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British Society of Rheology, Mid-Winter Meeting 2017

Monday 18th December 2017

Session 1 (TALKS) 11:00-11:30

Alan Whittington, KEYNOTE University of Missouri, Columbia, USA

Lava in the lab: quantifying the main variables in the rheology of multiphase magmas. Magma rheology exerts a fundamental control on volcanic activity. A thorough understanding of three-phase rheology and its dependence on temperature, composition, etc. is necessary to do accurate physics-based modeling of conduit processes and lava flows, and to be able to interpret how past volcanic landforms were produced, both on Earth and other planets. Experiments on lava are more complex than those on most analog materials, because we have to consider chemical and thermal interactions between components in the suspension, in addition to physical interactions. One approach is to break the problem down into tractable components. Starting with single phase magma, the viscosity of silicate liquids as a function of composition and temperature is well understood and can be modeled empirically or using thermodynamic theory. Basaltic lava flows can increase in viscosity from under 100 Pa s at the eruption temperature of ~1200˚C, to more than 1012 Pa s on quenching to glass at ~700˚C. Rhyolitic lava flows, have a highly polymerized melt structure, erupt at lower temperatures and higher viscosities. Dissolved water has a strong decreasing effect on viscosity, and water contents decrease as magmas ascend towards lower pressure at the surface. Most lavas are three-phase suspensions containing both crystals and bubbles. The main factors affecting their rheology are crystal and bubble fraction, and their size distributions. Both crystals and bubbles result in a transition from Newtonian to other rheological behaviors such as Bingham, power-law, and Herschel-Bulkley. Which of the many variables (temperature, composition, crystal content, bubble content, strain rate) exerts the main controls on rheology depends on the specific example, and can change throughout the eruption history of a single quantum of lava. Feedbacks between magma physics, chemistry, heat flow and rheology are fascinating and complex, and will provide a rich area of study for many years to come.

11:30-12:00 Oryaelle Chevrel, KEYNOTE

Université Clermont Auvergne, FRANCE Rheological control of lava flow emplacement

In this work, we focus on our understanding of the complexity of lava flow mechanical behavior and its influence on emplacement. Lava flows are multiphase fluid travelling downslope whose velocity and length depend on the characteristics of the eruption such as emitted lava volume, output rate and underlying topography and the rheology of the lava itself that is directly linked to its temperature and to its chemical and physical properties (chemical composition, redox state, volatile content, and shape and size of bubbles and crystals). During flowing downslope, the lava rheology continuously changes upon cooling, degassing and crystallization. This dynamic process has a direct influence on lava flow emplacement because it controls its speed and leads to cessation of the flow when the rheological parameters are such that they impede further motion. This rheological control needs to be well understood in order to model and predicts lava flow paths. Here we will see how the rheology of lava flows is known and measured; and which rheological models are used to describe their emplacement dynamics.

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12:00-12:20 Simone Colucci 1, Federico Brogi 1,2, Paolo Papale 1

INGV, ITALY From 1D to 3D simulations of multiphase magmatic flows with real properties

Rheology is known to play a major role in controlling the dynamics of magmatic flows. Although magmas can exhibit a non-Newtonian rheology arising from the presence of dispersed phases, either solid particles or gas bubbles, many models include the simplifying assumption of Newtonian rheology. We have developed a quasi-2D multiphase flow model of magma ascent along the volcanic conduit that extends a previous numerical code incorporating a constitutive equation to describe the non-Newtonian behavior of gas bubble-bearing magmas. A parametric study varying the melt viscosity and the water content reveals that non-Newtonian effects can be large for low-viscosity magmas, resulting in plug-like distribution of velocity and an increasing mass flow-rate of the eruption. Current advances towards multiphase 3D flows include the development of magmaFoam, a computational tool built on the open source library openFoam. MagmaFoam includes equations of states for real magmas, constitutive equations for complex rheologies, thermal properties of magmatic mixtures and thermodynamics and kinetics of phase change. Preliminary test results describing the consequences of simplifying assumptions regarding the behavior of real magmas will be shown. 1 Istituto Nazionale di Geofisica e Vulcanologia INGV, sezione di Pisa (Italy) 2 Istituto Nazionale di Oceanografia e di Geofisica Sperimentale, OGS, Trieste (Italy) 12:20-12:40

Janine L. Kavanagh *a, Alec J. Burns b, David J.C. Dennis b University of Liverpool, UK

