direction. Quantitative results obtained from the well-known Furmidge's equation reveal that force for sliding inception increases as evaporation time increases. This study can be of support for control of biofilm contamination and removal and possible design of antimicrobial/antibiofouling surfaces.
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Pseudomonas fluorescens , Pseudomonas fluorescens/química , Humectabilidad , Interacciones Hidrofóbicas e Hidrofílicas , Volatilización , ViscosidadRESUMEN
Mixtures of anionic sodium oleate (NaOl) and nonionic ethoxylated or alkoxylated surfactants improve the selective separation of magnesite particles from mineral ores during the process of flotation. Apart from triggering the hydrophobicity of magnesite particles, these surfactant molecules adsorb to the air-liquid interface of flotation bubbles, changing the interfacial properties and thus affecting the flotation efficiency. The structure of adsorbed surfactants layers at the air-liquid interface depends on the adsorption kinetics of each surfactant and the reformation of intermolecular forces upon mixing. Up to now, researchers use surface tension measurements to understand the nature of intermolecular interactions in such binary surfactant mixtures. Aiming to adapt better to the dynamic character of flotation, the present work explores the interfacial rheology of NaOl mixtures with different nonionic surfactants to study the interfacial arrangement and viscoelastic properties of adsorbed surfactants under the application of shear forces. Interfacial shear viscosity results reveal the tendency on nonionic molecules to displace NaOl molecules from the interface. The critical nonionic surfactant concentration needed to complete NaOl displacement at the interface depends on the length of its hydrophilic part and on the geometry of its hydrophobic chain. The above indications are supported by surface tension isotherms.
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This study aims to provide insights into biofilm resistance associated with their structural properties acquired during formation and development. On this account, the wetting and imbibition behavior of dehydrated Pseudomonas fluorescens biofilms grown on stainless steel electropolished substrates is thoroughly examined at different biofilm ages. A polar liquid (water) and a non-polar liquid (diiodomethane) are employed as wetting agents in the form of sessile droplets. A mathematical model is applied to appraise the wetting and imbibition performance of biofilms incorporating the evaporation of sessile droplets. The present results show that the examined biofilms are hydrophilic. The progressive growth of biofilms leads to a gradual increase of substrate surface coverageâup to full coverageâaccompanied by a gradual decrease of biofilm surface roughness. It is noteworthy that just after 24 h of biofilm growth, the surface roughness increases about 6.7 times the roughness of the clean stainless steel surface. It is further found that the imbibition of liquid in the biofilm matrix is restricted only to the biofilm region under the sessile droplet. The lack of further capillary imbibition into the biofilm structure, beyond the droplet deposition region, implies that the biofilm matrix is not in the form of an extended network of interconnected micro/nanopores. All in all, the present results indicate a resilient biofilm structure to biocide penetration despite its hydrophilic nature.
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Desinfectantes , Pseudomonas fluorescens , Biopelículas , Acero Inoxidable/química , HumectabilidadRESUMEN
Wetting of dehydrated Pseudomonas fluorescens biofilms grown on glass substrates by an external liquid is employed as a means to investigate the complex morphology of these biofilms along with their capability to interact with external fluids. The porous structure left behind after dehydration induces interesting droplet spreading on the external surface and imbibition into pores upon wetting. Static contact angles and volume loss by imbibition measured right upon droplet deposition indicate that biofilms of higher incubation times show a higher porosity and effective hydrophilicity. Furthermore, during subsequent rotation tests, using Kerberos device, these properties dictate a peculiar forced wetting/spreading behavior. As rotation speed increases a long liquid tail forms progressively at the rear part of the droplet, which stays pinned at all times, while only the front part of the droplet depins and spreads. Interestingly, the experimentally determined retention force for the onset of droplet sliding on biofilm external surface is lower than that on pure glass. An effort is made to describe such complex forced wetting phenomena by presenting apparent contact angles, droplet length, droplet shape contours, and edges position as obtained from detailed image analysis.
