Gravity-driven Flow Research Articles

Investigation of Moving Beds for Heat Recovery from Solid Granular

Moving beds have been regarded as a promising alternative for the heat recovery from the gravity-driven granular flow, which includes counter-current moving bed (CCMB) and gravity-driven moving bed (GDMB). However, the heat transfer characteristics still deserve investigating to optimise the direct heat transfer (CCMB) and the indirect transfer (GDMB), particularly for the appropriate particle size in different moving beds. In this paper, the simple analytical models were established to compare CCMB and GDMB in different particle sizes, which was interwoven with the effects of solid granular density, thermal conductivity, the inlet temperature. It was found that, as the technology significantly affected by the solid-to-gas ratio of mass flow rate, CCMB enables the efficient heat recovery for the particles larger than 3 – 4 mm. For the other fine solid granular, GDMB becomes a good candidate once there is enough heat transfer area, fins in the airside and particles mixing in the granular side. It has more advantages in the quick flow with the compact design. The study can provide useful suggestions for improvement and optimisation in the future.

A Theoretical and Experimental Study to Optimize Cell Differentiation in a Novel Intestinal Chip.

Microphysiological systems have potential as test systems in studying the intestinal barrier, in which shear stress is critical for the differentiation of Caco-2 cells into enterocytes. The most commonly used in vitro gut model for intestinal barrier studies is based on trans-well cultures. Albeit useful, these culture systems lack physiological shear stress which is believed to be critical for the differentiation of Caco-2 cells into enterocytes and to form tight monolayers. Conversely, organ-on-chip models have presented themselves as a promising alternative since it provides cells with the required shear stress. To this end, a novel biocompatible 3D-printed microfluidic device was developed. In this device, Caco-2 cells were seeded under physiologically-relevant unidirectional shear stress and compared to cells cultured under gravity-driven flow. Using numerical studies, the flow rate that corresponds to the required shear stress was calculated. Experimental tests were conducted to verify the effect of this on cell differentiation. The experiments clearly showed an enhancement of cell differentiation potential in a unidirectional physiologically-relevant pump-driven flow system (PDFS) as opposed to the simpler bidirectional gravity-driven flow system (GDFS). Additionally, computational modeling of an adapted design confirmed its ability to supply all cells with a more homogeneous shear stress, potentially further enhancing their differentiation. The shear stress in the adapted design can be well-approximated with analytic methods, thus allowing for efficient predictions for all parameter values in the system. The developed novel microfluidic device led to the formation of a tighter monolayer and enhanced functional properties of the differentiated Caco-2 cells, which presents a promising tool for preclinical in vitro testing of drugs in an animal-free platform.

Slab-parallel advection versus Rayleigh-Taylor instabilities in melt-rich layers in subduction zones: A criticality analysis

We show slab-parallel advection and Rayleigh-Taylor instability (RTI) as two competing gravity-driven flow mechanisms in the melt-rich layer atop a subducting slab. Scaled laboratory model results, supported by CFD simulations, indicate a transition of the RTI to advection mechanism at a threshold slab-dip angle (α) between 20° and 30°. The advection mechanism results in updip flow, forming a single plume at the upper edge of the melt-rich layer. Based on lubrication approximation, we present an analytical solution of the linear stability problem to perform a criticality analysis of α for the transition between RTI and advection, as observed in the experiments. The solution indicates this transition to occur at α⁎ = 28°, in favorable agreement with the experimental values. The article finally highlights the implications of this criticality analysis in interpreting the spatial distributions of subduction volcanism.

Instabilities and bifurcations of liquid films flowing down a rotating fibre

Abstract

An analytical comprehensive solution for the superficial waves appearing in gravity-driven flows of liquid films

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.

Trapping of swimming microalgae in foam.

