Turbulent Liquid Research Articles

B-156 Extraction strategy for therapeutic drug monitoring of sirolimus and tacrolimus using volumetric absorptive microsampling

Abstract Background Following organ transplantation, patients are placed on immunosuppressant drugs (ISDs) to minimize the risk of rejection. Sirolimus and tacrolimus are two of the most widely used ISDs, however, due to their narrow therapeutic indices, patients require frequent therapeutic drug monitoring (TDM). Recurrent venipuncture can become uncomfortable and disruptive, especially in the pediatric population. Therefore, we describe an extraction method using dried whole blood from volumetric absorptive microsampling (VAMS) devices for the detection of sirolimus and tacrolimus by turbulent flow liquid chromatography tandem mass spectrometry (TFC-MS/MS). The use of VAMS in the clinical laboratory will provide ISD patients with a convenient alternative to traditional blood draws. Methods MassTrak immunosuppressant calibrators based on a whole blood matrix (Waters) were applied to 30 μL VAMS Mitra devices (Neoteryx) and dried overnight. To extract the whole blood off of VAMS tip, we tested various methanol:water solvent ratios, of which 30 μL was added to the device. Tips were extracted using ultrasonication (30 min), vortexing (5 min), and centrifugation. Once extracted from the tip, 25 mM zinc sulfate was added to whole blood extract at a 1:1 (v/v) ratio. An acetonitrile and methanol extraction reagent was then added to the whole blood/zinc sulfate solution at a 2:1 (v/v) ratio. After brief vortexing, samples were centrifuged at 16,060 × g (10 min) and tested using an established TFC-MS/MS method which deploys a TLX-2 system for sample preparation coupled to a Q-Trap tandem mass spectrometer (AB Sciex 5500). Results A 80:20 (v/v) water:methanol extraction solvent yielded the greatest extraction efficacy for both sirolimus and tacrolimus from the VAMS tips compared to other tested ratios. We established a 5-point calibration curve to correlate the measured values of ISDs with known MassTrak calibration standard concentrations. The resulting average calibration curve from 3 independent experiments was highly linear for both sirolimus (R2= 0.992; slope= 1.1; intercept= 0.94) and tacrolimus (R2= 0.996; slope= 1.1; intercept = 0.8819). Our VAMS whole blood extraction strategy was correlated to the established neat whole blood protocol, which utilized all of the sample preparation steps outlined above except the initial extraction from the VAMS tip. The average extraction efficacy was 89.1% for sirolimus with an average coefficient of variation (CV%) of 12.1% across 3 independent experiments. For tacrolimus, we demonstrated an average extraction efficacy of 100.1% with an average CV% of 8.4%, again across 3 independent experiments. Conclusions We demonstrate the feasibility of using a VAMS approach to TDM of sirolimus and tacrolimus. Our results demonstrate favorable recoveries for both of the tested drugs, evidenced by high recoveries of the external calibration standards. Additionally, our method exhibited high extraction efficacy and low variability. Further validation studies, including the utilization of clinical samples is necessary to confirm our preliminary findings.

Numerical simulations of particle concentration and size effects in a slurry bubble column with a CFD‐PBM coupled model

AbstractThe combined effects of particle concentration (0–20 vol%) and particle size on the hydrodynamics of a slurry bubble column were studied by computational fluid dynamics coupled with population balance model (CFD‐PBM) in a wide range of superficial gas velocity (0.02–0.20 m/s). This CFD‐PBM coupled model included multiple effects of particles, namely increased slurry viscosity, reduced drag force, promoted bubble coalescence, and attenuated liquid turbulence, among which turbulence attenuation was crucial. To quantify liquid turbulence attenuation, a mechanistic model was established by equating the energy dissipated by particle motion to the attenuated liquid turbulence energy calculated from turbulent energy spectrum. The turbulent energy dissipation rate was reduced by over 60% at a solid concentration of 20%. Using this model, the effects of particle concentration and particle size on overall gas holdup were well predicted. This model advanced our understanding of how particles affect the gas holdup in a slurry bubble column.

