My research in rheology and thixotropy focuses on the mathematical and computational modelling of complex materials whose flow resistance and internal structure evolve with deformation and time. This work combines non-Newtonian fluid mechanics, constitutive modelling and numerical simulation to investigate the transport and deposition of sediment-rich and tailings materials.
A central aspect of my work is thixotropy: the time-dependent breakdown of material structure under shearing and its gradual recovery during periods of rest. These processes can strongly influence viscosity, yield stress, flow depth, velocity, runout distance, channel formation and the final geometry of deposited material.
I develop numerical models in which the Navier–Stokes equations are coupled with constitutive rheological relations and a transported structural parameter. This enables the material properties to evolve dynamically according to the local shear conditions and deformation history rather than being prescribed as constant values.
My work includes the implementation and comparison of different thixotropic formulations, including the Houska and Parent–Simms models, within free-surface flow simulations. Particular attention is given to numerical stability, fully implicit time integration, generalized coordinate systems, finite-volume discretization, adaptive free-surface grids and efficient multigrid solution methods.
The broader objective is to improve the physical realism and predictive capability of computational models for treated tailings, sediment–water mixtures and other complex fluids in which rheology evolves during transport, deposition and periods of rest.
Advanced Rheology and Thixotropy
My research addresses an important limitation of conventional flow-modelling approaches: time-dependent thixotropic behaviour is generally not represented in the standard rheological formulations used in conventional hydraulic and CFD modelling. This is particularly important for treated tailings and sediment-rich mixtures, where material structure can break down under shear and rebuild during periods of rest, substantially changing the subsequent flow and deposition behaviour.
I develop numerical models that couple the governing flow equations with constitutive rheological models and a dynamically evolving structural parameter. This allows viscosity, yield behaviour and material strength to evolve according to both the instantaneous flow conditions and the deformation history of the material.
The resulting framework provides capabilities beyond conventional time-independent rheological modelling. It enables direct investigation of how structural breakdown, recovery, shear history and changing rheology influence free-surface flow, runout and deposition. The integration of these processes within a fully coupled numerical flow model makes this research a distinctive and innovative contribution to computational rheology and thixotropic-flow modelling.
Areas of Expertise
Rheology and Thixotropic Behaviour
My expertise covers the physical and mathematical modelling of non-Newtonian and thixotropic materials, with particular emphasis on materials whose flow resistance, viscosity and internal structure evolve with deformation and time.
Non-Newtonian fluid mechanics
Time-dependent rheological behaviour
Thixotropy and structural evolution
Shear-rate-dependent viscosity
Constitutive rheological modelling
Houska thixotropic model
Parent–Simms thixotropic model
Coupling of rheology with flow dynamics
Free-surface flow of complex fluids
Flow and deposition of treated tailings
Sediment-rich and water–soil mixtures
A particular focus of my work is the coupling between material structure and flow. The local deformation history determines the evolution of the material structure and rheological properties, while those changing properties subsequently modify the velocity, stresses and overall flow behaviour. This two-way interaction is essential for realistically modelling thixotropic materials during transport, deposition, rest and remobilisation.
Computational Modelling of Thixotropic Flows
I develop numerical models for thixotropic free-surface flows in which fluid dynamics and time-dependent material behaviour are solved as a coupled system. The flow equations are combined with structural evolution equations so that the rheological properties evolve continuously according to the local deformation and shear history of the material.
Coupled flow and thixotropy equations
Transport equations for structural parameters
Time-dependent viscosity and yield behaviour
2DV Navier–Stokes-based flow formulation
Applied Finite Volume Method (FVM)
Generalized and curvilinear coordinate systems
Implicit time integration
Adaptive treatment of the free surface
Geometric multigrid solution methods
Numerical treatment of strongly varying viscosity
Normalization
A distinctive aspect of this work is the direct coupling between flow dynamics and the evolving material structure. The model can therefore represent how shearing changes the material properties during motion, how structure recovers during periods of rest, and how these changes subsequently influence flow, free-surface evolution and deposition.
Material structure → Rheological behaviour → Constitutive model → Structural evolution → Flow dynamics → Free-surface transport → Deposition and recovery
From Rheological Behaviour to Thixotropic Flow Simulation
Thixotropic flow modelling connects the physical behaviour of complex materials with constitutive rheology, structural evolution and computational fluid dynamics. My work covers this complete modelling chain, from understanding how material structure responds to deformation to simulating the resulting free-surface flow, spreading and deposition.
The rheological behaviour of the material is characterized, including yield behaviour, shear-dependent viscosity, structural breakdown under deformation and structural recovery during periods of rest.
The material behaviour is formulated mathematically using appropriate constitutive rheological relations together with a structural parameter that represents the evolving state of the material.
A structural evolution equation is coupled with the governing flow equations, allowing the rheological properties to evolve dynamically according to the local shear conditions and deformation history.
The coupled flow and thixotropy equations are discretized and solved numerically, including the treatment of strongly varying viscosity, free-surface deformation and nonlinear material behaviour.
The resulting model is used to investigate how thixotropy influences flow mobility, velocity, free-surface evolution, spreading, deposition, stopping and subsequent remobilisation.
My expertise therefore combines physical rheology, non-Newtonian fluid mechanics, constitutive modelling, numerical methods and free-surface flow simulation. The key distinction is that the material properties are not treated as fixed or determined only by the instantaneous flow conditions. Instead, the model accounts for the evolving structural state and the deformation history of the material.