The impact of rheology on fluid dynamics within experimental volcanic plumbing systems The rheology of magma is of fundamental importance to a wide spectrum of intrusive and extrusive volcanic phenomenon. Magma is a multiphase fluid that comprises melt (liquid rock), crystals and bubbles, but the relative proportions of these distinct components varies as the magma ascends, depressurises and cools. Magma rheology controls how magma transits the Earth’s crust in fractures called dykes, influencing the tendency for dykes to erupt, and the potential for them to stall at depth and build magma chambers capable of feeding the largest volcanic eruptions on Earth. The dynamics of magma ascent in dykes in nature can be monitored using geophysical networks and by studying ancient volcanic systems, where the host-rock damage and solidified magma may record evidence of dyke propagation and magma flow. Laboratory experiments have proved to be an important tool to help bridge the diverse information available from studying dykes in nature and to test ascent models. We present results from laboratory experiments where a range of Newtonian and non-Newtonian magma analogues are used to explore the impact of magma rheology on dyke dynamics. The fluids represent a spectrum of magmas from melt-rich to crystal- and/or bubble-rich. An experimental dyke is created by injecting the fluid at constant flux into the base of a homogenous elastic medium that represents the Earth’s crust. Passive-tracer particles in the fluid are fluoresced by a laser sheet, and post-processing of the experimental images using particle image velocimetry (PIV) quantifies the evolving flow velocities within the growing dyke. The PIV patterns reveal channelization, recirculation and jet-instability within the growing dyke. The results have wide implications for interpreting magma propagation in nature; including the physical, geochemical, petrological, magnetic, and atmospheric evidence of magma intrusion before, during and between e ruptive episodes. a Department of Earth, Ocean and Ecological Sciences, University of Liverpool, Liverpool L69 3GP, United Kingdom b School of Engineering, University of Liverpool, Liverpool L69 3GH, United Kingdom * Corresponding author: Janine.Kavanagh@liverpool.ac.uk

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12:40-13:00 Gautier Nicoli 1,2, Marian Holness 1, Rob Farr 3, Jerome Neufeld 1,2,4

University of Cambridge, UK Olivine size distribution in mafic intrusions: evidence for settling from turbulently convecting

magma, Little Minch Sill Complex, Scotland The evolution of mafic intrusions depends on the physical behaviour of crystal-bearing magmas. Recent work has argued that coarsening-upwards crystal accumulations on the floor of magma bodies are evidence that settling occurred from a vigorously convecting magma. In this study, we demonstrate that convection can be also detected by close analysis of a fining-upwards crystal accumulation. In the case of gravitational settling from a static magma, the sedimentation rate of particles (i.e. cluster or single grain) is determined by their Stokes’ velocity and leads to a fining-upwards sequence characterised by the complete disappearance of progressively smaller size classes upwards in the accumulation. On the other hand, settling from a vigorously convecting magma creates a fining-upwards sequence characterized by a gradual phasing out of each size class instead of the abrupt termination of size classes seen for settling from a static magma. The cumulative distribution curves describing the size distribution of olivine grains in a fining-upwards accumulation on the floor of a picrodolerite-crinanite sill from the Little Minch Sill Complex (Isle of Skye, Scotland ) depart significantly from those expected for a simplified settling model of the original crystal cargo from either a static or a convecting magma. In particular, the upper parts of the fining-upwards sequence contain too many large particles, which therefore must have remained in suspension in the magma until late times before they accumulated on the floor of the sill. Therefore, with the absence of significant overgrowth, we argue that this over-abundance of large particles is the record of continued cluster formation by synneusis of suspended particles in a turbulently convecting magma. 1 Department of Earth Sciences, University of Cambridge 2 BP Institute for Multiphase Flow, University of Cambridge 3 Jacobs Douwe Egberts, Banbury, Oxfordshire 4 Department of Applied Mathematics and Theoretical Physics, University of Cambridge

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British Society of Rheology, MIdWinter Meeting 2017