Computational Fluid Dynamics Modeling of Multiphase Flows in a Side-Blown Furnace: Effects of Air Injection and Nozzle Submerged Depth

The side-blown smelting process is becoming popular in the modern metallurgical industry due to its large potential for dealing with complex materials. To further enhance its efficiency, it is essential to comprehensively understand the complex gas–liquid flow behavior in the smelting bath. In this study, the volume-of-fluid method is employed to establish computational fluid dynamics modeling on a 1:5 scaled model of a side-blown furnace. The simulation was validated against the experimental results. Notably, the influences of the nozzle’s submerged depth, injection velocity, and angle were systematically investigated. The results show that increasing the injection velocity from 29.44 to 58.88 m/s resulted in 52.97%, 116.67%, 500.00%, and 5.88% increases in the interface area, liquid velocity, liquid turbulent kinetic energy, and gas penetration depth, respectively. The maximum gas–liquid interface area, gas penetration depth, velocity, and turbulence of the liquid were found at an injection angle of 30°. Furthermore, increasing the submerged depth increased the interface area and the velocity of the liquid but decreased the turbulent kinetic energy of the liquid. Overall, increasing the injection velocity is considered a more effective measure to strengthen the smelting intensity.

Gas-liquid mass transfer in microbubble column reactors

Microbubble column reactors (MBCRs) present great potential in gas-liquid reactions due to their superior mass transfer efficiency. In this work, an automated platform was built to investigate the effect of gas/liquid superficial velocity, and liquid viscosity on mass transfer performance. Compared to conventional bubble column reactors, MBCRs exhibit significantly enhanced mass transfer efficiency. The findings show that kLa initially increases, followed by a subsequent decrease with the increase of gas superficial velocity. This behavior is attributed to transitioning from a homogeneous to a heterogeneous regime as gas superficial velocity increases. The liquid viscosity has a dual effect on kLa within a homogeneous regime. However, the kL in MBCRs is smaller than that in conventional bubble column reactors due to the movement of large bubbles enhancing liquid turbulence. Moreover, a dimensionless correlation was developed integrating the Weber number to predict the mass transfer coefficient.

Effect of hemispherical ash slag simulants on the thickness distribution and fluctuation characteristics of turbulent liquid film

To explore the influence of ash slag adhering to the scrubbing-cooling tube on the turbulent falling film flow, three hemispheres with different radii (R = 2 mm, 4 mm, and 6 mm) were used to simulate the slag. Ultrasonic Doppler Velocimetry was used to investigate the liquid film’s thickness distribution and fluctuation characteristics under Reynolds number of liquid film Ref ≈8.75 × 103 ––2.63 × 104. The liquid film thickness distribution at low Reynolds numbers exhibits an isosceles triangle when subjected to R = 4 mm and 6 mm hemispheres. At high Reynolds numbers, the average thickness of the liquid film is smaller downstream of the three simulants. The simulants can enhance the liquid film’s perturbations. A mathematical model has been established to predict the mean liquid film thickness on hemispherical simulants, and the relative difference is within 10 %. The probability density distribution curves of the instantaneous liquid film thickness on the simulant exhibit multimodality.

Modeling of primary breakup considering turbulent nozzle flow, internal turbulence and surface instability of liquid jet using turbulence decay theory

In heat engines utilizing fuel injection, the processes of atomization and spray formation have a significant impact on the combustion process, thereby determining both efficiency and emission characteristics. Accurate prediction and control of spray formation in fuel injection systems play a key role in improving the efficiency and environmental performance of thermal engines, especially with the emergence of carbon-neutral fuels. To achieve accurate prediction of spray mixture formation, it is imperative to refine the atomization model for the liquid jet within numerical simulations. This requires a phenomenological representation of the atomization process that avoids reliance on computational constants obtained from spray experimental results. Consequently, the present study attempts to mathematically model the turbulent nozzle flow and liquid jet atomization process, leading to the development of a novel primary breakup model. The construction of the primary breakup model involves an analysis of the turbulence at the nozzle inlet. By merging this turbulence with the turbulence resulting from wall shear flow within the nozzle, the model provides insight into the internal turbulence and surface instability of the liquid jet, encompassing the turbulence spectrum. Consequently, the influence of nozzle length on the turbulent flow within the nozzle can be understood, and the droplet formation characteristics of the liquid jet can be predicted along with its multi-wavelength dispersion characteristics. The model effectively captures the experimental results in terms of breakup length and droplet dispersion characteristics, thus adding a higher level of accuracy to numerical simulations. Ultimately, the in-depth study of this model, coupled with its comparison with experimental results, enhances the understanding of the liquid jet atomization process.