Massive foam formation in aquatic environments is a seasonal event that has a significant impact on the stability of marine ecosystems. Liquid foams are known to filter passive solid particles, with large particles remaining trapped by confinement in the network of liquid channels and small particles being freely advected by the gravity-driven flow. By contrast, the potential role of a similar retention effect on biologically active particles such as phytoplankton cells is still relatively unknown. To assess if phytoplankton cells are passively advected through a foam, the model unicellular motile alga Chlamydomonas reinhardtii (CR) was incorporated in a bio-compatible foam, and the number of cells escaping the foam at the bottom was measured in time. Comparing the escape dynamics of living and dead CR cells, we found that dead cells are totally advected by the liquid flow towards the bottom of the foam, as expected since the diameter of CR remains smaller than the typical foam channel diameter. By contrast, living motile CR cells escape the foam at a significantly lower rate: after 2 hours, up to 60% of the injected cells may remain blocked in the foam, while 95% of the initial liquid volume in the foam has been drained out of the foam. Microscopic observation of the swimming CR cells in a chamber mimicking the cross-section of foam internal channels revealed that swimming CR cells accumulate near channels corners. A theoretical analysis based on the probability density measurements in the micro chambers has shown that this trapping at the microscopic scale contributes to explain the macroscopic retention of the microswimmers in the foam. At the crossroads of distinct fields including marine ecology of planktonic organisms, fluid dynamics of active particles in a confined environment and the physics of foam, this work represents a significant step in the fundamental understanding of the ecological consequences of aquatic foams in water bodies.

Rivulet flow down a slippery substrate

A detailed analysis of small-scale locally unidirectional gravity-driven rivulet flow with prescribed volume flux down an inclined slippery substrate for a rivulet with either constant width (i.e., pinned contact lines) or constant contact angle is undertaken. In particular, we determine the effect of varying the Navier slip length λ (i.e., the strength of the slip at the solid–fluid interface) on the rivulet. The present analysis shows that the shape and size of the rivulet and the velocity within it depend strongly on the value of λ. Increasing the value of λ reduces the viscous resistance at the substrate and, hence, leads to a larger velocity within the rivulet, and so the prescribed flux is achieved with a smaller rivulet. In particular, in the limit of strong slip, λ → ∞, for a rivulet of a perfectly wetting fluid and a rivulet with constant width, the velocity becomes large and plug-like like O(λ1/2) ≫ 1, and the rivulet becomes shallow like O(λ−1/2) ≪ 1, while for a rivulet with positive constant contact angle, the velocity becomes large and plug-like like O(λ2/3) ≫ 1, and the rivulet becomes narrow like O(λ−1/3) ≪ 1 and shallow like O(λ−1/3) ≪ 1.

Numerical investigation of tube oscillation in gravity-driven granular flow with heat transfer by discrete element method

In this paper, the gravity-driven granular flow was investigated by discrete element method (DEM) in the moving bed heat exchanger with tube oscillation. The particle update, the particle contact and the heat transfer were all discussed around tube out-wall. Moreover, the heat resistance analysis was developed to reveal the heat transfer mechanisms. It was found that, tube oscillation can significantly improve heat transfer coefficients (h). The relative growth of locally optimal h varies from 59.2% to 22.6%, when the outlet velocity (u) ranges from 0.65 mm/s to 6 mm/s. In details, the heat transfer can be enhanced by tube oscillation due to the smoother flow in the upstream, the denser contact in the downstream and the more particle mixing inside the flow. However, the particle separation aside the tube has a negative effect simultaneously. Therefore, there is a best frequency (f) to optimize h. The frequency is inversely proportional to the amplitude (DA) and decreases with u. Furthermore, the larger DA can increase the best h. In the present study, the optimal h was obtained as f locates between 3 and 5 Hz at DA > 1 mm.

