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Papers by Tomás Trewhela

Journal of Fluid Mechanics, 2024

The feedback between particle-size segregation and rheology in bidisperse granular flows is studi... more The feedback between particle-size segregation and rheology in bidisperse granular flows is studied using the Stokes' problem configuration. A method of lines scheme is implemented to solve the coupled momentum and segregation equations for a normally graded particle size distributed bulk at constant solids volume fraction. The velocity profiles develop quickly into a transient state, decoupled from segregation yet determined by the particle size. From this transient state, the velocity profile changes due to the particles' relative movement, which redistributes the frictional response, hence its rheology. Additionally, the particles' relative friction is modified via a frictional coefficient ratio, by analogy with the particles' size ratio. While positive values of this coefficient exacerbate the nonlinearity of the velocity profiles induced by size differences, negative values dampen this behaviour. The numerical solutions reproduce well the analytical solutions for the velocity profile, which can be obtained from the steady-state conditions of the momentum and segregation equations for the transient and steady states, respectively. Segregation-momentum balances and four characteristic time scales can be established to propose two non-dimensional quantities, including specific Schmidt and Péclet numbers that describe broadly the segregation-rheology feedback. The proposed scheme, theoretical solutions and non-dimensional numbers offer a combined approach to understand segregation and flow dynamics within a granular bulk, extensible across many flow configurations.

Physical review fluids, May 21, 2021

We studied the segregation of single large intruder particles in monodisperse granular materials.... more We studied the segregation of single large intruder particles in monodisperse granular materials. Experiments were carried out in a two-dimensional shear cell using different intruder and media diameters, whose quotient defined a size ratio R that ranged from 1.2 to 3.333. When sheared, the intruders segregated and rotated at different rates, which depended on their R values and depth. The vertical intruder trajectories as a function of time were curved due to nonconstant depth-dependent segregation rates. An analysis that considered the lithostatic pressure distribution and a size ratio dependence was done to capture the trajectories and the general segregation rate behavior. As a result of a strain rate analysis, we observed a greater expansion rate around the intruders when R values were larger, which in turn promoted faster segregation. Experiments with large R values showed that intruder rotation was weak and local shear rates were low. In contrast, experiments with R closer to unity resulted in strong intruder rotation, high local shear rates, and contraction below the intruder. Therefore, an intruder with a diameter close to that of the medium was likely to segregate due to a rotation mechanism. We propose that large particle segregation depends on size ratio, local expansion rate, and, to a lesser extent, the local shear rate. Based on our observations we redefine large particle segregation as two well-defined processes dependent on R and the local strain rate.

Journal of Fluid Mechanics, Apr 20, 2021

Particles of differing sizes are notoriously prone to segregation in shear driven flows under the... more Particles of differing sizes are notoriously prone to segregation in shear driven flows under the action of gravity. This has important implications in many industrial processes, where particle-size segregation can lead to flow problems and reduced product quality, as well as longer product development and start-up times. Particle-size segregation also readily occurs in many hazardous geophysical mass flows (such as snow avalanches, debris flows and volcanic pyroclastic flows) and can lead to the formation of destructive bouldery flow fronts and significantly longer runouts. Although general theories exist to model particle-size segregation, the detailed functional dependence of the segregation flux on the shear rate, gravity, pressure, particle concentration, grain size and grain-size ratio is still not known. This paper describes refractive-index matched oscillatory shear-cell experiments that shed light on the segregation velocity in the two extreme cases of (i) a single large intruder rising up through a matrix of smaller grains, and (ii) a single small intruder percolating down through a matrix of large particles. Despite the sometimes markedly different time scales for segregation in these two situations, a unifying scaling law has been found that is able to collapse all the experimental data over a wide range of shear rates and grain-size ratios in the range [1.17, 4.17]. The resulting functional form is easily generalizable to intermediate concentrations and can quantitatively capture laboratory experiments and numerical simulations with a 50 : 50 mix of large and small grains.

Experiments in Fluids, Sep 25, 2021

This paper shows how a conveyor belt setup can be used to study the dynamics of stationary granul... more This paper shows how a conveyor belt setup can be used to study the dynamics of stationary granular flows. To visualise the flow within the granular bulk and, in particular, determine its composition and the velocity field, we used the refractive index matching (RIM) technique combined with particle tracking velocimetry and coarse-graining algorithms. Implementing RIM posed varied technical, design and construction difficulties. To test the experimental setup and go beyond a mere proof of concept, we carried out granular flow experiments involving monodisperse and bidisperse borosilicate glass beads. These flows resulted in stationary avalanches with distinct regions whose structures were classified as: (i) a convectivebulged front, (ii) a compact-layered tail and, between them, (iii) a breaking size-segregation wave structure. We found that the bulk strain rate, represented by its tensor invariants, varied significantly between the identified flow structures, and their values supported the observed avalanche characteristics. The flow velocity fields' interpolated profiles adjusted well to a Bagnold-like profile, although a considerable basal velocity slip was measured. We calculated a segregation flux using recent developments in particle-size segregation theory. Along with vertical velocity changes and high expansion rates, segregation fluxes were markedly higher at the avalanche's leading edge, suggesting a connection between flow rheology and grain segregation. The experimental conveyor belt's results showed the potential for further theoretical developments in rheology and segregation-coupled models.