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Pseudomonas fluorescens , Biopelículas , Interacciones Hidrofóbicas e Hidrofílicas , Porosidad , HumectabilidadRESUMEN
Biofilms are complex porous materials formed by microorganisms, polysaccharides, proteins, eDNA, inorganic matter, and water. They are ubiquitous in various environmental niches and are known to grow at solid-liquid, solid-air and air-liquid interfaces, often causing problems in several industrial and sanitary fields. Their removal is a challenge in many applications and numerous studies have been conducted to identify promising chemical species as cleaning agents. While these substances target specific components of biofilm structure, the role of water content in biofilm, and how it can influence wettability and detergent absorption have been quite neglected in the literature. Estimating water content in biofilm is a challenging task due to its heterogeneity in morphology and chemical composition. In this study, we controlled water content in Pseudomonas fluorescens AR 11 biofilms grown on submerged glass slides by regulating environmental relative humidity after drying. Interfacial properties of biofilm were investigated by measuring wetting of water and soybean oil. The morphology of biofilm structure was evaluated using Confocal Laser Scanning Microscopy and Scanning Electron Microscopy. The results showed that biofilm water content has a significant and measurable effect on its wettability, leading to the hypothesis that a preliminary control of water content can play a crucial role in biofilm removal process.
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Pseudomonas fluorescens , Humectabilidad , Pseudomonas fluorescens/fisiología , Humedad , Biopelículas , AguaRESUMEN
Periodically, the European Space Agency (ESA) updates scientific roadmaps in consultation with the scientific community. The ESA SciSpacE Science Community White Paper (SSCWP) 9, "Biology in Space and Analogue Environments", focusses in 5 main topic areas, aiming to address key community-identified knowledge gaps in Space Biology. Here we present one of the identified topic areas, which is also an unanswered question of life science research in Space: "How to Obtain an Integrated Picture of the Molecular Networks Involved in Adaptation to Microgravity in Different Biological Systems?" The manuscript reports the main gaps of knowledge which have been identified by the community in the above topic area as well as the approach the community indicates to address the gaps not yet bridged. Moreover, the relevance that these research activities might have for the space exploration programs and also for application in industrial and technological fields on Earth is briefly discussed.
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Progress in mechanobiology allowed us to better understand the important role of mechanical forces in the regulation of biological processes. Space research in the field of life sciences clearly showed that gravity plays a crucial role in biological processes. The space environment offers the unique opportunity to carry out experiments without gravity, helping us not only to understand the effects of gravitational alterations on biological systems but also the mechanisms underlying mechanoperception and cell/tissue response to mechanical and gravitational stresses. Despite the progress made so far, for future space exploration programs it is necessary to increase our knowledge on the mechanotransduction processes as well as on the molecular mechanisms underlying microgravity-induced cell and tissue alterations. This white paper reports the suggestions and recommendations of the SciSpacE Science Community for the elaboration of the section of the European Space Agency roadmap "Biology in Space and Analogue Environments" focusing on "How are cells and tissues influenced by gravity and what are the gravity perception mechanisms?" The knowledge gaps that prevent the Science Community from fully answering this question and the activities proposed to fill them are discussed.
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This study aims to develop a phantom that simulates the electrical properties of a human blood vessel surrounded by tissues, inside which bubbles can be infused to mimic Decompression Sickness (DCS) conditions. This phantom may be used to calibrate novel electrical methods for bubbles detection in humans and study bubble dynamics during DCS. It may contribute to the limitation of in-vivo trials and time/effort saving, while its use can be extended to other biomedical applications. To facilitate the design of the phantom, we perform first in-vitro measurements in a flow-loop and in-vivo measurements in a swine, in order to detect infused bubbles of a few tenths µm-representing Decompression Sickness conditions-in the test liquid flow and blood flow, respectively, by means of "I-VED" EU patented electrical impedance spectroscopy technique. Results show that the proposed phantom, consisting of a spongy specimen soaked in agar gel in the presence of electrolyte with a hole along it, simulates adequately the electrical properties of a human blood vessel surrounded by tissues. I-VED demonstrates pretty high sensitivity to sense micro-bubbles over the partially conductive vessel walls of the phantom or the isolated animal vein, as well as in the flow-loop: bubbles presence increases electrical impedance and causes intense signal fluctuations around its mean value.