Multiscale analysis of turbulence in horizontal pipes: Liquid and particle-liquid flow investigation

An experimental–theoretical methodology is developed to investigate the characteristics of turbulence in horizontal particle-liquid pipe flows. Using a discrete wavelet transform, the three-dimensional Lagrangian trajectories of the liquid phase experimentally determined by positron emission particle tracking are decomposed into their deterministic and stochastic sub-trajectories, which are then utilized to construct profiles of local fluctuating velocity components and turbulent kinetic energy. The results for a single-phase flow are independently validated using computational fluid dynamic simulation and the analysis parameters are fine-tuned using direct numerical simulation data from the literature. In a particle-liquid flow, the investigation explores the influence of various factors including particle size, density, and concentration on turbulence intensity. Remarkably, the results demonstrate significant effects of the particle size and density on liquid turbulence. The enhanced understanding gained regarding turbulence intensity helps to advance our fundamental interpretation of the dynamics of particle-liquid flows, thus potentially aiding the rational design of such complex flows and associated equipment.

Validation and Assessment of a Hybrid VOF-Lagrangian Numerical Methodology for Turbulent Liquid Fuel Jets in High-Speed Crossflow

Abstract For gas turbine combustors, injecting liquid fuel in crossflow can achieve superior mixing characteristics to improve performance and reduce emissions. Robust numerical design tools are needed to accelerate the development of low-emissions technologies. Atomization modeling is often facilitated by using the Lagrangian approach rather than the more complex and computationally expensive Volume-of-Fluid (VOF) approach. However, most Lagrangian breakup models rely on empirical constants that must be fully calibrated for jets in crossflow and representative conditions. A hybrid approach could deliver a better compromise between accuracy and computational cost. This study proposes and validates a novel numerical methodology for coupling the VOF and Lagrangian approaches using a stochastic breakup model with Adaptive Mesh Refinements for turbulent liquid fuel jets in crossflow under more representative gas turbine conditions. The predictions were validated in the near and far-field regions using datasets at high pressures (1–8 bar), Weber numbers (720–1172), and momentum flux ratios (6–33). The predictive capabilities and computational cost were also compared to the Lagrangian approach coupled with large eddy simulations (LES) and with the unsteady Reynolds-Averaged Navier–Stokes (RANS) methodology previously developed and validated by the authors. The effect of different VOF-Lagrangian transition criteria on the computational cost was also assessed and recommendations were provided for further improvements. The overall LES predictions were significantly improved by the proposed hybrid methodology. Although it tends to underpredict the spray trajectory and Sauter Mean Diameter compared to the URANS methodology, it better captures the diameter in the wake region and the droplet velocities.

Simultaneous determination of oxacillin and cloxacillin in plasma and CSF using turbulent flow liquid chromatography coupled to high-resolution mass spectrometry: Application in therapeutic drug monitoring

Cloxacillin and oxacillin are group M penicillins. The therapeutic monitoring of plasma concentrations of these antibiotics and those of their hydroxymethylated metabolites is of great clinical interest, especially in the choice of an adequate dosage allowing an effective treatment while limiting the occurrence of undesirable effects and the development of bacterial resistance. In this context, we conducted this work aiming at developing and validating a method allowing the determination of cloxacillin and oxacillin as well as the identification of their active metabolites in different biological matrices (CSF and plasma) using turbulent flow liquid chromatography coupled to high-resolution mass spectrometry. To do this, we carried out several optimisation tests. Subsequently, we validated our method according to the latest bioanalytical validation recommendations of the European Medicines Agency. The validation results showed that our method is specific and sensitive. We obtained good linearity in the range 0.5 to 100 µg/mL with correlation coefficients above 0.995. The lower limit of quantification was 0.5 µg/mL for each analyte. The method was found to be accurate with repeatability and reproducibility coefficients of variation below 15 %. Our method is also accurate with bias values below 15 %. Recovery values ranged from 87 % to 95 %. Finally, we were able to apply our method to the therapeutic monitoring of the analysed molecules and to identify their active metabolites. Our results suggest that LC-MS shows superiority in the therapeutic monitoring of these antibiotics due to the superiority of specificity shown by this method. This assay method can be routinely used for the daily plasma assays of patients treated with these antibiotics in the context of therapeutic monitoring.

