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The rheology of a fluid is often difficult to measure in situ and in real time. This work investigates whether it is possible to recover rheological information from direct field observations. We present a closed-form analytical solution for inverse problem of identification of the mobility coefficient in gravity-driven fluid flowed down an inclined plane. The lubrication approximation is used to model the three-dimensional thin film of fluid and the governing equation is solved numerically by the explicit finite difference method to calculate the fluid thickness. We show in this study that using very straightforward measurements of fluid thickness at only a few points and only two successive instants, the mobility coefficient of fluid flow can be estimated accurately. Then as an important application in Bingham fluids we show that the knowledge of the mobility coefficient together with velocity measurement at only one point and instant enable us to estimate temperature-dependent viscosity and yield stress of the Bingham fluid. Unlike other methods, the proposed method allows the local identification of the rheology which is particularly useful when the rheological parameters are functions of the local temperature and/or composition. The proposed inverse analysis is a non-iterative approach with negligible computational cost since our analysis revealed closed form formulae relating the rheological parameters to the local flow depth, its derivatives, and the local free surface velocity.

The force of attraction between two masses increases as gravity increases. Gravity is very important mechanism for mass transfer characteristics across the inclined shape. The significant purpose of current study is to examine amplitude in mass transfer under reduced gravity-driven flow. The impact of heat source/sink on periodic mixed convective gravity-driven flow across the inclined plate has been evaluated. The oscillatory characteristics of heat rate and mass transmission are explored at three inclined angles π/6, π/4 and π/3. The gravity is assumed under maximum temperature difference. The governing dimensional model is transformed into non-dimensional equations with appropriate scaling variables. The non-dimensional equations are again reduced in non-oscillatory, real and imaginary parts. For smooth coding, the primitive formulation is used with finite difference method to change non-dimensional forms in algebraic system. The algebraic equations are solved with Gaussian elimination scheme to display velocity field, temperature distribution and rate of concentration numerically. The impact of heat source/sink ±δ, reduced gravity Rg, buoyancy variable λT, modified buoyancy factor λC, Prandtl factor Pr, reduced gravitation factor Rg, and Schmidt variable Sc on the oscillating behavior of shear stress, rate of fluctuating heat transfer, and rate of fluctuating mass transfer is secured. It is found that the amplitude of fluid velocity and temperature increases for each parameter under heat source +δ=0.4. It can be seen that concentration distribution increases as reduced gravity Rg increases under heat sink −δ=0.3. It can be seen that amplitude of shearing stress and heat transfer increases as heat source +δ increases. It is obtained that oscillation in mass transfer increases as heat source/sink ±δ increases under reduced gravitation Rg=1.2.

Kinetic theory is used to propose and solve boundary value problems for fully developed, steady, dense gravity-driven flows of mixtures composed of identical inelastic spheres and water over both inclined erodible beds and rigid, bumpy bases confined by vertical sidewalls. We solve the boundary value problems assuming values of the mass density and of the size of the spheres typical of natural materials and show the numerical solutions for the profiles of the mean velocities of the particles and fluid, the intensity of the particle velocity fluctuations, and the granular concentration. In addition, we indicate how the features of the grain velocity fluctuations profile would influence segregation in three situations when the particle phase consists of two sizes of spheres: (1) the spheres are of the same material, and only gradients of temperature influence their segregation; (2) the mass densities of the material of the spheres are such that only gravity influences segregation; and (3) the mass densities are such that the coefficients of the temperature gradients and gravity segregation mechanisms are equal. For spheres of the same material, over a rigid bumpy base, the concentration of larger spheres increases from zero at the bed to the maximum value at the top of the flow; while over an erodible bed, this concentration has its maximum value at both the bed and the top of the flow. [ABSTRACT FROM AUTHOR]

The purpose of the current article is to explore the impact of thermal stratification and medium porosity on gravity-coerced transport of hybrid carbon nanotubes down an upright extending sheet inspired by a constant applied magnetic field along with heat transfer investigation in existence of thermal radiation, viscous dispersal, and joule heating effect. Rectangular coordinates are chosen for the mathematical interpretation of the governing flow problem. Homothetic analysis is employed for the sake of simplification process. The reduced system of coupled nonlinear differential equations is dealt numerically by dint of computational software MATLAB inbuilt routine function Bvp4c. The numerical investigation is carried out for the distinct scenarios namely, (i) Presence of favorable buoyancy force, (ii) Case of purely forced convection and (iii) Presence of opposing buoyancy force. Significant Findings: The key findings include that the presence of hybrid carbon nanotubes and medium porosity contributes significantly to upsurging surface shear stress magnitude whereas, external magnetic field and velocity slip effects in an altered manner. The present study may be a benchmark in study of fueling process in space vehicles and space technology.

The paper explores the gravity-driven flow of the thin film of a viscoelastic-fluid-based nanofluids (VFBN) along an inclined plane under non-isothermal conditions and subjected to convective cooling at the free-surface. The Newton's law of cooling is used to model the convective heat-exchange with the ambient at the free-surface. The Giesekus viscoelastic constitutive model, with appropriate modifications to account for non-isothermal effects, is employed to describe the polymeric effects. The unsteady and coupled non-linear partial differential equations (PDEs) describing the model problem are obtained and solved via efficient semi-implicit numerical schemes based on finite difference methods (FDM) implemented in Matlab. The response of the VFBN velocity, temperature, thermal-conductivity and polymeric-stresses to variations in the volume-fraction of embedded nanoparticles is investigated. It is shown that these quantities all increase as the nanoparticle volume-fraction becomes higher. [ABSTRACT FROM AUTHOR]