Water Resources Research, 2019

In the spring of 1818, ice avalanches from the Giétro Glacier created an ice dam, which in turn f... more In the spring of 1818, ice avalanches from the Giétro Glacier created an ice dam, which in turn formed a glacial lake in the Drance Valley (Canton of Valais, Switzerland). Today, its maximum volume is estimated to have been 25×106 m3. Cantonal authorities commissioned an engineer named Ignaz Venetz to mitigate the risk of the ice dam's failure. He supervised the construction of a tunnel through which a large volume of water was drained as the lake rose (9×106 m3 according to his estimates and 11×106 m3 according to our model). After 2.5 days of slow drainage, the ice dam failed on 16 June 1818 and caused major flooding in the Drance Valley up to 40 km downstream, resulting in about 40 deaths. Venetz's lake monitoring notes, numerous testimonies gathered in the disaster's aftermath, and our field survey have made it possible to collect a wealth of information on this event, which is one of the world's major documented glacial lake outburst floods. Reconstructing major...

Minerals Engineering, 2014

The use of computational fluid dynamics gives new and interesting insights for risk analysis of c... more The use of computational fluid dynamics gives new and interesting insights for risk analysis of crosscountry ore hydraulic transport operations. In particular, they offer the possibility to predict, with reasonable accuracy, the progression and final condition of spills driven by pipeline leaks at selected locations, at a relatively modest computational cost. In this work, a depth-averaged, two-dimensional numerical model is used to simulate an ore concentrate pipeline rupture and subsequent spill, reproduced as a constant flow condition at the leak point. Although the model is well suited to solve the governing flow equations on arbitrary topographies by means of digital elevation models, two specific locations featuring relatively mild and steep slopes, are analysed with regard to their implications on the potential requirements for emergency team response. Results, obtained using different slurry rheologies, are compared with those obtained using a simpler, common flow resistance model derived for water flowing over rough surfaces.

Journal of Fluid Mechanics, 2024

The feedback between particle-size segregation and rheology in bidisperse granular flows is studi... more The feedback between particle-size segregation and rheology in bidisperse granular flows is studied using the Stokes' problem configuration. A method of lines scheme is implemented to solve the coupled momentum and segregation equations for a normally graded particle size distributed bulk at constant solids volume fraction. The velocity profiles develop quickly into a transient state, decoupled from segregation yet determined by the particle size. From this transient state, the velocity profile changes due to the particles' relative movement, which redistributes the frictional response, hence its rheology. Additionally, the particles' relative friction is modified via a frictional coefficient ratio, by analogy with the particles' size ratio. While positive values of this coefficient exacerbate the nonlinearity of the velocity profiles induced by size differences, negative values dampen this behaviour. The numerical solutions reproduce well the analytical solutions for the velocity profile, which can be obtained from the steady-state conditions of the momentum and segregation equations for the transient and steady states, respectively. Segregation-momentum balances and four characteristic time scales can be established to propose two non-dimensional quantities, including specific Schmidt and Péclet numbers that describe broadly the segregation-rheology feedback. The proposed scheme, theoretical solutions and non-dimensional numbers offer a combined approach to understand segregation and flow dynamics within a granular bulk, extensible across many flow configurations.

Physical review fluids, May 21, 2021

We studied the segregation of single large intruder particles in monodisperse granular materials.... more We studied the segregation of single large intruder particles in monodisperse granular materials. Experiments were carried out in a two-dimensional shear cell using different intruder and media diameters, whose quotient defined a size ratio R that ranged from 1.2 to 3.333. When sheared, the intruders segregated and rotated at different rates, which depended on their R values and depth. The vertical intruder trajectories as a function of time were curved due to nonconstant depth-dependent segregation rates. An analysis that considered the lithostatic pressure distribution and a size ratio dependence was done to capture the trajectories and the general segregation rate behavior. As a result of a strain rate analysis, we observed a greater expansion rate around the intruders when R values were larger, which in turn promoted faster segregation. Experiments with large R values showed that intruder rotation was weak and local shear rates were low. In contrast, experiments with R closer to unity resulted in strong intruder rotation, high local shear rates, and contraction below the intruder. Therefore, an intruder with a diameter close to that of the medium was likely to segregate due to a rotation mechanism. We propose that large particle segregation depends on size ratio, local expansion rate, and, to a lesser extent, the local shear rate. Based on our observations we redefine large particle segregation as two well-defined processes dependent on R and the local strain rate.