Monday 18th December 2017

Session 2 (TALKS) 14:00-14:30

Elisabeth Guazzelli, KEYNOTE Aix Marseille University, FRANCE

Rheology of dense granular suspensions Dense suspensions of non colloidal particles are materials with broad applications both in industrial processes (e.g. waste disposal, concrete, drilling muds, metalworking chip transport, pulp and paper, and food processing) and in natural phenomena (e.g. flows of slurries, debris, and lava). Despite its long research history and its practical relevance, the mechanics of dense suspensions remain poorly understood. The major difficulty is that the grains interact both by hydrodynamic interactions through the liquid and by mechanical contact. These systems thus belong to an intermediate regime between pure suspensions and granular flows. We show that we can unify suspension and granular rheology under a common framework by transferring the frictional approach of dry granular media to wet suspensions of spherical particles. We also discuss non-Newtonian behaviour such as normal-stress differences and shear-induced migration. Beyond the classical problem of dense suspension of hard spheres which is far from being completely resolved, there are also entirely novel avenues of study concerning more complex mixtures of particles and fluids such as those involving other types of particles (e.g. fibres) or non-Newtonian fluids (e.g. yield-stress and shear-thickening fluids). Nott P., Guazzelli E, and Pouliquen O. 2011 The suspension balance model revisited, Phys. Fluids 23, 043304. Boyer F., Pouliquen O., and Guazzelli E. 2011 Dense suspensions in rotating-rod flows: normal stresses and particle migration, J. Fluid Mech. 686, 5-25 (Focus on Fluid: Hinch E. J. 2011 The measurement of suspension rheology, J. Fluid Mech. 686, 1-4). Couturier E., Boyer F., Pouliquen O., and Guazzelli E. 2011 Dense suspensions in a tilted trough: second normal stress difference, J. Fluid Mech. 686, 26-39. Boyer F., Guazzelli E., and Pouliquen O. 2011 Unifying Suspension and Granular Rheology, Phys. Rev. Lett. 107, 188301. Snook B., Davidson L. M., Butler, J. E., Pouliquen O., and Guazzelli, E. 2014 Normal stress differences in suspensions of rigid fibres, J. Fluid Mech. 758, 486-507. Dagois-Bohy S., Hormozi S., Guazzelli, E., and Pouliquen O. 2015 Rheology of dense suspensions of non-colloidal spheres in yield-stress fluids, J. Fluid Mech. 776, R2. Snook B., Butler, J. E., and Guazzelli, E. 2016 Dynamics of shear-induced migration of spherical particles in oscillatory pipe flow, J. Fluid Mech. 786, 128-153. Madraki, Y., Hormozi, S., Ovarlez, G., Guazzelli, E., and Pouliquen, O. 2017. Enhancing shear thickening. Phys. Rev. Fluids 2, 033301. Tapia, F., Shaikh, S., Butler, J. E., Pouliquen, O., and Guazzelli, E. 2017. Rheology of concentrated suspensions of non-colloidal rigid fibres, J. Fluid Mech. 827, R5. This work has been done in collaboration with F. Boyer, J. E. Butler, E. Couturier, S. Dagois-Bohy, L. M. Davidson, S. Hormozi,Y. Madraki, G. Ovarlez, O. Pouliquen, P. R. Nott, S. Shaikh, B. Snook, S. Strednak, F. Tapia.

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14:30-14:50 Nico Gray

The University of Manchester, UK A depth-averaged μ(I)-rheology for shallow granular free-surface flows

The μ(I)-rheology is a nonlinear viscous law, with a strain-rate invariant and pressure- dependent viscosity, that has proved to be effective at modelling dry granular flows in the intermediate range of the inertial number, I. This paper shows how to incorporate the rheology into depth-averaged granular avalanche models. To leading order, the rheology generates an effective basal friction, which is equivalent to a rough bed friction law. A depth-averaged viscous- like term can be derived by integrating the in-plane deviatoric stress through the avalanche depth, using pressure and velocity profiles from a steady-uniform solution to the full μ(I)- rheology. The resulting viscosity is proportional to the thickness to the three halves power, with a coefficient of proportionality that is angle dependent. When substituted into the depth- averaged momentum balance this term generates second-order derivatives of the depth-averaged velocity, which are multiplied by a small parameter. Its inclusion therefore represents a singular perturbation to the equations. However, it is shown that the depth-averaged μ(I)-rheology plays a crucial role in accurately predicting the growth rate of roll-wave instabilities, as well as the dependence of the cutoff frequency on the Froude number and inclination angle. The depth- averaged μ(I)-rheology also plays a vital role in regularizing the equations for segregation- induced fingering and levee formation, as well as for predicting erosion-deposition waves in geophysical mass flows (e.g. debris-flows, pyroclastic flows and snow avalanches). Gray, J.M.N.T. & Edwards, A.N. (2014) A depth-averaged μ(I)-rheology for shallow granular free-surface flows. J. Fluid Mech. 755, 503-534. Johnson, C.G., Kokelaar, B.P., Iverson, R.M., Logan, M., LaHusen, R.G. & Gray J.M.N.T. (2012) Grain-size segregation and levee formation in geophysical mass flows. J. Geophys. Res 117, F01032 Kokelaar B.P., Graham R.L., Gray J.M.N.T. & Vallance J.W. (2014) Fine-grained linings of leveed channels facilitate runout of granular flows. Earth Planet. Sci. Lett. 385, 172-180. Woodhouse M.J., Thornton A.R., Johnson C.G., Kokelaar B.P. & Gray J.M.N.T. (2012) Segregation-induced fingering instabilities in granular free surface flows. J. Fluid Mech. 709, 543-580. Baker J.L., Johnson C.G. & Gray J.M.N.T. (2016) Segregation-induced finger formation in granular free-surface flows. J. Fluid Mech. 809, 168–212. Edwards A.N. & Gray J.M.N.T. (2015) Erosion-deposition waves in shallow granular free-surface flows. J. Fluid Mech. 762, 35–67. A. N. Edwards, S. Viroulet, B. P. Kokelaar & J. M. N. T. Gray (2017) Formation of levees, troughs and elevated channels by avalanches on erodible slopes. J. Fluid Mech. 823, 278–315. 14:50-15:10