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Vasos Sanguíneos , Enfermedad de Descompresión , Fantasmas de Imagen , Animales , Humanos , PorcinosRESUMEN
Dietary nutrition and uptake of earth-like foods are extremely important aspects for the health and performance of astronauts, especially during future planned long-term space missions. Despite the major progress in studying and designing systems for crop cultivation in microgravity conditions in the last years, there hasn't been equal interest in food preparation processes and cooking. There are several reasons for this but it is chiefly because at present astronauts stay in space for a few months at most, so there is no serious nutritional or psychological need for earth-like food habits. This, however, will change drastically in long-term missions, e.g., to Moon and Mars. French fries are a very popular food commodity across many cultural backgrounds on earth and as such they may be appreciated by long-term space travelers of different origin. The process of frying in hot oil is associated with complex heat and mass transfer along with the growth and detachment of water vapor bubbles. These phenomena are strongly affected by buoyancy and gravitational acceleration making the study of frying at space conditions a challenging task. The present work examines potato frying in hot oil during the short duration low gravity conditions achieved in a Parabolic Flight Campaign organized by the European Space Agency. An innovative device has been constructed, allowing the simultaneous observation of bubbles dynamics above the potato surface and the thermal behavior inside the potato flesh. It is seen that even in the absence of buoyancy i.e., during parabolas, vapor bubbles still detach and depart from the surface of potato permitting hot oil to maintain contact with the potato surface and leading eventually to a fried product. Instantaneous overpressure inside potato pores due to vapor formation upon boiling of potato water is suggested as the mechanism generating the force for bubbles detachment and departure. Moreover, the amount of produced vapor is comparable among the examined values of gravitational acceleration, including the low gravity conditions during parabolas. All in all, the results of the present study provide primary experimental evidence that frying can occur in space.
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Culinaria , Manipulación de Alimentos , Culinaria/métodos , Fenómenos MecánicosRESUMEN
Astronauts are spending longer periods locked up in ships or stations for scientific and exploration spatial missions. The International Space Station (ISS) has been inhabited continuously for more than 20 years and the duration of space stays by crews could lengthen with the objectives of human presence on the moon and Mars. If the environment of these space habitats is designed for the comfort of astronauts, it is also conducive to other forms of life such as embarked microorganisms. The latter, most often associated with surfaces in the form of biofilm, have been implicated in significant degradation of the functionality of pieces of equipment in space habitats. The most recent research suggests that microgravity could increase the persistence, resistance and virulence of pathogenic microorganisms detected in these communities, endangering the health of astronauts and potentially jeopardizing long-duration manned missions. In this review, we describe the mechanisms and dynamics of installation and propagation of these microbial communities associated with surfaces (spatial migration), as well as long-term processes of adaptation and evolution in these extreme environments (phenotypic and genetic migration), with special reference to human health. We also discuss the means of control envisaged to allow a lasting cohabitation between these vibrant microscopic passengers and the astronauts.
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The present white paper concerns the indications and recommendations of the SciSpacE Science Community to make progress in filling the gaps of knowledge that prevent us from answering the question: "How Do Gravity Alterations Affect Animal and Human Systems at a Cellular/Tissue Level?" This is one of the five major scientific issues of the ESA roadmap "Biology in Space and Analogue Environments". Despite the many studies conducted so far on spaceflight adaptation mechanisms and related pathophysiological alterations observed in astronauts, we are not yet able to elaborate a synthetic integrated model of the many changes occurring at different system and functional levels. Consequently, it is difficult to develop credible models for predicting long-term consequences of human adaptation to the space environment, as well as to implement medical support plans for long-term missions and a strategy for preventing the possible health risks due to prolonged exposure to spaceflight beyond the low Earth orbit (LEO). The research activities suggested by the scientific community have the aim to overcome these problems by striving to connect biological and physiological aspects in a more holistic view of space adaptation effects.