Design and operation of a von Kármán reactor for droplet breakage experiments

The dispersion of an immiscible fluid in a turbulent liquid flow is a frequent occurrence in various natural and technical processes, with particular importance in the chemical, pharmaceutical, mining, petroleum, and food industries. Understanding the dynamics and breakup of liquid droplets is crucial in many scientific and engineering applications, as poor control and optimization of droplet systems results in significant financial losses annually. Although a theoretical background for describing droplet breakup exists, many assumptions still require experimental verification. Numerous mathematical models have been proposed to describe the rate coefficient of droplet breakup and child distribution functions. However, the validation and discrimination between models have been hindered by the lack of experimental data gathered under well-controlled and well characterized conditions. Thus, to validate the current models, novel equipment and methodology for optical droplet breakage research are required. In this work, a von Kármán swirling flow apparatus was designed and constructed to carry out optical based droplet breakage experiments under low-intensity, homogeneous turbulent flow. The methodology presented here describes the procedure for generating and controlling the size of the droplets being injected into the homogeneous turbulent flow field. The experiments involved introducing single droplets into the test section, using peanut oil to be the droplet phase and the continuous phase is water. Automated image analysis algorithms were utilized to determine breakage time, breakage probability, and child droplet size distribution for different turbulence intensities.

Determination of Treosulfan and Fludarabine in Plasma by Turbulent Flow Liquid Chromatography-Tandem Mass Spectrometry (TFLC-MS/MS).

Treosulfan is a structural analog of the alkylating agent busulfan which has been shown in clinical trials to exhibit comparable myeloablative activity while causing fewer serious side effects. Treosulfan is currently being considered for FDA approval in combination with fludarabine, one of the most commonly used myeloablative agents, as a conditioning regimen prior to hematopoietic stem cell transplantation (HSCT). Because plasma concentrations of both treosulfan and fludarabine exhibit significant interindividual variability, therapeutic drug monitoring (TDM) is indicated to ensure dosages are administered that maximize efficacy while minimizing toxicity. In this chapter, we describe a rapid, accurate assay to detect treosulfan and fludarabine simultaneously in human plasma using turbulent flow liquid chromatography coupled to electrospray ionization tandem mass spectrometry (TFLC-ESI-MS/MS). Treosulfan and fludarabine are extracted from only 100μL of acidified plasma via protein precipitation with methanol containing isotope-labeled internal standards. The extract is injected into the TFLC-ESI-MS/MS system, and the analytes are quantified using multiple reaction monitoring and a six-point calibration curve.

A numerical study of an atomizing jet in a resonant acoustic field

By applying state-of-the-art, high-fidelity methods for compressible multiphase flows, this work features a parametric study of a turbulent liquid jet atomizing under the influence of standing acoustic waves with five different amplitude values. We perform these simulations in a semi-periodic domain to isolate interactions between acoustic and atomization processes and to emulate a pure liquid fuel spray placed at the pressure node of a resonant acoustic field. Characterization of the flow includes measurements of the mean dimensions, droplet number, and surface area of the liquid distribution, alongside qualitative depictions of the interface evolution, breakup events, and hydrodynamic fields. As acoustic forcing is provided to the flow, the added energy provokes atomization when shear would otherwise be insufficient for breakup. The magnitude of the forcing determines the rate of droplet production, which accelerates as the evolving liquid surface modifies the induced motion of the gas phase. At the nodal plane, the acoustic field produces an organizing effect on the liquid structures.

A-038 An Improved Multiplexed HTLC-HESI-MSMS Method for the Measurement of Total Testosterone in Serum