A reactive transport model has been developed to simulate the bio-chemo-hydro-mechanical coupled process associated with soil improvement by Microbially Induced Calcite Precipitation (MICP) in shallow submerged conditions. Besides including the key processes of bacterial attachment and decay, urea hydrolysis, and CaCO 3 precipitation, this study demonstrates the necessity to account for variable fluid density and associated gravity-driven flow, to select the appropriate boundary conditions by including the water adjacent to the sand as a separate domain and to include bacterial detachment. After fitting the parameters describing bacterial attachment, detachment, decay, and the reaction kinetics, the final precipitated calcium carbonate from the numerical simulations exhibits a decent agreement with the experimental results presented by Montoya et al. (2021) in terms of quantity and distribution pattern. However, still differences exist between the simulated and measured shear wave velocity (V s) and its increment through multiple treatment cycles, which suggests a more complex coupling between porosity, hydraulic conductivity, small strain stiffness, and the type or pore habit and heterogeneity of the distribution of the precipitated CaCO 3. The limitations of the model and directions for further development to capture the complexity of this coupled process are discussed. [ABSTRACT FROM AUTHOR]

An inverse analysis for simultaneous identification of three rheological parameters of non-Newtonian Herschel-Bulkley fluids from free surface data is presented. The three-dimensional gravity-driven thin film of the Herschel-Bulkley fluid flowed down an inclined plane is modeled using the lubrication approximation. The governing equation is solved by an explicit finite difference method to obtain the fluid thickness. Based on a defined least square objective function and a gradient-based minimization method (here steepest-descent method), linearly-independent explicit expressions are derived for sensitivity coefficients which enable us to estimate simultaneously three rheological parameters of Herschel-Bulkley fluids accurately using the transient readings at only one point (sensor). Three test cases are considered to reveal the accuracy and efficiency of the proposed inverse analysis.

Based on new explicit expressions for sensitivity coefficients, this study proposes a new method to solve two inverse problems in time-dependent three-dimensional gravity-driven thin film flow down an inclined plane governed by free-surface lubrication approximation. The flow is developed by time-dependent injection through a circular hole in the plane. The first inverse problem, a parameter estimation problem, consists in simultaneously estimating the temperature-dependent viscosity and a constant injection. The second inverse problem, a function estimation problem, involves the determination of the time-dependent injection. It is shown here that using the derived sensitivity coefficients, a parameter estimation approach can still be used for the second inverse problem, efficiently and accurately, and without the need to solve the adjoint and sensitivity problems as well as additional direct problem solutions.

We present an experimental and theoretical study of unsaturated flow in discrete fracture networks. The focus is on the breakthrough time of infiltrating liquid through the fracture networks as well as the spatial distribution of local flow status under a wide range of flow rates. Through visualized experiments, the fluid motion in the fracture network is recorded and analyzed, and gravity‐driven preferential pathways are observed. The location of the breakthrough path is found to be insensitive to the flow rate under the single‐inlet flow condition. Based on analogy with slug migration in a single fracture and considering liquid accumulation due to the capillary barrier effect at the fracture intersections, we propose a theoretical model of liquid breakthrough time through an initially dry fracture network. The theoretical predictions are found to be in excellent agreement with the experimental results. Using the model, we analyze the relative contribution of times needed for liquid migration and for local liquid accumulation to the breakthrough time. We also find that the spatial distribution of local flow status at the steady‐state varies significantly with the flow rate. The improved understanding and the proposed model are of significance for predicting the time required for a fluid/contaminant to reach a certain depth in unsaturated fractured media, and may provide new physical insights on the complex unsaturated flow dynamics. Key Points: We propose a theoretical expression of liquid breakthrough time through an unsaturated fracture networkModel predictions are in excellent agreement with results from carefully controlled visualized experiments of unsaturated flowRelative contribution of times for slug migration and local liquid accumulation to the breakthrough time is analyzed [ABSTRACT FROM AUTHOR]

This paper is devoted to analytical solutions for the base flow and temporal stability of a liquid film driven by gravity over an inclined plane when the fluid rheology is given by the Carreau–Yasuda model, a general description that applies to different types of fluids. In order to obtain the base state and critical conditions for the onset of instabilities, two sets of asymptotic expansions are proposed, from which it is possible to find four new equations describing the reference flow and the phase speed and growth rate of instabilities. These results lead to an equation for the critical Reynolds number, which dictates the conditions for the onset of the instabilities of a falling film. Different from previous works, this paper presents asymptotic solutions for the growth rate, wavelength and celerity of instabilities obtained without supposing a priori the exact fluid rheology, being, therefore, valid for different kinds of fluids. Our findings represent a significant step toward understanding the stability of gravitational flows of non-Newtonian fluids. [ABSTRACT FROM AUTHOR]

Understanding the mechanisms of liquid movement through fracture intersections is important for prediction of fluid flow and solute transport in unsaturated fractured media. Here we present a quasi‐static model to predict the dynamic splitting behavior of liquid slugs at a T‐junction, as a simplified representation of a fracture intersection and consisting of a main channel and a branch channel. The proposed model is validated against carefully controlled visualization experiments. We find that there exists a critical initial slug length at which the splitting behavior shifts from flow dominated by the main channel to that dominated by the branch. The influence of key parameters, including the inclination angle of the junction, the channel widths, and the dynamic contact angles, on the splitting dynamics is systematically investigated. We show that the splitting ratio depends nonmonotonically on the relative width of the branch channel to the main channel. Furthermore, it is demonstrated that the dynamic contact angles have a profound impact on the splitting ratios and meniscus velocities. It is shown that taking velocity‐dependent contact angle into account is essential to predict the meniscus velocities and the dynamic flow process. Key Points: A quasi‐static model for dynamic splitting of liquid slugs at a T‐junction is proposed and validated against experimentsA critical initial slug length is identified that separate two splitting regimesDynamic contact angles strongly impact meniscus velocities and splitting dynamics [ABSTRACT FROM AUTHOR]