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BACKGROUND: This work performs two-dimensional Computational Fluid Dynamics (CFD) simulations of pulsatile bubbly flow in a column resembling the flow inside human vena cava during Decompression Sickness (DCS), aiming to illustrate the effect of certain parameters in bubbly blood flow and so facilitate the design of the: a) corresponding in-vitro bubbly flow experiments under pulsatile flow conditions inside a flow loop and b) in-vivo trials on swines for assessing a novel electrical impedance spectroscopy technique on the detection of bubbles (as those found during DCS) in their bloodstream. MATERIALS AND METHODS: The commercially available ANSYS 2019-R3 CFD code was employed to simulate the pulsatile bubbly flow that resembled DCS. Simulations were validated against experiments conducted in a vertical co-current upward pulsatile bubbly flow provided by a flow loop equipped with electrical, optical and pressure diagnostics. RESULTS: CFD simulations under pulsatile conditions were initially validated by oscillatory in-vitro bubbly flow experiments. Then, the influence of pulsation parameters on void fraction, α, and flow velocity, U, profiles was computationally investigated. Intense periodic fluctuations of void fraction were observed along the column and their intensity increases with pulsation amplitude. Moreover, U and α radial profiles were uniform for bubbles 30 µm but showed a core-peaking profile for bubbles 300 µm. CONCLUSIONS: CFD simulations of pulsatile bubbly flow resembling DCS provided unconventional information about the influence of different-sized sub-millimetre bubbles on the flow velocity and void fraction profiles, which are expected to improve the design of in-vitro and in-vivo trials for the detection of bubbles such as those found in DCS.
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Enfermedad de Descompresión , Hidrodinámica , Humanos , Animales , Porcinos , Flujo Pulsátil , Enfermedad de Descompresión/diagnóstico , Simulación por Computador , HemodinámicaRESUMEN
Biofilms are resilient to environmental conditions and often resistant even to strong disinfectants. It is crucial to investigate their interfacial properties, which can be effectively characterized by wetting analysis. Wetting phenomena on biofilm surfaces have been poorly investigated in literature, in particular a systematic study of wetting on real biofilm-coated substrates including the application of external body forces (forced wetting, i.e.: centrifugal and gravitational forces) is missing. The aim of this work is to study the role of nutrient and shear flow conditions on wetting properties of Pseudomonas fluorescens dehydrated biofilms, grown on glass substrates. An innovative device (Kerberos®), capable to study spreading/sliding behavior under the application of external body forces, is used here for a systematic analysis of wetting/de-wetting liquid droplets on horizontal substrates under the action of tangential forces. Results prove that, under different growth conditions, (i.e., nutrients and imposed flow), biofilms exhibit different wetting properties. At lower nutrient/shear flow conditions, biofilms show spreading/sliding behavior close to that of pure glass. At higher nutrient and shear flow conditions, droplets on biofilms show spreading followed by imbibition soon after deposition, which leads to peculiar droplet depinning during the rotation test. Wetting properties are derived as a function of the rotation speed from both top and side views videoframes through a dedicated image analysis technique. A detailed analysis of biofilm formation and morphology/topography is also provided here.