Thomas Barker The University of Manchester, UK

Partial Regularisation of the Incompressible μ(I)-Rheology for Granular Flow In recent years considerable progress has been made in the continuum modelling of granular flows, in particular the μ(I)-rheology, which links the local viscosity in a flow to the strain rate and pressure through the non-dimensional inertial number I. This formulation greatly benefits from its similarity to the incompressible Navier–Stokes equations as it allows many existing numerical methods to be used. Unfortunately, this system of equations is ill posed when the inertial number is too high or too low. The consequence of ill posedness is that the growth rate of small perturbations tends to infinity in the high wavenumber limit. Due to this, numerical solutions are grid dependent and cannot be taken as being physically realistic. Here we modify the μ(I)-rheology to make the equations well-posed for all inertial numbers below a large maximal limit. This allows us, for the first time, to reliably simulate complex two-dimensional flows such as decelerating flows on inclined planes and granular rollwaves.

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15:10-15:30 Olivier Roche 1, S. van den Wildenberg 1, R. Delannay 2, A. Mangeney 3, A. Valance 2

Université Clermont Auvergne, FRANCE Experimental study of the basal forces in geological granular flows

The basal forces are fundamental in controlling the emplacement of geological granular flows. We measured forces generated at the base of experimental granular flows of 1.5 mm glass beads. Our setup consisted of a reservoir which was connected to an inclined channel and from which particles were released at a controlled mass rate of 1-5 kg/s. The channel was 1.5 m-long, 0.3 m-wide, and had a smooth base. The flow thickness at the entrance of the channel was set by the aperture of the reservoir gate and varied from 0.5-2 cm. A plate inserted at the base of the channel was connected to a 3-component force-sensor that measured, at a sampling frequency of 3 kHz, the basal normal (N), the shear longitudinal (S) and transverse components of the force transmitted by the granular flows. Effective friction angles equal to atan (S/N) were obtained for slope angles varying from 13 to 84 degrees. At low angles (<20 degrees) the flows were in steady state at velocities <1 m/s, but at higher inclinations the flows were accelerating and their velocity at the plate-sensor device increased with the channel slope angle. The effective friction angles revealed three distinct regimes as the slope angle and the corresponding flow velocity increased: (i) for steady flows at slope angles <20 degrees the effective friction angle was equal to the slope angle, (ii) for intermediate slope angles of 20-50 degrees and velocities of ~1-3 m/s the effective friction angle reached a plateau of 21-22 degrees, and (iii) for high slope angles of 50-84 degrees the effective friction angle decreased to 18 degrees as the flow velocity increased to ~3 m/s. 1 Laboratoire Magmas et Volcans, Université Clermont Auvergne-CNRS-IRD, OPGC, Clermont-Ferrand, France. 2 Institut de Physique, Université de Rennes, France. 3 Institut de Physique du Globe, Paris, France. 15:30-15:50