Contourites and bottom current reworked sands: Bed facies model and implications

The differentiation of pure turbidites and contourites from mixed deposits —as the bottom current reworked sands (BCRS) — in sedimentary cores and outcrops from the modern or ancient records is still challenging. An accurate evaluation of facies associations calls for detailed understanding of processes controlling these deep-water systems and how they record interactions of along- and down-slope processes. Connecting features to processes is of particularly relevant in the study of contouritic drifts that include sandy deposits. This research describes and interprets BCRS within a Pleistocene contouritic drift located along the middle continental slope of the Gulf of Cadiz. Seismic, wireline, and sedimentological analyses of sediment samples were applied to core material representing a muddy drift that hosts sandy deposits. A sedimentary sequence, comprising five facies (F1 to F5) is defined here; it records background sedimentation influenced by the initial deposition of a gravity-driven flow followed by bottom current reworking. It is moderately bioturbated and contains distinctive trace fossil assemblages, often dominated by ichnofabrics of the Planolites and Thalassinoides. These assemblages represent intermittent deposition between down-slope and along-slope processes during relatively short time scales. The sequence is defined as a partial bi-gradational contourite sequence including BCRS reworked from underlying turbiditic deposits due to the interaction of down- and along- slope processes within the contouritic drift and its adjacent contouritic channel. Longer-term trends include an increase and subsequent decrease in both sediment supply and bottom currents. The sedimentary facies model presented here represents a new end member for a mixed turbiditic-contouritic system in which turbiditic flows influence a contourite drift. As such, it may support basic sedimentological interpretation and petroleum exploration strategies.

Periodic instationarities of granular flows in conical hoppers

Granular flows through converging sections such as conical hoppers have been reported to be submitted to instationarities, which in certain circumstances can appear to be organized and periodic. In this paper, we explore this phenomenon by conducting discrete element modelling simulations of a 3D gravity-driven hopper flow and varying a large number of parameters such as hopper geometry and granular sample properties. Dedicated postprocessing techniques are developed and used to investigate the spatial and temporal patterns of these instationarities and to bring some understanding on the physics of this spontaneous phenomenon. Numerical results show that a clear structure appears for these instationarities, under the form of rapidly propagating waves relating variations in velocity magnitude and coordination number. While very faint, periodic variations of the sample density are also detected. The parametric study reveals that the self-organization of these variations requires a narrow set of conditions in terms of hopper geometry and intergranular contact friction coefficient.

Experimental Analysis of Velocity Distribution in a Coarse-Grained Debris Flow: A Modified Bagnold’s Equation

Today, Bagnold’s theory is still applied to gravity-driven flows under the assumption of uniform sediment concentration. This study presents findings of flume experiments conducted to investigate the velocity and concentration distributions within the debris body by using high-resolution images. The analysis has shown that the concentration and mobility of grains vary along the depth. A linear law to interpret the grains concentration distribution, starting from the knowledge of the packing concentration and of the surface concentration, Cs, has been identified. By considering such a law, modified expressions of the Bagnold’s number and the velocity in stony-type debris flows are also presented. By using these expressions, three regimes of motion have been identified along the depth, and the velocity profile within the debris body is determined as a function of the parameter Cs. It has been verified that the velocity profiles estimated by using the modified equation compare well (mean square error less than 0.1) with the literature’s measured profiles when Cs is correctly measured or estimated. Results of cutting tests, conducted for a sample of the used material, have also allowed us to verify that Cs could be determined as a function of the static friction angle of the material.