Microfluidic nanoprecipitation makes use of hydrodynamic focusing (HF) to accurately control the diffusive mixing of reactants. Both stability and precise handling of flow streams are essential for this application. However, flow stability is hardly attained when fluids are supplied by syringe pumps, due to the unavoidable fluctuations associated to the driving mechanical system. The alternative use of hydrostatic pressure is constantly increasing in microfluidic laboratories, though precise mathematical descriptions have not been reported so far. This paper presents a quantitative model for the HF driven by gravity in slit microchannels. The model analytically predicts the focusing width of the sample stream from the relative heights of the sample and sheath reservoirs. Fluids with different densities and viscosities are considered, which impact on the pressure provided by the hydrostatic columns, as well as on the flow pattern of HF. Theoretical predictions were successfully validated against experimental data. Flow-focusing experiments were carried out in hybrid PMMA/OCA chips with slit microchannels, using fluids with different physicochemical properties. Finally, a color reaction induced by pH-shift was implemented as a practical example. Different levels of diffusive mixing and reaction were attained along the focused stream by varying the relative heights of the fluid columns, precisely as predicted by calculations. The model thus provides a rational basis for the design of HF experiments using hydrostatics. [ABSTRACT FROM AUTHOR]

Droplet microfluidics offers a wide range of applications, including high-throughput drug screening and single-cell DNA amplification. However, these platforms are often limited to single-input conditions that prevent them from analyzing multiple input parameters (e.g., combined cellular treatments) in a single experiment. Droplet multiplexing will result in higher overall throughput, lowering cost of fabrication, and cutting down the hands-on time in number of applications such as single-cell analysis. Additionally, while lab-on-a-chip fabrication costs have decreased in recent years, the syringe pumps required for generating droplets of uniform shape and size remain cost-prohibitive for researchers interested in utilizing droplet microfluidics. This work investigates the potential of simultaneously generating droplets from a series of three in-line T-junctions utilizing gravity-driven flow to produce consistent, well-defined droplets. Implementing reservoirs with equal heights produced inconsistent flow rates that increased as a function of the distance between the aqueous inlets and the oil inlet. Optimizing the three reservoir heights identified that taller reservoirs were needed for aqueous inlets closer to the oil inlet. Studying the relationship between the ratio of oil-to-water flow rates (Φ) found that increasing Φ resulted in smaller droplets and an enhanced droplet generation rate. An ANOVA was performed on droplet diameter to confirm no significant difference in droplet size from the three different aqueous inlets. The work described here offers an alternative approach to multiplexed droplet microfluidic devices allowing for the high-throughput interrogation of three sample conditions in a single device. It also has provided an alternative method to induce droplet formation that does not require multiple syringe pumps.

Gravity-driven thin film flow of two immiscible non-Newtonian Sisko fluids over a flat inclined plane is investigated. The equation, describing the flow, is nonlinear in nature and does not have a closed form of solution in general. In this study, the nonlinear governing differential equations are solved analytically by employing homotopy perturbation method (HPM). Besides, an exact solution for a special case of the non-Newtonian index is also obtained. The results of the solution based on HPM are compared with the exact solution for the special case, and it shows close agreement between the two results. This demonstrates the efficacy of HPM for solving nonlinear problems. The expression for the velocity is obtained, and the effects of various parameters like Sisko fluid parameters, density ratio, and viscosity ratio are also analyzed and discussed. The results indicate that with increase in the density ratio, it causes a significant increase in the velocity of fluids in both the layers and the velocities in both the layers are decreasing significantly with an increase in the Sisko fluid parameters. This study has got wider application in various industrial activities such as protective and decorative coating, painting. [ABSTRACT FROM AUTHOR]

Gravity-driven flows of liquid films are frequent in nature and industry, such as in landslides, lava flow, cooling of nuclear reactors, and coating processes. In many of these cases, the liquid is non-Newtonian and has particular characteristics. In this paper, we analyze numerically the temporal stability of films of non-Newtonian liquids falling by gravity, on the onset of instability. The liquid flows over an incline, where surface waves appear under certain conditions, and we do not fix a priori its rheological behavior. For that, we made used of the Carreau–Yasuda model without assigning specific values to its constants, and we compute general stability solutions. The numerical strategy is based on expansions of Chebyshev polynomials for discretizing the Orr–Sommerfeld equation and boundary conditions, and a Galerkin method for solving the generalized eigenvalue problem. In addition, an Inverse Iteration method was implemented to increase accuracy and improve computational time. The result is a robust and light numerical tool capable of finding the critical conditions for different types of fluids, which we use to analyze some key fluids. We show that the outputs of the general code match previous solutions obtained for specific computations. Besides increasing our knowledge on surface-wave instabilities in non-Newtonian liquids, our findings provide a new tool for obtaining comprehensive solutions on the onset of instability. • The stability of gravity-driven flows of non-Newtonian films is analyzed. • Equations based on the Carreau–Yasuda model are discretized with a Galerkin method. • A comprehensive code, that is valid for different kinds of fluids, is proposed. • Outputs of the comprehensive code match previous solutions of dedicated codes. • The code is robust, light and capable of accurately finding the critical conditions. [ABSTRACT FROM AUTHOR]

Spheroid-on-a-chip platforms are emerging as promising in vitro models that enable screening of the efficacy of biologically active ingredients. Generally, the supply of liquids to spheroids occurs in the steady flow mode with the use of syringe pumps; however, the utilization of tubing and connections, especially for multiplexing and high-throughput screening applications, makes spheroid-on-a-chip platforms labor- and cost-intensive. Gravity-induced flow using rocker platforms overcomes these challenges. Here, a robust gravity-driven technique was developed to culture arrays of cancer cell spheroids and dermal fibroblast spheroids in a high-throughput manner using a rocker platform. The efficiency of the developed rocker-based platform was benchmarked to syringe pumps for generating multicellular spheroids and their use for screening biologically active ingredients. Cell viability, internal spheroid structure as well as the effect of vitamin C on spheroids' protein synthesis was studied. The rocker-based platform not only offers comparable or enhanced performance in terms of cell viability, spheroids formation, and protein production by dermal fibroblast spheroids but also, from a practical perspective, offers a smaller footprint, requires a lower cost, and offers an easier method for handling. These results support the application of rocker-based microfluidic spheroid-on-a-chip platforms for in vitro screening in a high-throughput manner with industrial scaling-up opportunities., (© 2023 Wiley-VCH GmbH.)