Abstract Background Testosterone is an anabolic steroid produced primarily in the testicles of males and mainly in the ovaries of females. Imbalance of testosterone is the primary cause of hypogonadism in males, hirsutism and virilization in females, osteoporosis, and diabetes mellitus. Accurate and fast-turnaround measurement of testosterone is critical for diagnosis, prevention, and treatment of testosterone-related diseases in adults and children. In a previous study, testosterone was derivatized with methoxyamine and hydroxylamine in a multiplexed high turbulence liquid chromatography with heated-electrospray ionization-tandem mass spectrometry (HTLC-HESI-MS/MS) method. Using these reagents, differential mass-tagging of testosterone allowed different specimens to be combined in a single injection to increase assay throughput. However, interference was observed for hydroxylamine-derivatized testosterone in serum collected in serum separator tubes (SST). In the current study, our objectives were to (1) replace hydroxylamine with a new derivatizing agent not subject to interference and (2) develop an improved HTLC-HESI-MS/MS method for multiplexed total testosterone measurement. Methods Healthy male and female donor specimens were collected in SST and red-top tubes. Serum was mixed with stable isotope-labeled testosterone as internal standard (ISTD) prior to protein precipitation. Testosterone in the supernatants was derivatized, enriched by solid phase extraction, dried, and reconstituted. Specimens were injected on the HTLC system for on-line extraction, transferred to analytical columns, and eluted using binary gradient. Testosterone derivatives and ISTDs were detected and analyzed on a Triple Quadrupole Mass Spectrometer (Thermo) equipped with HESI. Ionization and multiple reaction monitoring (MRM) scan parameters were optimized for maximized ion transmission and sensitive, specific, and stable quantitation. MRM transitions were used as quantifiers and qualifiers for both testosterone derivatives. Also assessed were ion suppression using T-column infusion, specimen stability by storage in SST tubes at 4 °C, isobaric interference from dehydroepiandrosterone (DHEA), and carryover. Results Intra- and inter-assay coefficients of variation (CV%) for total testosterone levels were <5% at 12, 80, 250, and 1200 ng/dL for both testosterone derivatives. Limits of quantitation (LOQs) for both derivatives were <1 ng/dL. Calibration linearity was verified across the measurement range of 2.5–2000 ng/dL. Both agents were equivalent in derivatizing and recovering testosterone from serum based on a comparison of their quantitative results (R = 0.991, bias = −3.8 ng/dL). No interference was observed in serum collected in SST. Serum specimens collected in SST and red-top tubes from same donors gave equivalent results (R = 0.991, bias = 0.2 ng/dL). Ion suppression was calculated as less than 20% for both derivatives. CV% of the ion-ratios of both derivatives were less than 15% and were stable across the linear range. Testosterone levels were stable in SST for 72 h (at 4 °C) with the serum not separated from the gel. No isobaric interference and no carry over were observed. Conclusion We have developed and validated an improved multiplexed HTLC-HESI-MS/MS testosterone assay using new derivatizing agents. The current method allowed accurate, rapid, specific, and stable analysis of serum total testosterone. SST is an acceptable specimen type for the current method. Precision, accuracy, linearity, ion suppression, and sample stability in SST were validated.

Model for core catcher ablation and cavity shape in the film regime

During core meltdown in a nuclear reactor the corium may propagates toward the lower head and hit the vessel or structural elements as a coherent liquid jet. This could occur for instance in sodium fast reactors (SFR) if discharge tubes and an in-vessel core-catcher are used as mitigation devices. This can result in the ablation of the core-catcher and potential loss of its integrity. During ablation, a cavity is formed within the solid. Therefore the ablation of a solid structure by a liquid jet is studied here, with a focus on the cavity shape to improve future core-catcher designs. During the cavity formation, liquid flows over the cavity being formed as a liquid film in the film ablation regime, and ultimately results in the formation of a liquid pool. In the film ablation regime, two types of cavity shapes have been identified previously. To describe the process of the cavity formation, a mathematical model valid in this film ablation regime is here proposed which links the local melting rate to the local curvature of the cavity. It is applied with two sets of assumptions applicable to the two types of cavity previously identified. For the first assumption set, the heat transfer coefficient varies along the liquid/solid interface while the liquid temperature is held constant, it is representative of laminar boundary layer growth in laminar film. For the second assumption set, the heat transfer coefficient is held constant while the temperature varies along the liquid/solid interface, this is consistent with a turbulent liquid film. The two modeling approaches are compared with experimental data acquired from the HAnSoLO experimental setup. Numerical predictions show promising agreements with experimental observations, particularly for the laminar boundary layer growth zone of the cavity.