Stability of liquid film flow laden with the soluble surfactant sodium dodecyl sulphate: predictions versus experimental data

Gravity-driven liquid film flows laden with a soluble surfactant are considered, and aqueous solutions of sodium dodecyl sulphate (SDS) are taken as a case-study. Literature measurements of the critical Reynolds number for the onset of instability are set in perspective with predictions of linear stability theory. The theory is based on a Frumkin model of adsorption equilibrium, modified by the inclusion of finite compressibility of the adsorbed monolayer. Quantitative comparison between data and theory is first attempted in the limit of infinite wavelength. Though wave characteristics are satisfactorily predicted, the theoretical critical Reynolds number is an order of magnitude below measurements. This discrepancy is understood in terms of the large difference between momentum and mass diffusivities and indicates that the assumption of infinite wavelength is far more restrictive for the mass transfer than for the flow problem. Finite-wavelength effects are taken into account by numerical solution of the Orr–Sommerfeld eigenvalue problem, leading to predictions of maximum stabilization in good agreement with the measurements. Introduction of realistic values of monolayer compressibility improves further the agreement at high surfactant loadings. Finally, a strong stabilizing effect of salinity is confirmed.

Traction and attraction: haptotaxis substrates collagen and fibronectin interact with chemotaxis by HGF to regulate myoblast migration in a microfluidic device

Cell migration is central to development, wound healing, tissue regeneration, and immunity. Despite extensive knowledge of muscle regeneration, myoblast migration during regeneration is not well understood. C2C12 mouse myoblast migration and morphology were investigated using a triple-docking polydimethylsiloxane-based microfluidic device in which cells moved under gravity-driven laminar flow on uniform (=) collagen (CN=), fibronectin (FN=), or opposing gradients (CN-FN or FN-CN). In haptotaxis experiments, migration was faster on FN= than on CN=. At 10 h, cells were more elongated on FN-CN and migration was faster than on the CN-FN substrate. Net migration distance on FN-CN at 10 h was greater than on CN-FN, as cells rapidly entered the channel as a larger population (bulk-cell movement, wave 1). Hepatocyte growth factor (HGF) stimulated rapid chemotaxis on FN= but not CN=, increasing migration speed at 10 h early in the channel at low HGF in a steep HGF gradient. HGF accelerated migration on FN= and bulk-cell movement on both uniform substrates. An HGF gradient also slowed cells in wave 2 moving on FN-CN, not CN-FN. Both opposing-gradient substrates affected the shape, speed, and net distance of migrating cells. Gradient and uniform configurations of HGF and substrate differentially influenced migration behavior. Therefore, haptotaxis substrate configuration potently modifies myoblast chemotaxis by HGF. Innovative microfluidic experiments advance our understanding of intricate complexities of myoblast migration. Findings can be leveraged to engineer muscle-tissue volumes for transplantation after serious injury. New analytical approaches may generate broader insights into cell migration.

Stability of gravity-driven free-surface flow past a deformable solid: The role of depth-dependent modulus.

The linear stability of a Newtonian liquid layer flowing down an inclined plane lined with a deformable linear elastic solid characterized by a continuously varying modulus is analyzed in this study. A low-wave-number asymptotic analysis is performed to obtain an analytical expression for the complex wavespeed which shows striking similarity with the earlier results of Sahu and Shankar [Sahu and Shankar, Phys. Rev. E 94, 013111 (2016)10.1103/PhysRevE.94.013111] for gravity-driven flow of Newtonian fluid past a solid bilayer having constant shear modulus (in each layer) lined on a rigid inclined plane. This shows that a deformable solid layer having a continuously varying shear modulus can be treated as a generalization of a system having multiple solid layers of constant shear modulus. Also, in the low-wave-number limit, we show that the stability of the free surface is governed by the value of effective shear modulus G_{eff}, and not by the detailed spatial variation of the modulus. Here the effective shear modulus (H/G_{eff}=∫_{1}^{1+H}1/[E_{0}+E[over ¯](z)]dz, where [E_{0}+E[over ¯](z)] represents the modulus gradient function) characterizes the overall modulus of the elastic solid, which is obtained by treating the continuous variation to be the limit of the arrangement of solid layers of infinitesimal thickness (each having a constant shear modulus) in a series. At finite wave numbers, we show that the free-surface and the liquid-solid interface become unstable as we increase the value of Γ, where Γ indicates the ratio of viscous stresses in the fluid to elastic stresses in the solid. When the system is analysed for different types of spatial modulus variations, we find results similar to those of Gkanis and Kumar [Gkanis and Kumar, Phys. Rev. E 73, 026307 (2006)10.1103/PhysRevE.73.026307], i.e., when we have two different configurations of the shear modulus function that have the same spatially averaged modulus, but have different values at the interface, the system is more stable for the configuration having higher shear modulus at the liquid-solid interface. In a similar manner, when we examined systems having the same shear modulus at the liquid-solid interface and same average modulus, the more stable case is the one which has a higher value of shear modulus just below the interface. Thus the use of deformable solids with a depth-dependent modulus potentially offers more control in the passive manipulation of the instabilities.