B. Peter Kokelaar 1, R. S. Bahia 2, K. H. Joy 2, S. Viroulet 3 and J. M. N. T. Gray 4 University of Liverpool, UK

Granular avalanches on the Moon: Mass-wasting conditions, processes and features Seven lunar crater sites of granular avalanches are studied utilizing high-resolution images (0.42-1.3 m/pixel) from the Lunar Reconnaissance Orbiter Camera. All sites are slopes of debris extensively aggraded by frictional freezing at their dynamic angle of repose, four in craters formed in basaltic mare and three in the anorthositic highlands. Diverse styles of mass wasting occur and three types of dry-debris-flow deposit are recognized: (1) multiple channel-and-lobe type, with coarse-grained levees and lobate terminations that impound finer debris, (2) single-surge polylobate type, with sub-parallel arrays of lobes and fingers with segregated coarse-grained margins, and (3) multiple ribbon type, with tracks reflecting reworked substrate, minor levees and no coarse terminations. The latter type results from propagation of granular erosion-deposition waves down slopes dominantly of fine regolith and it is the first recognized natural example. Dimensions, architectures and granular segregation styles of the two coarse-grained deposit types are like those formed in natural and experimental avalanches on Earth, although the timescale of motion differs due to the reduced gravity. Influences of reduced gravity and fine-grained regolith on dynamics of granular flow and deposition appear slight, but we distinguish, for the first time, extensive remobilization of coarse talus by inundation with finer debris. The (few) sites show no clear difference attributable to the contrasting mare basalt and highland megaregolith host-rocks and their fragmentation. This lunar study offers a benchmarking of deposit types that can be attributed to formation without influence of interstitial liquid or gas. 1 School of Environmental Sciences, University of Liverpool, Liverpool L69 3BX, UK 2 School of Earth & Environmental Sciences, University of Manchester, Manchester M13 9PL, UK 3Institut de Physique du Globe de Paris, Sorbonne Paris Cité, 75005 Paris, France 4 School of Mathematics, University of Manchester, Manchester M13 9PL, UK

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British Society of Rheology, MIdWinter Meeting 2017

Tuesday 19th December 2017

Session 4 (TALKS)

9:30-10:00

Stuart Dalziel, KEYNOTE University of Cambridge, UK Dropping stuff with strength

Impacts of different material, whether due to natural phenomena or human activities, are important on a huge range of scales. The limiting cases of solid-solid, solid-liquid, liquid-solid and liquid-liquid are reasonably well understood, at least for rigid solids and Newtonian liquids. However, impacts where there is a finite 'strength' have received less attention. Here, using simple laboratory experiments, we shall explore the behaviour of a Newtonian droplet impacting a granular medium and impacts of yield-stress fluids. Although these scenarios have fundamental differences, they reveal common features that offer insight into geophysically relevant impacts. Understanding their differences provides insight into the level of detail needed to gain a more complete picture. 10:00-10:20

Joerg Laeuger Anton Paar

High Temperature Rheometry Rheometrical methods are well established for investigation on complex materials. An accurate temperature control is essential for correct results. However, standard heating accessories for commercial rheometers are limited to temperatures of about 500°C or 600°C. Many materials such as for example glass, ceramics, metals, and geological materials such as lava, are still below their glass transition and their melting points at these temperatures. Existing devices for evaluating the rheological behavior of such materials at high temperatures are often limited to being either of a simple viscometer type or individually designed self-made. In this contribution two devices are being described which extend the temperature range for doing full rheological measurements beyond its current limits. First, a redesigned convection oven, which still fits onto a standard commercial rheometer, allows measurements up to 1000°C in parallel-plate, concentric cylinder, and solid torsion bar geometries. With the later torsional DMTA investigations are possible. Second, a combination of a rheometer head with an external oven pushes the accessible temperature range up to 1800°C. In this device concentric cylinder geometries made of ceramics or platinum are used. Applications discussed in the paper range from glass, enamel, slags, aluminum alloys, basaltic melts to molten salt and demonstrate the high value of the described devices in performing high accurate and high precision rheological measurements at really high temperatures.

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10:20-10:40

Christopher Ness 1, Adam Khan 1, Amalia Thomas 2 and Nathalie Vriend 2 University of Cambridge, UK

Revealing particle-particle contact forces in flowing granular suspensions using photoelasticity From subsea landslides to industrial fluidized beds, submerged granular materials under flow pose an ongoing challenge to scientists and engineers. The particles self-arrange into fragile networks of contacts, leading to an unpredictable mechanical response that is distinct from that of the constituent solids and liquid. Consequently, the design of industrial processes and geohazard defenses often relies on inadequate constitutive equations and empiricism. Photoelastic disks provide a unique opportunity to address this issue experimentally. They refract light differently depending on the forces applied to them, allowing us to ‘see inside’ the material and observe the particle-particle forces directly. Here, we present for the first time our bespoke photoelastic suspension rheometer. The device comprises glass disks of 1m diameter, between which we suspend a monolayer of photoelastic particles in viscous liquid. An inner wheel drives a shear flow so that the set up operates as a 2D wide-gap couette rheometer. The glass confining walls allow us to shine polarized light through the suspension under flowing conditions, and the resulting fringe patterns on the suspended particles allow us to observe directly the intensity and distribution of particle-particle contacts. Using this device, we aim to precisely quantify the force transmission, and, importantly, to relate this microstructural information to the bulk stress-strain properties of the material in the dense regime. The findings will improve our ability to describe and predict a priori the flow properties of submerged granular materials. 1 Department of Chemical Engineering and Biotechnology, University of Cambridge, Cambridge CB3 0AS, United Kingdom 2 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom 10:40-11:00