Effect of Isochronous Annealings on the Microstructure and Mechanical Properties of the Ti49.8Ni50.2 (at.%) Alloy after abc Pressing at 573 K

The regularities and features of the evolution of the grain–subgrain structure, phase composition and mechanical properties in Ti49.8Ni50.2 (at.%), depending on the temperature of isochronous annealings at 573–973 K are herein studied. The state of the Ti49.8Ni50.2 (at.%) alloy samples after abc pressing at T = 573 K with the given true strain e = 9.55 was taken as the initial state. It is shown that the grain–subgrain structure of the samples after annealing for 1 h in the temperature range of 573–673 K changes slightly. In samples annealed at 673 K, regions with the microband structure similar to the microstructure of a fast-frozen turbulent liquid flow were found. It has been established that during annealing at 773 K the beginning of an active recrystallization process is realized; the size of grains does not exceed the submicrocrystalline scale (~200 nm). At 873 K, the recrystallization process occurs in the entire volume of the samples; the grains with an average size of 2 ± 0.5 µm are almost equiaxed. The microstructure of the samples after annealing at 973 K (with average grain sizes of 5 ± 0.5 µm) is qualitatively similar to the microstructure of the samples after annealing at 873 K. It was found that the phase composition of the samples as a result of isochronous annealing at 573–973 K changes from R and B19’ immediately after abc pressing to a three-phase state: B2, R and B19’ phases. It is shown that the highest values of yield stress σy, ultimate tensile strength σUTS (1043 MPa and 1232 MPa, correspondingly) and low ductility (the deformation to fracture εf = 48%) are observed in the initial samples. Increasing the temperature of post-deformation annealing and, correspondingly, the development of recrystallization, led to a decrease in σy, σUTS and an increase in εf to the values of these characteristics in the coarse-grained samples (σy = 400 MPa, σUTS = 920 MPa and εf = 90%).

Combined Effect of Bubble Size and Gas Volume Fraction on Natural Convective Heat Transfer Enhancement in Homogeneous Bubbly Flow: Eulerian–Eulerian Numerical Simulations

Abstract Natural convective heat transfer can be enhanced through either fins or riblets, wall roughness elements, or the injection of bubbles in the flow. Bubble injections in a quiescent (pseudo-turbulent) liquid phase or an already turbulent liquid phase had been shown to enhance the natural convective heat transfer from literature. However, study of the combined effect of bubble size and gas volume fraction rather than individual effect on natural convective heat transfer enhancement for homogeneous bubbly flow is lacking. The present work intends to fill in that data gap through conducting numerical simulations to study the combined effect of bubble size and gas volume fraction on natural convective heat transfer enhancement. The present numerical work employs the validated interphase force models and the Eulerian–Eulerian model. ansysfluent is used to simulate a bubbly flow in a three-dimensional rectangular channel with a natural convective heat transfer. Bubbles ranging from microto millimeter diameter with inlet gas volume fraction varied in the range of 0.351–3.725% are injected upward to a quiescent liquid phase in a rectangular channel with a heated left wall and a cooled right wall. The flow regime is homogeneous without bubble coalescence and breakup effect. Validated computational models are employed to study the combined effect of bubble size and gas volume fraction on heat transfer enhancement. A relation between Nusselt number, bubble Reynolds number, Rayleigh number, nondimensional bubble size, and inlet gas volume fraction is constructed using the power regression method.

Approximate Method for Calculating the Velocity Profile of a Two-Dimensional Stationary Turbulent Liquid Flow

Approximate Method for Calculating the Velocity Profile of a Two-Dimensional Stationary Turbulent Liquid Flow

Evolution of turbulent liquid films on the corrugated plate—rivulets and slender water columns necking rupture

The evolution of turbulent liquid film on the corrugated plate is experimentally studied with the help of ultrasonic Doppler velocimetry and a high-speed camera, revealing the formation mechanism of rivulets and water columns necking rupture. The results show that the flow pattern of the liquid film on the corrugated plate is divided into three regions: stable region, fluctuating region, and oscillating region. In the fluctuating region, the connection between adjacent solitary waves leads to the generation of primary rivulets. In contrast, the formation of secondary rivulets mainly comes from the extinction of solitary waves. In the oscillating region, the collision between secondary rivulets promotes the formation of slender water columns. The necking diameter of the water column tended to decrease exponentially with time. The increase in Rel (liquid phase Reynolds number) promotes the necking rupture process of the water column due to the presence of corrugated structures. When Rel increased from 1.72 × 104 to 2.57 × 104, the characteristic time of necking rupture was shortened by about 25.7%.

Impact of the jet velocity on the turbulent liquid jet

Impact of the jet velocity on the turbulent liquid jet

An integral model for turbulent wave liquid film

An integral model for turbulent wave liquid film