The unexpected release of hazardous gases due to natural/industrial accidents or man-made disasters can have tragic consequences. Compared with other gaseous pollutants, heavy gases easily accumulate in personnel working areas and are more difficult to eliminate through existing mechanical ventilation systems. In this paper, to improve air quality in enclosed environments, the spatial characteristics of heavy gas dispersion were obtained based on an analysis of the basic properties of heavy gas dispersion. Schlieren experiments and image processing were conducted with shadow correction and noise reduction. The computational fluid dynamics (CFD) was used for predicting the dispersion of heavy gas. The numerical simulations cover a wide range of the densimetric Froude number (Fr) from 6.45 to 25.79, and a best-fit relation of Fr and the height of heavy gas fountain was provided. The radial velocity, radial density and axial density at cross-section of heavy gas dispersion were normalized using the unified scaling law. The axial density reached a minimum value at a height of 10 times the inlet diameter. Further decreases in the inertial force or decreases in the buoyant force can reduce the dilution of heavy gas by ambient fluids, which means that heavy gases diffuse faster and farther. An alternative method for estimating volume flux during gas dispersion using Fr was also proposed. • Visualization of heavy gas dispersion was realized through Schlieren experiments. • A best-fit relation of Fr(6.45∼25.79) and heavy gas fountain height was provided. • Normalization of spatial characteristics of dispersion by the unified scaling law. • A novel and concise method for estimating mass flux of dispersion was proposed. [ABSTRACT FROM AUTHOR]

Open Microchannel Manifold (OMM) with taper has been effective in enhancing heat transfer performance during flow boiling with low pressure drop. This makes it very attractive in low pressure drop systems like a thermosiphon loop. A gravity-driven flow boiling system was used to generate the performance data using ethanol at low flow rates. Based on the pressure drop and heat transfer data, a two-phase thermosiphon loop with a small ethanol head of 0.2 m was developed and tested with OMM configuration. A maximum heat flux of 136 W/cm 2 was recorded at a wall superheat of 42 °C resulting in a highest heat transfer coefficient of 34,100 W/m 2 K with 6% taper manifold. The thermosiphon loop provided a maximum flow rate of approximately 35 mL/min. Pressure drop data showed stable thermosiphon operation and a very low pressure drop of only 4 kPa near CHF. The heat transfer performance was independent of the orientation of the test section as the horizontal and the vertical upflow configurations yielding similar values of heat transfer. [ABSTRACT FROM AUTHOR]

The purpose of the current article is to explore the impact of thermal stratification and medium porosity on gravity-coerced transport of hybrid carbon nanotubes down an upright extending sheet inspired by a constant applied magnetic field along with heat transfer investigation in existence of thermal radiation, viscous dispersal, and joule heating effect. Rectangular coordinates are chosen for the mathematical interpretation of the governing flow problem. Homothetic analysis is employed for the sake of simplification process. The reduced system of coupled nonlinear differential equations is dealt numerically by dint of computational software MATLAB inbuilt routine function Bvp4c. The numerical investigation is carried out for the distinct scenarios namely, ( i ) Presence of favorable buoyancy force, ( i i ) Case of purely forced convection and ( i i i ) Presence of opposing buoyancy force. Significant Findings: The key findings include that the presence of hybrid carbon nanotubes and medium porosity contributes significantly to upsurging surface shear stress magnitude whereas, external magnetic field and velocity slip effects in an altered manner. The present study may be a benchmark in study of fueling process in space vehicles and space technology., Competing Interests: The authors declare the following financial interests/personal relationships which may be considered as potential competing interests., (© 2023 The Authors. Published by Elsevier Ltd.)

The turbulent flow characteristics of an isothermal dry granular dense matter with incompressible grains are investigated by the proposed first-order k- $${\varepsilon}$$ turbulence closure model. Reynolds-filter process is applied to obtain the balance equations of the mean fields with two kinematic equations describing the time evolutions of the turbulent kinetic energy and dissipation. The first and second laws of thermodynamics are used to derive the equilibrium closure relations satisfying turbulence realizability conditions, with the dynamic responses postulated by a quasi-linear theory. The established closure model is applied to analyses of a gravity-driven stationary flow down an inclined moving plane. While the mean velocity decreases monotonically from its value on the moving plane toward the free surface, the mean porosity increases exponentially; the turbulent kinetic energy and dissipation evolve, respectively, from their minimum and maximum values on the plane toward their maximum and minimum values on the free surface. The evaluated mean velocity and porosity correspond to the experimental outcomes, while the turbulent dissipation distribution demonstrates a similarity to that of Newtonian fluids in turbulent shear flows. When compared to the zero-order model, the turbulent eddy evolution tends to enhance the transfer of the turbulent kinetic energy and plane shearing across the flow layer, resulting in more intensive turbulent fluctuation in the upper part of the flow. Solid boundary as energy source and sink of the turbulent kinetic energy becomes more apparent in the established first-order model. [ABSTRACT FROM AUTHOR]

Rapid, isothermal, gravity-driven dry granular flows with incompressible solid grains down an incline are investigated by the thermodynamically consistent constitutive model. To this end, the revised Goodman-Cowin theory is applied for the time evolution of the volume fraction, in which a kinematic internal length is introduced. The Müller-Liu entropy principle is carried out to derive the equilibrium constitutive models, with their dynamic responses postulated in the context of a quasi-static theory. Numerical simulations show that both the volume fraction and velocity increase from the minimum values on the plane toward the maximum values on the free surface with an 'exponential-like' tendency, while the internal length increases in a logarithmic manner. With the equilibrated stress system in the revised Goodman-Cowin theory, the kinematic internal length is recognized as a characteristic length of the long-term enduring frictional contact and sliding between the grains (a characteristic length of the inelastic network among the grains). [ABSTRACT FROM AUTHOR]