Jim McElwaine Durham University, UK

High resolution imaging of snow avalanches: What we have learnt about avalanche dynamics. GEODAR, a custom radar system, images avalanches over the entire slope with high spatial (0.7m) and temporal (111Hz) resolution at the experimental test-site Vallee de la Sionne in Switzerland. Data has been aquired from 77 avalanches and these encompass a wide range of types. We can classify the flow regimes into seven types each with different rheological properties. The behaviour of the four dense flow regimes primarily depends on snow temperature and we show how this leads to different stopping mechanisms. A cold dense regime and a warm shear regime behave like non-cohesive granular flows with velocity shear throughout the flow. A sliding slab regime and a warm plug regime occur when cohesion dominates and causes the flow units to act as solid-like objects sliding on a thin shear zone. An intermittent regime connects the cold dense regime with the suspension regime, and is characterised by highly fluctuating density and surging activity. GEODAR enables localization of these flow regimes and transitions between them in time and space. We discuss flow regime transitions in terms of snow properties, topography, speed and size of the avalanches.

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British Society of Rheology, MIdWinter Meeting 2017

Tuesday 19th December 2017

Session 5 (TALKS) 11:20-11:40

Aurore Loisy University of Bristol, UK

Rheology of active suspensions: negative apparent viscosities, non-monotonic flow curves and multiple mechanical equilibria

Active suspensions, such as swarms of bacteria and the cytoskeleton of living cells, consist of anisotropic motile units interacting in a passive medium. Because these units self-organize and collectively induce mechanical stresses in the bulk, active suspensions exhibit unconventional rheological properties. For example, Lopez et al. (PRL 115, 2015) were able to measure, using a highly sensitive rheometer, zero and possibly negative values of the apparent viscosity in a suspension of E. Coli. In this talk, we will use a minimal model of an active liquid crystal to explain how a negative apparent viscosity is realisable in active suspensions. We will then show that this remarkable property is associated with a non-monotonic stress vs. strain rate flow curve. As a consequence, fixed stress and fixed strain rate ensembles are not equivalent for active fluids. This implies in particular that the outcome of a shear experiment fundamentally depends on the chosen ensemble, and means that the past history of a sample of such active matter affects how it will behave in the future. 11:40-12:00

Andrew I. Croudace, David Pritchard, Stephen K. Wilson University of Strathclyde, UK

Unsteady Flow of a Thixotropic Fluid in a Slowly Varying Pipe We use lubrication theory to develop the governing equations for unsteady axisymmetric flow of thixotropic fluid along a circular pipe of slowly varying radius. The strength of thixotropy is described by advective and temporal Deborah numbers, which are the ratios of the structure response timescale to, respectively, the timescales of advection and of an unsteady applied pressure gradient. In the regimes of 'weak thixotropy', in which the Deborah numbers are comparable to the small aspect ratio of the pipe, we follow the expansion method proposed by Pritchard, Wilson, and McArdle [J. Non-Newton. Fluid Mech. 238: 140-157, 2016] to obtain the effects of thixotropy and antithixotropy as perturbations to a generalised Newtonian flow. We present illustrative results for the Moore-Mewis-Wagner and Houska rheologies. Pritchard, Wilson, and McArdle (2016) showed that in a widening channel (or, by analogy, a decelerating flow), thixotropy increases the fluid velocity near the centre of the pipe and decreases it near the wall, while antithixotropy has the opposite effect. These results are generic for steady pipe flow, for thixotropic and antithixotropic fluids. However, unsteady pipe flow of an antithixotropic fluid is more complicated and the velocity profile depends on some subtle dynamical balances. In particular, we show that, rather unexpectedly, for some rheological models the velocity perturbation for a strongly antithixotropic fluid mimics that for a thixotropic fluid. Counter-intuitive behaviour also arises in the viscoplastic Houska model. Details of the analysis for the MMW and Houska models are given by Croudace, Pritchard, and Wilson [Phys. Fluids. 29: 083103, 2017]. These results cast doubt on the extent to which generic statements can be made about the effects of thixotropy and antithixotropy on lubrication flow.