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Desinfectantes , Pseudomonas fluorescens , Biopelículas , HumectabilidadRESUMEN
Accounting for SARS-CoV-2 adsorption on solids suspended in wastewater is a necessary step towards the reliable estimation of virus shedding rate in a sewerage system, based on measurements performed at a terminal collection station, i.e., at the entrance of a wastewater treatment plant. This concept is extended herein to include several measurement stations across a city to enable the estimation of spatial distribution of virus shedding rate. This study presents a pioneer general model describing the most relevant physicochemical phenomena with a special effort to reduce the complicated algebra. This is performed both in the topology regime, introducing a discrete-continuous approach, and in the domain of independent variables, introducing a monodisperse moment method to reduce the dimensionality of the resulting population balance equations. The resulting simplified model consists of a large system of ordinary differential equations. A sensitivity analysis is performed with respect to some key parameters for a single pipe topology. Specific numerical techniques are employed for the integration of the model. Finally, a parametric case study for an indicative-yet realistic-sewerage piping system is performed to show how the model is applied to SARS-CoV-2 adsorption on wastewater solids in the presence of other competing species. This is the first model of this kind appearing in scientific literature and a first step towards setting up an inverse problem to assess the spatial distribution of virus shedding rate based on its concentration in wastewater.
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COVID-19 , SARS-CoV-2 , Adsorción , Humanos , Modelos Teóricos , Aguas ResidualesRESUMEN
Epidemic spread models are useful tools to study the spread and the effectiveness of the interventions at a population level, to an epidemic. The workhorse of spatially homogeneous class models is the SIR-type ones comprising ordinary differential equations for the unknown state variables. The transition between different states is expressed through rate functions. Inspired by -but not restricted to- features of the COVID-19 pandemic, a new framework for modeling a disease spread is proposed. The main concept refers to the assignment of properties to each individual person as regards his response to the disease. A multidimensional distribution of these properties represents the whole population. The temporal evolution of this distribution is the only dependent variable of the problem. All other variables can be extracted by post-processing of this distribution. It is noteworthy that the new concept allows an improved consideration of vaccination modeling because it recognizes vaccination as a modifier of individuals response to the disease and not as a means for individuals to totally defeat the disease. At the heart of the new approach is an infection age model engaging a sharp cut-off. This model is analyzed in detail, and it is shown to admit self-similar solutions. A hierarchy of models based on the new approach, from a generalized one to a specific one with three dominant properties, is derived. The latter is implemented as an example and indicative results are presented and discussed. It appears that the new framework is general and versatile enough to simulate disease spread processes and to predict the evolution of several variables of the population during this spread.
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COVID-19 , Humanos , PandemiasRESUMEN
Conventional SARS-CoV-2 surveillance based on genotyping of clinical samples is characterized by challenges related to the available sequencing capacity, population sampling methodologies, and is time, labor, and resource-demanding. Wastewater-based variant surveillance constitutes a valuable supplementary practice, since it does not require extensive sampling, and provides information on virus prevalence in a timely and cost-effective manner. Consequently, we developed a sensitive real-time RT-PCR-based approach that exclusively amplifies and quantifies SARS-CoV-2 genomic regions carrying the S:Δ69/70 deletion, indicative of the Omicron BA.1 variant, in wastewater. The method was incorporated in the analysis of composite daily samples taken from the main Wastewater Treatment Plant of Thessaloniki, Greece, from 1 December 2021. The applicability of the methodology is dependent on the epidemiological situation. During Omicron BA.1 global emergence, Thessaloniki was experiencing a massive epidemic wave attributed solely to the Delta variant, according to genomic surveillance data. Since Delta does not possess the S:Δ69/70, the emergence of Omicron BA.1 could be monitored via the described methodology. Omicron BA.1 was detected in sewage samples on 19 December 2021 and a rapid increase of its viral load was observed in the following 10-day period, with an estimated early doubling time of 1.86 days. The proportion of the total SARS-CoV-2 load attributed to BA.1 reached 91.09 % on 7 January, revealing a fast Delta-to-Omicron transition pattern. The detection of Omicron BA.1 subclade in wastewater preceded the outburst of reported (presumable) Omicron cases in the city by approximately 7 days. The proposed wastewater surveillance approach based on selective PCR amplification of a genomic region carrying a deletion signature enabled rapid, real-time data acquisition on Omicron BA.1 prevalence and dynamics during the slow remission of the Delta wave. Timely provision of these results to State authorities readily influences the decision-making process for targeted public health interventions, including control measures, awareness, and preparedness.