The exact analytical solutions have been obtained for the problem of the gravity-driven rising of gas stored in a stratified aquifer. The practical objective is to retard gas rising in order to avoid its consecutive losses, which is ensured by low permeable horizontal barriers. The problem of gas rising through water is formulated as the Riemann problem for a system of first-order hyperbolic flow equations coupled with nonlinear algebraic equations describing the dissolution of chemical components in gas and water. The interaction of the forward front of gas with a barrier represents a collision between a shock wave and a medium discontinuity, which produces reverse shock waves and significantly retards gas rising. The method of solution is a combination between the method of characteristics and the technique of geometrical diagrams for coherent waves. The exact analytical solution was constructed for two- and three-component cases. The two-dimensional flow was studied numerically. [ABSTRACT FROM AUTHOR]

The paper proposes the involvement of preliminary regional hydrodynamic analysis for the reconnaisance phase water-based geothermal exploration in sedimentary basins. This approach is based on basin-scale pore pressure evaluation, it complements the usual reservoir and temperature analyses. Understanding of subsurface pore pressure distribution is beneficial not only in planning thermal water production but also in reinjection. The method is demonstrated for a sedimentary basin characterized by overpressured and superimposed gravity-driven flow. The key point of the approach is the understanding of regional pressure regimes and the delineation of the boundary of overpressured and gravitational flow domains. [ABSTRACT FROM AUTHOR]

There is a dear need for cooling high heal flux generating electronic devices using a dielectric fluid without using a pump. This paper explores the feasibility of employing ethanol as a dielectric fluid in a horizontal, open microchannel heat sink configuration with a tapered gap manifold to yield very low pressure head requirements. The paper presents experimental results for such a system utilizing ethanol as a working fluid under gravity-driven flow. A heat flux of 217W/cm² was dissipated with a pressure drop of only 9 kPa. The paper further presents parametric trends regarding flow rate and pressure drop characteristics that provide basic insight into designing high heat flux systems under a given gravity head requirement. Based on the results, interrelationships and design guidelines are developed for the taper, ethanol flow rate and imposed heat flux on heat transfer coefficient and gravity head requirement for electronics cooling. Reducing flow instability, reducing pressure drop, and enhancing heat transfer performance for a dielectric fluid will enable the development of pumpless cooling solutions in a variety of electronics cooling applications. [ABSTRACT FROM AUTHOR]

The complete thermodynamically consistent turbulent closure models of isochoric and isothermal dry granular dense flows with incompressible grains and weak turbulent intensity are established on the basis of a linearized theory with respect to the granular coldness for the dynamic responses of the closure conditions. The models are applied to study a gravity-driven stationary turbulent flow down an inclined moving plane, and the numerical simulations are compared with the experimental outcomes. It shows that while the mean velocity decreases monotonically from its boundary value on the moving plane toward the free surface, the mean porosity and granular coldness display more 'exponential-like' increasing/decreasing tendencies. Of particular interest is that the granular coldness evolves from its maximum value on the moving plane toward its minimum value on the free surface, leading to the turbulent dissipation evolving in a similar manner, while the turbulent kinetic energy demonstrate a reverse tendency. The obtained results show good agreements to the experimental outcomes and are similar to the characteristics of conventional Newtonian fluids in turbulent shear flows. [ABSTRACT FROM AUTHOR]

The Waipaoa River Sedimentary System in New Zealand, a focus site of the MARGINS Source-to-Sink program, contains both a terrestrial and marine component. Poverty Bay serves as the interface between the fluvial and oceanic portions of this dispersal system. This study used a three-dimensional hydrodynamic and sediment-transport numerical model, the Regional Ocean Modeling System (ROMS), coupled to the Simulated WAves Nearshore (SWAN) wave model to investigate sediment-transport dynamics within Poverty Bay and the mechanisms by which sediment travels from the Waipaoa River to the continental shelf. Two sets of model calculations were analyzed; the first represented a winter storm season, January–September, 2006; and the second an approximately 40 year recurrence interval storm that occurred on 21–23 October 2005. Model results indicated that hydrodynamics and sediment-transport pathways within Poverty Bay differed during wet storms that included river runoff and locally generated waves, compared to dry storms driven by oceanic swell. During wet storms the model estimated significant deposition within Poverty Bay, although much of the discharged sediment was exported from the Bay during the discharge pulse. Later resuspension events generated by Southern Ocean swell reworked and modified the initial deposit, providing subsequent pulses of sediment from the Bay to the continental shelf. In this manner, transit through Poverty Bay modified the input fluvial signal, so that the sediment characteristics and timing of export to the continental shelf differed from the Waipaoa River discharge. Sensitivity studies showed that feedback mechanisms between sediment-transport, currents, and waves were important within the model calculations. [ABSTRACT FROM AUTHOR]

Abstract: Development, characterization and application of a portable dual-channel analyzer based on gravity driven flow for continuous monitoring of CO2 in gas streams are presented. The analyzer is constructed from (i) a carrier/stripping solution reservoir, (ii) a diffusion scrubber (DS) in the form of a hollow fiber membrane (HFM) module integrated with a custom-designed flow-through pH-detector cell, and (iii) a waste solution reservoir. The analyzer is designed in such a way that the dilute sodium bicarbonate carrier/stripping solution flows downward by gravity into the lumen side of the hollow fibers in the HFM module which allows efficient contact with the gas stream. Absorption of CO2 into the carrier solution produces pH changes that constituted the analytical signal. Flat-bottom glass electrode and solid-state IrO2 electrodes were used as pH detectors in two types of custom-built flow cells, respectively. Under the optimized conditions, the measured pH signal showed Nernstian response to the CO2 concentration (59.6 and 62.0mV/log[CO2] and r2 =0.9992 and 0.9984 for the glass and IrO2 pH detectors, respectively) in the gas stream over a wide dynamic range (0.1-100 % CO2 in balance of nitrogen). Moreover, the presented analyzer based on either detector offered several favorable performance characteristics such as reasonably short response and recovery times; excellent signal stability and reproducibility and high selectivity in the presence of non-ionogenic gases, e.g., CH4, N2, O2, CO, etc. The suggested analyzer was applied successfully in the dual-channel monitoring of CO2 absorption from CO2-CH4 binary feed gas mixtures. [Copyright &y& Elsevier]