Numerical Study of Heat Transfer in Gravity-Driven Particle Flow around Tubes with Different Shapes

In the present paper, the heat transfer of gravity-driven dense particle flow around five different shapes of tubes is numerically studied using discrete element method (DEM). The velocity vector, particle contact number, particle contact time and heat transfer coefficient of particle flow at different particle zones around the tube are carefully analyzed. The results show that the effect of tube shape on the particle flow at both upstream and downstream regions of different tubes are remarkable. A particle stagnation zone and particle cavity zone are formed at the upstream and downstream regions of all the tubes. Both the stagnation and cavity zones for the circular tube are the largest, and they are the smallest for the elliptical tube. As the particle outlet velocity (vout) changes from 0.5 mm/s to 8 mm/s at dp = 1.72 mm/s, when compared with the circular tube, the heat transfer coefficient of particle flow for the elliptical tube and flat elliptical tube can increase by 20.3% and 15.0% on average, respectively. The proper design of the downstream shape of the tube can improve the overall heat transfer performance more efficiently. The heat transfer coefficient will increase as particle diameter decreases.

Numerical study of heat transfer in gravity-driven dense particle flow around a hexagonal tube

In the present paper, the heat transfer of gravity-driven dense particle flow around a hexagonal tube is numerically studied. The velocity vector, time-averaged particle contacting number, particle contacting time and heat transfer coefficient of particle flow are carfully analyzed. Furthermore, the heat transfer performances of particle flow around a hexagonal tube, circular tube and elliptical tube are also compared. The results show that, the effect of top angle (Θ) on the particle flow around a hexagonal tube is noticeable. When Θ decreases from 120° to 60° (vout = 2 mm/s), the averaged heat transfer coefficient of particle flow would increase by 29.7%. The heat transfer performances of particle flow around different shape tubes are quite different. When Θ equals 60° (vout = 2 mm/s), as compared with circular tube, the averaged heat transfer coefficient of particle flow around an elliptical tube and a hexagonal tube increases by 17.2% and 20.5%, respectively.

Delineation of Hydraulic Flow Regime Areas Based on the Statistical Analysis of Semicentennial Shallow Groundwater Table Time Series

Shallow groundwater acts as an important source of water for the ecosystem, agriculture, drinking water supply, etc.; it is, however, among those water resources most sensitive to climate change, and especially to aridification. In the present study, the delineation of regional recharge and discharge zones of the Danube–Tisza Interfluve (Hungary, 8000 km2) is presented via the combination of multivariate time series and geomathematical methods to explore the subregions most sensitive to dewatering. The shallow groundwater level time series of 190 wells, covering a semicentennial period (1961 to 2010), were grouped into three validated clusters representing characteristically different subregions. Then, the subregions’ means and individual shallow groundwater level time series were investigated for long-term trends and compared with local meteorological variability (precipitation, evapotranspiration, etc.) to determine their regime characteristics. As a result, shallow recharge and discharge zones, a gravity-driven flow system, and the discharge zone of a deeper, overpressured flow system could be discerned with distinctive long-term changes in water levels. The semicentennial trends in shallow groundwater levels were significant (p < 0.05) in the recharge (−0.042 m y−1) and in the overpressured discharge zone (0.009 m y−1), and insignificant in the rest of the area (−0.005 m yr−1). The present results concur with previous findings from the area but provide a statistically sound and reproducible delineation of the regime areas on a much finer scale than before. With the determination of the different climatic processes driving the semicentennial trends prevailing in the shallow groundwater, the high vulnerability of the recharge zone is underlined, while the outlined overpressured flow system seems to act independently from semicentennial precipitation trends. This study provides a more in-depth picture of the long-term changes in shallow groundwater and its drivers in of one of the most important agricultural areas in Hungary. It outlines, in a generally applicable way, the most vulnerable subareas for irrigation relaying on shallow groundwater extraction. In addition, the results can help adaptation-strategy decision makers to initiate a more effective and area-focused intervention in the case of the predicted negative trends for vulnerable recharge areas under various climate change scenarios.