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COVID-19 , Aguas Residuales , COVID-19/epidemiología , Prueba de COVID-19 , Humanos , Reacción en Cadena de la Polimerasa/métodos , ARN Viral , SARS-CoV-2/genética , Aguas Residuales/análisis , Monitoreo Epidemiológico Basado en Aguas ResidualesRESUMEN
The COVID-19 pandemic represents an unprecedented global crisis necessitating novel approaches for, amongst others, early detection of emerging variants relating to the evolution and spread of the virus. Recently, the detection of SARS-CoV-2 RNA in wastewater has emerged as a useful tool to monitor the prevalence of the virus in the community. Here, we propose a novel methodology, called lineagespot, for the monitoring of mutations and the detection of SARS-CoV-2 lineages in wastewater samples using next-generation sequencing (NGS). Our proposed method was tested and evaluated using NGS data produced by the sequencing of 14 wastewater samples from the municipality of Thessaloniki, Greece, covering a 6-month period. The results showed the presence of SARS-CoV-2 variants in wastewater data. lineagespot was able to record the evolution and rapid domination of the Alpha variant (B.1.1.7) in the community, and allowed the correlation between the mutations evident through our approach and the mutations observed in patients from the same area and time periods. lineagespot is an open-source tool, implemented in R, and is freely available on GitHub and registered on bio.tools.
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Mutación , SARS-CoV-2/genética , SARS-CoV-2/aislamiento & purificación , Programas Informáticos , Aguas Residuales/virología , HumanosRESUMEN
Flotation is a very important separation process in the mining industry. In addition, it finds important application as a water treatment process. The better design of flotation devices and operation strategies requires development of reliable and consistent mathematical models. Flotation is much more complex than typical unit processes, involving physicochemical interactions in small size scale and hydrodynamic interactions between bubbles, particles and liquid in a variety of size scales. The only feasible integrated approach to modeling the flotation process is by incorporating multiple scales. In the heart of such an approach there is a submodel for the frequency of collisions between bubbles and particles. Literature on this subject in the absence of intense turbulence is very extensive and there are many well-accepted models. Yet, the situation is quite different for the case of turbulence being an important collision mechanism, which is exactly what happens in industrial dispersed air flotation devices. The corresponding literature models are limited and focused on different aspects of the process. The present work is a review study attempting to unify these models in a general framework. The review is not restricted to presenting existing models but all relevant physical principles and fundamental theories are examined and assessed properly. In this respect, there are two levels of classification of literature material in this work. The first is a classification as general collision models and flotation models. It is important to critically examine the general collision models of engineering and physics literature since they constitute the basis on which flotation models rely. The second classification is with respect to the level of detail and sophistication of models (from distributed multibubble/multiparticle model to lumped models based on statistical theory of turbulence). The outcome of the work comes to the conclusion that existing models focus only to specific parts of the phenomena leading to bubble-particle collisions and for this, further improvement is needed to integrate them to obtain a better and more general picture. The material and comments presented in this work are meant as a decisive milestone towards this integration procedure.
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Process modeling is a valuable tool for process design and optimization. Nonetheless, the extent of its use depends on the physical complexity of each particular application. Flotation is one of the most complex processes to model. In particular, in mechanical flotation cells, turbulent flow prevails and promotes bubble particle collisions. Many size and time scales of both hydrodynamic and physicochemical nature have to be resolved to model the process. The only way to achieve this is a combination of co-current (pulp and froth) and sequential multiscale modeling. A generalized framework for modeling the pulp phase from the device scale to thin film scale separating bubbles and particles is presented here. The core of the model is the term describing the collision frequency between bubbles and particles. Existing approaches to derive this term are reviewed and critically commented demonstrating several inconsistencies. A unified and consistent approach for deriving this collision frequency term is described overcoming all the inconsistencies of previous approaches. Specific results are presented for the case of flotation of fine particles, being practically the only case for which a simplified collision frequency expression of algebraic complexity can be derived.