Highlights: [•] We developed a Smoothed Particle Hydrodynamics model to study droplet flow on rough surfaces. [•] The model is verified using empirical and semi-analytical solutions for a wide range of parameters. [•] Gravity driven flow on initially dry and prewetted surfaces is investigated. [•] Flow regimes based on Reynolds numbers and static contact angles are delineated. [•] Surface roughness is shown to systematically decrease droplet velocities. [ABSTRACT FROM AUTHOR]

HIV/AIDS is a growing global pandemic. A microbicide is a formulation of a pharmaceutical agent suspended in a delivery vehicle, and can be used by women to protect themselves against HIV infection during intercourse. We have developed a three-dimensional (3D) computational model of a shear-thinning power-law fluid spreading under the influence of gravity to represent the distribution of a microbicide gel over the vaginal epithelium. This model, accompanied by a new experimental methodology, is a step in developing a tool for optimizing a delivery vehicle's structure/function relationship for clinical application. We compare our model with experiments in order to identify critical considerations for simulating 3D free-surface flows of shear-thinning fluids. Here we found that neglecting lateral spreading, when modeling gravity-induced flow, resulted in up to 47% overestimation of the experimental axial spreading after 90?s. In contrast, the inclusion of lateral spreading in 3D computational models resulted in rms errors in axial spreading under 7%. In addition, the choice of the initial condition for shape in the numerical simulation influences the model's ability to describe early time spreading behavior. Finally, we present a parametric study and sensitivity analysis of the power-law parameters' influence on axial spreading, and to examine the impact of changing rheological properties as a result of dilution or formulation conditions. Both the shear-thinning index (n) and consistency (m) impacted the spreading length and deceleration of the moving front. The sensitivity analysis showed that gels with midrange m and n values (for the ranges in this study) would be most sensitive (over 8% changes in spreading length) to 10% changes (e.g., from dilution) in both rheological properties. This work is applicable to many industrial and geophysical thin-film flow applications of non-Newtonian fluids; in addition to biological applications in microbicide drug delivery. [ABSTRACT FROM AUTHOR]

Liquid food products stick to solid surfaces. This problem occurs in all supply chain steps from production to recycling. Although the basic problem has been known for a long time, the parameters influencing the interfacial adhesion have not been clarified yet. Here, two methods (product depletion test and tack test) to evaluate the adhesion of highly viscous liquids to solid surfaces have been developed. The product depletion test allows the assessment of the residue amounts and covered surface areas during the gravity-driven flow on an inclined plane. The tack test is conducted by filling the gap between two parallelly mounted, horizontally oriented plates with a liquid product and measuring the normal force while separating the plates by pulling off the upper plate under defined conditions. The influence of the experimental parameters on the maximum normal force (Fmax) could be shown. While the correlation between the pull off velocity of the upper plate and Fmax follows a power law, the dependency between the gap size and Fmax follows an exponential function. Although no significant correlation between Fm„ or the work of adhesion (Wa) and the solid's properties could be identified, a correlation between Fmax and Wa was observed. As shown by product depletion with ketchup, although the surface coverage is only slightly influenced by the packaging material, the opposite is the case for the covered surface area which, therefore, determines the residue amounts. For some coated samples a large residue reduction was observed. [ABSTRACT FROM AUTHOR]

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Abstract: The non-equilibrium Richards equation is solved using a moving finite element method in this paper. The governing equation is discretized spatially with a standard finite element method, and temporally with second-order Runge–Kutta schemes. A strategy of the mesh movement is based on the work by Li et al. [R.Li, T.Tang, P.W. Zhang, A moving mesh finite element algorithm for singular problems in two and three space dimensions, Journal of Computational Physics, 177 (2002) 365–393]. A Beckett and Mackenzie type monitor function is adopted. To obtain high quality meshes around the wetting front, a smoothing method which is based on the diffusive mechanism is used. With the moving mesh technique, high mesh quality and high numerical accuracy are obtained successfully. The numerical convergence and the advantage of the algorithm are demonstrated by a series of numerical experiments. [Copyright &y& Elsevier]

The steady, gravity-driven, incompressible, hydromagnetic, laminar flow of a viscous, electrically conducting, micropolar liquid along an inclined plane subjected to a uniform transverse magnetic field is examined, neglecting surface tension effects. The governing two-dimensional boundary layer equations in an (x, y) coordinate in the absence of pressure gradient are reduced to a pair of ordinary differential equations for linear momentum and angular momentum conservation subject to generalized micro-rotation and velocity boundary conditions at the plane surface. The film thickness is assumed uniform along the plane. The reduced conservation equations are then nondimensionalized and solved numerically with the network simulation method (NSM) and Sparrow-Quack-Boerner local non-similarity method (LNM) for a wide range of the governing dimensionless fluid dynamics parameters. Excellent agreement is obtained between the NSM and LNM solutions. The computations indicate that increasing micropolarity, i.e., Eringen number, elevates micro-rotation magnitudes but reduces linear velocity, i.e., decelerates the flow. The study has significant applications in magnetic field control of materials processing systems. [ABSTRACT FROM AUTHOR]