Journal of Fluid Mechanics, Apr 20, 2021

Particles of differing sizes are notoriously prone to segregation in shear driven flows under the... more Particles of differing sizes are notoriously prone to segregation in shear driven flows under the action of gravity. This has important implications in many industrial processes, where particle-size segregation can lead to flow problems and reduced product quality, as well as longer product development and start-up times. Particle-size segregation also readily occurs in many hazardous geophysical mass flows (such as snow avalanches, debris flows and volcanic pyroclastic flows) and can lead to the formation of destructive bouldery flow fronts and significantly longer runouts. Although general theories exist to model particle-size segregation, the detailed functional dependence of the segregation flux on the shear rate, gravity, pressure, particle concentration, grain size and grain-size ratio is still not known. This paper describes refractive-index matched oscillatory shear-cell experiments that shed light on the segregation velocity in the two extreme cases of (i) a single large intruder rising up through a matrix of smaller grains, and (ii) a single small intruder percolating down through a matrix of large particles. Despite the sometimes markedly different time scales for segregation in these two situations, a unifying scaling law has been found that is able to collapse all the experimental data over a wide range of shear rates and grain-size ratios in the range [1.17, 4.17]. The resulting functional form is easily generalizable to intermediate concentrations and can quantitatively capture laboratory experiments and numerical simulations with a 50 : 50 mix of large and small grains.

Experiments in Fluids, Sep 25, 2021

This paper shows how a conveyor belt setup can be used to study the dynamics of stationary granul... more This paper shows how a conveyor belt setup can be used to study the dynamics of stationary granular flows. To visualise the flow within the granular bulk and, in particular, determine its composition and the velocity field, we used the refractive index matching (RIM) technique combined with particle tracking velocimetry and coarse-graining algorithms. Implementing RIM posed varied technical, design and construction difficulties. To test the experimental setup and go beyond a mere proof of concept, we carried out granular flow experiments involving monodisperse and bidisperse borosilicate glass beads. These flows resulted in stationary avalanches with distinct regions whose structures were classified as: (i) a convectivebulged front, (ii) a compact-layered tail and, between them, (iii) a breaking size-segregation wave structure. We found that the bulk strain rate, represented by its tensor invariants, varied significantly between the identified flow structures, and their values supported the observed avalanche characteristics. The flow velocity fields' interpolated profiles adjusted well to a Bagnold-like profile, although a considerable basal velocity slip was measured. We calculated a segregation flux using recent developments in particle-size segregation theory. Along with vertical velocity changes and high expansion rates, segregation fluxes were markedly higher at the avalanche's leading edge, suggesting a connection between flow rheology and grain segregation. The experimental conveyor belt's results showed the potential for further theoretical developments in rheology and segregation-coupled models.

Water Resources Research, 2019

In the spring of 1818, ice avalanches from the Giétro Glacier created an ice dam, which in turn f... more In the spring of 1818, ice avalanches from the Giétro Glacier created an ice dam, which in turn formed a glacial lake in the Drance Valley (Canton of Valais, Switzerland). Today, its maximum volume is estimated to have been 25×106 m3. Cantonal authorities commissioned an engineer named Ignaz Venetz to mitigate the risk of the ice dam's failure. He supervised the construction of a tunnel through which a large volume of water was drained as the lake rose (9×106 m3 according to his estimates and 11×106 m3 according to our model). After 2.5 days of slow drainage, the ice dam failed on 16 June 1818 and caused major flooding in the Drance Valley up to 40 km downstream, resulting in about 40 deaths. Venetz's lake monitoring notes, numerous testimonies gathered in the disaster's aftermath, and our field survey have made it possible to collect a wealth of information on this event, which is one of the world's major documented glacial lake outburst floods. Reconstructing major...

Minerals Engineering, 2014

The use of computational fluid dynamics gives new and interesting insights for risk analysis of c... more The use of computational fluid dynamics gives new and interesting insights for risk analysis of crosscountry ore hydraulic transport operations. In particular, they offer the possibility to predict, with reasonable accuracy, the progression and final condition of spills driven by pipeline leaks at selected locations, at a relatively modest computational cost. In this work, a depth-averaged, two-dimensional numerical model is used to simulate an ore concentrate pipeline rupture and subsequent spill, reproduced as a constant flow condition at the leak point. Although the model is well suited to solve the governing flow equations on arbitrary topographies by means of digital elevation models, two specific locations featuring relatively mild and steep slopes, are analysed with regard to their implications on the potential requirements for emergency team response. Results, obtained using different slurry rheologies, are compared with those obtained using a simpler, common flow resistance model derived for water flowing over rough surfaces.