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12:00-12:20 Simon Cox

Aberystwyth University, UK Foam Flow in Porous Media

Foams [1] are widely used as a way of displacing oil from partially-swept reservoirs, in so-called "enhanced" or "improved" oil recovery [2], and in the related application of soil remediation [3]. Continuum models of foam flow in porous media often neglect the local geometry of the lamellae, the influence of the walls, and the strong effect of the capillary pressure at the pore scale, so that it is difficult to interpret their predictions. This presentation will demonstrate how this lamella-scale structure can be used as the basis for models of foam rheology. Simulations of collections of lamellae traversing idealised rock pores allow us to show how the pore geometry influences the motion of, and the pressure difference across, each lamella [4]. By integrating the pressure differences in time [5], we are able to estimate the significant pressure drops required to force lamellae through porous media, i.e. the effective yield stress of the foam. Different pore geometries allow the importance of effects such as bubble break-up and route selection to be explored [6]. This research is supported by EPSRC (EP/N002326/1) and EU FP7 (PIAP-GA-2009-251475-HYDROFRAC). [1] I. Cantat et al. (2013) Foams: structure and dynamics. Oxford University Press, Oxford. [2] W.R. Rossen (1996) in R.K. Prud’homme and S. Khan (Eds.), Foams: Theory, Measurements and Applications, Marcel Dekker, New York. [3] S.A. Jones et al. (2013) Phys. Fluids. 25: 063101. [4] D.J. Ferguson and S.J. Cox (2013) Coll. Surf. A 438: 56-62. [5] S.J. Cox et al. (2004) Coll. Surf. A 245:143-151. [6] S.J. Cox (2015) Coll. Surf A. 473: 104-108. 12:20-12:40

Michal Solarski University of Birmingham, UK

Foam flow regimes in microfluidic channels of complex geometry Foams have been well researched in the past few decades due to their academic interest as well as numerous industrial applications such as froth flotation, enhanced oil recovery, food, consumer products and cosmetics. In many such applications foams are forced to flow through channels of various complex geometries such as valves, nozzles, narrow gaps and porous media. Since foams have complex structures that exhibit complex non-Newtonian viscoelastic and metastable behaviour, their flow dynamics through such complex geometries are poorly understood. Examples of relevant industrial applications include flow and moulding of aerated food products such as ice-cream and flow of foam-cement slurries in narrow oil-well annuli. The Deepwater Horizon (BP) oil spill caused by the failure of pumped foamed cement in 2010, is an example of the rheological challenges posed by foam flows. It is therefore crucial to be able to understand the various phenomena which characterise foam flow including topological changes, bubble coalescence, elongation and break-up, and foam regeneration under various flow conditions. Microfluidics is a useful tool for studying many fundamental multiphase flow problems with the ability to accurately control bubble volume and velocity. This paper reports on a fundamental study of well-controlled gas-liquid foam flow in a microfluidic channel containing narrow constrictions in the form of gradual/sudden contractions and expansions. The effect of the constriction geometry on the foam structure is analysed in terms of flow regimes including various patterns of bubble deformation, coalescence and break-up, as well as topological changes. Foam flow through these constrictions is studied as a function of gas and liquid flowrate, initial bubble size, liquid viscosity and surface tension.

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12:40-13:00 Arndt Ryo Koblitz

University of Cambridge, UK Interacting circular cylinders in viscoplastic media

We present direct numerical simulation (DNS) of interacting circular cylinders in a Bingham fluid. First, DNS of close pairwise interaction is compared to asymptotic solutions based on lubrication theory in the gap. We show that unlike for a Newtonian fluid, the macroscopic flow outside of the gap has a large effect on the pressure profile within the gap, and thereby on the resulting lubrication force. This has implications for the use of sub-grid-scale lubrication models in simulations of non-colloidal particulate suspensions in viscoplastic fluids. Second, we present DNS results for suspensions of cylinders at dilute and intermediate volume fraction in viscoplastic fluids, as a model for (i) particle sedimentation and (ii) suspensions under shear. In both cases the viscoplastic nature of the fluid leads to novel features when compared to the same systems in a Newtonian fluid.