Abstract: The Waiapu River sedimentary system, New Zealand, provides a prototype for investigating the relative importance of wave- versus current-supported gravity flows on continental shelf deposition. A two-dimensional model was used to represent gravity-driven sediment transport and deposition on the Waiapu shelf over an annual cycle of storm events and associated Waiapu River floods. Model inputs of waves and wind-driven currents were derived from WAVEWATCH III hindcasts and constrained by benthic tripod data. The 12-month model run included a low-energy period (September 2003 to May 2004) with weak waves and currents and low river discharge, and a high-energy period (May to August 2004) with stronger waves and wind-driven currents and more frequent river floods. Model results suggested that during the low-energy period, riverine sediment was trapped between the 20- and 80-m isobaths. During the high-energy period, sediment was deposited obliquely across the shelf between the 60- and 120-m isobaths. The predicted deposit locations for the low- and high-energy periods, respectively, were consistent with short- and long-term observed accumulation patterns based on 7Be and 210Pb activity [Kniskern, T.A., Kuehl, S.A., Harris, C.K., Carter, L., 2010. Sediment accumulation patterns and fine-scale strata formation on the Waiapu River shelf, New Zealand. Marine Geology 270, 188–201]. Gravity flows were mainly wave-supported landward of the 60-m isobath, but became increasingly current-supported as wave orbital velocity attenuated in deeper water. Both analytical theory and numerical results indicated that wave-supported gravity currents were sensitive to local water depth and favored deposition parallel to isobaths as depth increased. In contrast, current-supported gravity currents were more sensitive to spatial variations in seabed slope, with seaward decreases in slope and along-shelf embayment of bathymetry favoring transport convergence and deposition. We conclude that the longer term (∼100yr) shelf-oblique mud deposit on the Waiapu shelf mainly reflects current-supported gravity flows responding to local variations in seabed slope and curvature of isobaths. [Copyright &y& Elsevier]

Free-surface flows of yield-stress fluids down inclined planes are modelled under the assumptions that they are shallow and sustained by a uniform oncoming stream to determine the steady state that emerges as the flow passes topographic features. In general, the flow may surmount the topography and be deflected around it depending on the thickness of the oncoming flow, the lateral extent and elevation of the mound, the inclination of the plane, and the magnitude of the yield stress relative to the gravitational stress of the flowing layer. Flows deepen upstream of mounds, with amplitude increasing with increasing yield stress. In the absence of a yield stress, flows around isolated mounds exhibit a maximum thickness at a location that is displaced laterally and downstream of the mound due to flow diversion. However, the location of the maximum thickness differs for yield-stress fluids: with increasing yield stress, the flow thickens immediately upstream of the mound and the deflected flux is diminished, leading to a sharp transition in the location of the maximum. Larger amplitude mounds may not be surmounted at all, leading to 'dry zones' downstream into which no fluid flows. It is shown that the steady shape of the dry zone is dependent on the initial condition, because the transient evolution towards it depends upon the plug at its margin, which is not unique. The results are computed by numerical integration of the governing equations and through their asymptotic analysis in various flow regimes to draw out the interplay of the dynamical processes. • Models of free-surface flow of yield-stress fluid around a topographic feature. • Flows deepen upstream of mounds, with amplitude increasing with yield stress. • The diversion of the flow by the mound is reduced at higher yield stresses. • For larger mounds, a 'dry zone' forms with non-unique shape due to the plugged edge. [ABSTRACT FROM AUTHOR]

Abstract: The growth of nanoporous alumina at an aluminium surface which is not completely covered by an electrolyte has been investigated. At one point the electrolyte forms three interfaces: oxide/electrolyte, metal/electrolyte, electrolyte/air. At this three-interfaces-point a self-wetting induced oxide growth occurs. The wetting increases up to 7mm from the electrolyte contact edge. At this final stage of wetting an equilibrium between the wetting induced flow (bottom-up) and the gravity-driven flow (top-down) is reached. The thickness of the nonporous layer decreases with the distance from the starting point. [Copyright &y& Elsevier]

Abstract: A disc infiltrometer with a disc diameter of 80 mm has been operated in the field at −0.2 kPa a few days after the spring of 2003 spraying of a mixture of bentazone and isoproturon on three dried tilled topsoils differing in texture but under the same climatic and vegetation conditions. In the first part of this series of papers, we characterized the transient water flow, allowing us to study the complementary transient herbicide transport in the studied field-dried topsoils. Proportions of initial herbicide which remained in the studied topsoils significantly decreased from the silt loam soil, where we suggested predominant capillary flow, to the sandy loam and silty clay soils, where we suggested a combination of capillary flow and gravity-driven transient flow. However, we attempted to use the capillary invasion theory to infer the retardation factors in the initially unsaturated soil aggregates, on the assumption of predominant transport of herbicide residues by capillary flow. We showed that the more clayey the soil, the more retarded was the invading herbicide against the invading water, the invading isoproturon being significantly more retarded than the invading bentazone, whatever the soil was, as it was expected from their significant difference of solubility in water. Moreover, the batch k d (or k f) sorption coefficient values were larger than their field capillary flow k d value counterparts. This discrepancy increased when the amount of organo-mineral clay increased and was also much more pronounced in this study, based on assumed capillary invasion of soil herbicide residues, than in laboratory studies carried out on mostly saturated soil columns under continuous flow conditions, but more experimental and conceptual work is required. [Copyright &y& Elsevier]

Abstract: A disc infiltrometer with a disc diameter of 80 mm has been operated in the field at −0.2 kPa few days after the Spring 2003 spraying of a mixture of bentazone and isoproturon on three dried tilled topsoils differing in texture but under the same climatic and vegetation conditions. We have derived both infiltration parameters from the disc infiltrometer records and capillary invasion parameters from the combined analyses of soil structure and soil water carried out on horizontal soil core slices of approximately 7 mm thickness. We assumed that the recorded transient flow can be subdivided into the capillary flow, estimated from sorptivity (differentiated linearization method), and the gravity-driven transient flow, calculated as the difference between the recorded total flow and the estimated capillary flow. Although gravity-driven flow occurred in this study, we assumed that capillary invasion theory is applicable because the topsoils were dry, leading to predominance of capillary flow, and the experiment was ended shortly after reaching the steady-state flow. Capillary invasion was the predominant transient flow process occurring into the silt loam soil whereas a combination of capillary flow and gravity-driven transient flow occurred into the sandy loam soil and the silty clay soil. Finally, capillary invasion theory was partly validated but more experimental and conceptual work is required. [Copyright &y& Elsevier]