Length of standing jumps along granular flows down smooth inclines

Predicting the flows of dense granular media is still a challenging issue. Here, numerical discrete element method simulations are used to investigate the diversity of patterns within granular jumps that accompany height, velocity, and density discontinuities in gravity-driven free-surface flows. It is demonstrated that standing granular jumps can serve as a useful gauge for evaluating the dissipation mechanisms that govern the flowability of granular media.

Using a Data Driven Approach to Predict Waves Generated by Gravity Driven Mass Flows

When colossal gravity-driven mass flows enter a body of water, they may generate waves which can have destructive consequences on coastal areas. A number of empirical equations in the form of power functions of several dimensionless groups have been developed to predict wave characteristics. However, in some complex cases (for instance, when the mass striking the water is made up of varied slide materials), fitting an empirical equation with a fixed form to the experimental data may be problematic. In contrast to previous empirical equations that specified the mathematical operators in advance, we developed a purely data-driven approach which relies on datasets and does not need any assumptions about functional form or physical constraints. Experiments were carried out using Carbopol Ultrez 10 (a viscoplastic polymeric gel) and polymer–water balls. We selected an artificial neural network model as an example of a data-driven approach to predicting wave characteristics. We first validated the model by comparing it with best-fit empirical equations. Then, we applied the proposed model to two scenarios which run into difficulty when modeled using those empirical equations: (i) predicting wave features from subaerial landslide parameters at their initial stage (with the mass beginning to move down the slope) rather than from the parameters at impact; and (ii) predicting waves generated by different slide materials, specifically, viscoplastic slides, granular slides, and viscoplastic–granular mixtures. The method proposed here can easily be updated when new parameters or constraints are introduced into the model.

Thermodynamical analysis of heat transfer of gravity-driven fluid flow via fractional treatment: an analytical study

This paper presents that how the characteristics of thermal radiation depend on the temperature of unsteady gravity-driven thermal convection flow of an incompressible fluid. A mathematical aspect involves the fractional treatment to the governing equations of gravity-driven thermal convection flow which is based on new derivations of velocity field and temperature distribution. The fractional techniques namely Atangana–Baleanu and Caputo–Fabrizio have been implemented for investigating the general solutions of velocity field as well as temperature distribution. The general solutions are expressed in terms of new defined special functions as Bessel–Maitland function $${\mathbf{J}}_{\upbeta }^{\alpha } (z)$$ and Wright function $${\mathbf{\varphi }}\left( {y,t,a,b} \right)$$ . The analytical solutions are tackled in the absence of thermal radiation by setting $$K_{1} \to 0$$ , horizontal plate by putting $$\cos \alpha \to 1,\,\sin \alpha \to 0$$ and $$\alpha \to 0$$ , vertical plate by putting $$\cos \alpha \to 0,\,\sin \alpha \to 1$$ and $$\alpha \to \frac{\pi }{2}$$ . The comparison of classical verses fractional results is depicted graphically and has proved to be very useful for gaining better insight into the interpretation of various rheological parameters.