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British Society of Rheology, MIdWinter Meeting 2017

Tuesday 19th December 2017

Session 6 (TALKS and AWARDS)

14:00-14:30

Adam Townsend, VERNON HARRISON AWARD and KEYNOTE University College London, UK

Adventures in Suspension Mechanics Suspension mechanics—the flow of a fluid with small fragments of solid material suspended in it—is an area of wide applicability in both industry and nature. Examples include the transport of silt in rivers, the manufacture of toothpaste, and inkjet printing where pigments remain solid within the ink. In this talk, I will share my experiences simulating flows of suspensions. I will look broadly at three investigations: how suspensions can themselves model viscoelastic fluids; how close we are to really understanding why cornflour-and-water suspensions (sometimes known as oobleck) shear thicken; and how the microstructure of a suspension can affect the motion of objects passing through it in surprising ways. I will discuss the things I have learnt about writing simulation software as we go along (and I promise to only curse Fortran once or twice) 14:30-14:50

Stephen Wilson University of Strathclyde, UK

Dispersion in Rivulet Flow Motivated by the need for a better understanding of the transport of solutes in microfluidic flows with free surfaces, the advection and dispersion of a passive solute in steady unidirectional flow of a thin uniform rivulet on an inclined planar substrate driven by gravity and/or a uniform longitudinal surface shear stress are analysed. Firstly, we describe the short-time advection of both an initially semi-infinite and an initially finite slug of solute of uniform concentration. Secondly, we describe the long-time Taylor-Aris dispersion of an initially finite slug of solute. In particular, we obtain the general expression for the effective diffusivity for Taylor-Aris dispersion in such a rivulet, and discuss in detail its different interpretations in the special case of a rivulet on a vertical substrate. This is joint work with Dr Fatemah Al Mukahal (now in the Department of Mathematics and Statistics, King Faisal University, PO Box 400, Hafouf 31982, Kingdom of Saudi Arabia) and Dr B. R. Duffy. F. H. H. Al Mukahal, B. R. Duffy and S. K. Wilson, “Advection and Taylor-Aris dispersion in rivulet flow,” to appear in Proc. R. Soc. A (2017) (doi: 10.1098/rspa.2017.0524) email: s.k.wilson@strath.ac.uk twitter: @S_K_Wilson

13

14:50-15:10

Rahul Chacko a, Romain Mari b, Suzanne Fielding a, Mike Cates b Durham University, UK

Fabric tensor dynamics of dense non-Brownian suspensions under shear reversal Despite the industrial importance of dense suspensions of hard particles, few constitutive models for them have been proposed or tested. Most of these are effectively “fabric evolution models” (FaEMs) based on a stress rule connecting the bulk stress to a rank-2 microstructural fabric tensor Q and a closed time-evolution equation for Q. In dense suspensions most of the stress comes from short-ranged pairwise steric or lubrication interactions at near-contacts, so a natural choice for Q is the deviatoric 2nd moment of the distribution P(p) of the near-contact orientations p. Here we test directly whether a closed time-evolution equation for such a Q can exist for inertialess non-Brownian hard spheres in a Newtonian solvent. We perform extensive numerical simulations for the evolution of P(p) under shear reversal, providing a stringent test for FaEMs. We consider a generic class of these as defined by Hand [1] constrained only by frame indifference, and conclude that no closed FaEM properly describes the dynamics of Q under reversal [2]. We attribute this to the fact that Q gives a poor description of the microstructure during large parts of the microstructural evolution following shear reversal. Specifically, the truncation of P(p) at 2nd spherical harmonic level describes two-lobed distributions of near-contact orientations, whereas on reversal we observe distributions that are markedly four-lobed; moreover dP/dt (p) has oblique axes, not collinear with those of Q in the shear plane. This structure likely precludes any adequate closure at second-rank level. Instead, our numerical data suggest that closures involving the coupled evolution of both a fabric tensor and a fourth-rank tensor might be reasonably accurate. [1] G. L. Hand, A theory of anisotropic fluids, J. Fluid Mech. 13, 33 (1962). https://doi.org/10.1017/S0022112062000476 [2] R. N. Chacko, R. M. Mari, S. M. Fielding, and M. E. Cates, arXiv:1707.01828 (2017). https://arxiv.org/abs/1707.01828 a Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, UK b DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, UK 15:10-15:40

Suzanne Fielding, ANNUAL AWARD and KEYNOTE Durham University, UK

Strain localisation during yielding of amorphous soft materials I will summarise recent progress concerning strain localisation in amorphous soft 'glassy' materials. In particular, I will show that shear banding may arise quite generically in these materials in protocols with a strong enough time-dependence as an inevitable consequence of certain signatures in the bulk rheological signals. These signatures include stress overshoot during shear startup (where the strain rate is jumped from zero to some constant value) and strain rate undershoot at the end of a regime of slow creep following the imposition of a step stress. The consequences of these findings for more general time dependent flows such as large amplitude oscillatory shear, in which the time-dependence is sustained, are also discussed. Time permitting, I will also show that these findings apply more widely still, for example in entangled polymeric fluids, suggesting that they may be generic across all complex fluids.