Dispersion is an important component of transport in gravity-driven flow in porous media. However, its detailed modeling requires large computer powers and long calculation times. In this paper, we theoretically and experimentally investigate the conditions for which dispersion may be treated (1) as a simple constant or (2) as a more complex velocity-dependent term for flow in a homogeneous porous medium. The fundamental equations for fluid flow and solute transport in a porous medium are solved using an augmented Lagrangian algorithm. A general numerical code is developed in which the dispersion coefficient can be set as either a constant or as velocity-dependent. The theoretical results predicted by these two models are compared with those of our new laboratory experiments. We also theoretically analyze case scenarios not easily realizable in the laboratory. On the basis of these results we propose a method for estimating representative constant dispersion coefficients and discuss the conditions for which such simplification is valid. [ABSTRACT FROM AUTHOR]

Stability analysis of gravity-driven unsaturated flow is examined for the general case of Darcian flow with a generalized nonequilibrium capillary pressure-saturation relation. With this nonequilibrium relation the governing equation is referred to as the nonequilibrium Richards equation (NERE). For the special case where the nonequilibrium vanishes, the NERE reduces to the Richards equation (RE), the conventional governing equation for describing unsaturated flow. A generalized linear stability analysis of the RE shows that this equation is unconditionally stable and therefore not able to produce gravity-driven unstable flows for infinitesimal perturbations to the flow field. A much stronger result of unconditional stability for the RE is derived using a nonlinear stability analysis applicable to the general case of heterogeneous porous media. For the general case of the NERE model, results of a linear stability analysis show that the NERE model is conditionally stable, with lower-frequency perturbations being unstable. A result of this analysis is that the nonmonotonicity of the pressure and saturation profile is a requisite condition for flow instability. [ABSTRACT FROM AUTHOR]

Droplet microfluidics offers a wide range of applications, including high-throughput drug screening and single-cell DNA amplification. However, these platforms are often limited to single-input conditions that prevent them from analyzing multiple input parameters (e.g., combined cellular treatments) in a single experiment. Droplet multiplexing will result in higher overall throughput, lowering cost of fabrication, and cutting down the hands-on time in number of applications such as single-cell analysis. Additionally, while lab-on-a-chip fabrication costs have decreased in recent years, the syringe pumps required for generating droplets of uniform shape and size remain cost-prohibitive for researchers interested in utilizing droplet microfluidics. This work investigates the potential of simultaneously generating droplets from a series of three in-line T-junctions utilizing gravity-driven flow to produce consistent, well-defined droplets. Implementing reservoirs with equal heights produced inconsistent flow rates that increased as a function of the distance between the aqueous inlets and the oil inlet. Optimizing the three reservoir heights identified that taller reservoirs were needed for aqueous inlets closer to the oil inlet. Studying the relationship between the ratio of oil-to-water flow rates (Φ) found that increasing Φ resulted in smaller droplets and an enhanced droplet generation rate. An ANOVA was performed on droplet diameter to confirm no significant difference in droplet size from the three different aqueous inlets. The work described here offers an alternative approach to multiplexed droplet microfluidic devices allowing for the high-throughput interrogation of three sample conditions in a single device. It also has provided an alternative method to induce droplet formation that does not require multiple syringe pumps. [ABSTRACT FROM AUTHOR]

Pumpless microfluidic systems are easy-to-use devices that can be used to culture cells that are sensitive to mechanical shear, such as lymphatic endothelial cells. However, previously developed pumpless systems either provide unidirectional shear where the cell culture medium is discarded, or bidirectional shear that produces endothelial cell cultures with disease characteristics. Here, we describe a PDMS-based system that produces cyclically rising and falling shear that is unidirectional, similar to what has been reported in lymphatic vessels. The system can recirculate cell culture medium, making it possible for proteins and growth factors produced by the cell culture to remain in circulation. In addition, we describe the custom-made rotating platform that we used to create this unique flow pattern. Using this rotating platform, the microfluidic device can be used to grow confluent layers of lymphatic endothelial cells under physiologically relevant growth conditions., (© 2022. Springer Science+Business Media, LLC, part of Springer Nature.)

Deposits in dam areas of large reservoirs, which are commonly composed of fine-grained sediment, are important for reservoir operation. Since the impoundment of the Three Gorges Reservoir (TGR), the sedimentation pattern in the dam area has been unexpected. An integrated dynamic model for fine-grained sediment, which consists of both sediment transport with water flow and gravity-driven fluid mud at the bottom, was proposed. The incipient motion driven by gravity in the form of fluid mud was determined by the critical slope. Shallow flow equations were simplified to simulate the gravity-driven mass transport. The gravity-driven flow model was combined with a 3D Reynolds-averaged water flow and sediment transport model. Solution routines were developed for both models, which were then used to simulate the integral movement of the fine-grained sediment. The simulated sedimentation pattern agreed well with observations in the dam area of the TGR. Most of the deposits were found at the bottom of the main channel, whereas only a few deposits remained on the bank slopes. Due to the gravity-driven flow of fluid mud, the deposits that gathered in the deep channel formed a nearly horizontal surface. By considering the gravity-driven flow, the averaged error of deposition thickness along the thalweg decreased from −13.9 to 2.2 m. This study improved our understanding of the mechanisms of fine-grained sediment transport in large reservoirs and can be used to optimize dam operations. [ABSTRACT FROM AUTHOR]