In the Rijpdijk project, I applied a two-dimensional vertical (2DV)
curvilinear free-surface flow model to simulate the gravity-driven
movement of clay-rich material from the crest of a dike towards
the collection pond at its toe.
The numerical model combines free-surface hydrodynamics with
time-dependent rheology. The material structure evolves according
to the local deformation and shear history, allowing changes in
viscosity and flow resistance to develop dynamically as the clay
moves down the slope.
The curvilinear formulation enables the computational grid to follow
the dike geometry and the evolving free surface. This provides a
physically based framework for investigating flow velocity, flow
depth, spreading and deposition over the complete dike profile.
Two-dimensional vertical (2DV) modelling
Boundary-fitted curvilinear coordinates
Free-surface flow
Gravity-driven clay flow
Non-Newtonian rheology
Thixotropic material behaviour
Time-dependent viscosity and flow resistance
Structural breakdown under shear
Structural recovery
Shear-history effects
Finite Volume Method
Moving free-surface grid
Flow-depth and velocity evolution
Downslope spreading
Deposition towards the collection pond
Comparison with field-scale observations
From Dike Crest to Collection Pond
Clay-rich material is introduced near the crest of the dike and
accelerates downslope under gravity. During this motion, the material
undergoes continuous deformation, causing its structural state and
rheological properties to evolve.
Farther downslope, changes in geometry, flow depth and material
rheology influence the mobility of the clay. The flow gradually
spreads and decelerates as it approaches the lower part of the dike
and the collection pond.
Field-Scale Rheological Application
The project provides an opportunity to connect rheological
characterization with field-scale flow behaviour. Material parameters
obtained from measurements can be introduced into the numerical
formulation, while calculated velocities, flow depths, spreading and
deposited profiles can be compared with observations from the
Rijpdijk experiment.
This creates a direct link between material rheology and engineering-
scale behaviour, enabling the influence of thixotropy on the mobility,
spreading and final deposition of clay to be investigated under
realistic dike-scale conditions.
Field-scale clay flow from the crest of the dike towards
the collection pond.
Numerical Simulation
Numerical simulation of gravity-driven thixotropic clay flow
from the crest of the dike towards the collection pond.
02 · Tailings Deposition and Management
Thixotropic Modelling of Treated-Tailings Deposition Flows
This research investigates the influence of time-dependent rheology
on the flow and deposition of treated tailings. Flocculated fine
tailings can exhibit pronounced thixotropic behaviour: their internal
structure changes during shearing and can recover during periods of
rest, causing the apparent viscosity and flow resistance to evolve
continuously during deposition.
I developed and applied a free-surface numerical flow model in which
the governing fluid-flow equations are coupled with time-dependent
rheological formulations. This enables the material structure and
rheological properties to evolve dynamically as the tailings are
transported and deposited.
Why Time-Dependent Rheology Matters
Conventional time-independent rheological models assume that the
material response is determined by the instantaneous flow
conditions. For thixotropic tailings, however, the current
material properties also depend on the preceding shear and rest
history.
The simulations demonstrate that the choice of thixotropic
formulation can influence predicted flow depth, flow velocity
and free-surface behaviour. Representing this time dependency is
therefore important when predicting the spreading and deposition
of treated tailings.
Flocculated and treated tailings
Non-Newtonian free-surface flow
Time-dependent rheology
Thixotropic material behaviour
Structural breakdown under shear
Structural recovery during rest
Shear-history effects
Transported structural parameters
Houska thixotropic formulation
Parent–Simms thixotropic formulation
Comparison of constitutive models
Spatially and temporally varying viscosity
Free-surface flow simulation
Flow-depth prediction
Velocity prediction
Deposition-flow behaviour
Flocculation effects
Runout and spreading behaviour
Comparison of Thixotropic Models
An important part of the work was the comparison of different
constitutive descriptions of thixotropy. The Houska and
Parent–Simms approaches were implemented within the numerical flow
framework and evaluated for flocculated mature fine tailings.
The comparison showed that different representations of structural
evolution can produce different predictions of flow depth, velocity
and free-surface behaviour. The work therefore provides insight not
only into tailings deposition itself, but also into the consequences
of selecting a particular constitutive description for time-dependent
material behaviour.
Deposition Behaviour and Free-Surface Dynamics
The later phase of the research examined time-dependent behaviour in
tailings deposition flows more broadly. The calculations investigated
how changes in rheological properties and flow conditions influence
the evolution of the free surface and the behaviour of material
during deposition.
The work also examined the role of flocculation. Because flocculation
changes the rheological properties of fine tailings, it can influence
predicted stream depth and flow velocity and may consequently affect
the development and runout of deposition flows.
Flocculation → Material structure →
Shear-induced breakdown and recovery →
Time-dependent rheology → Free-surface flow →
Spreading and deposition
Application to Tailings Management
The practical objective is to improve the physical basis of numerical
tools used to understand and predict tailings deposition. Better
representation of time-dependent rheology can support assessment of
how treated tailings spread, develop flow paths and establish their
deposited geometry.
The project therefore connects fundamental rheological behaviour with
an important engineering application: improving physics-based
prediction of deposition processes in tailings storage facilities.
Simulation
Numerical modelling of free-surface tailings flow with time-dependent rheological behaviour.
Publications
The subsequent research was published as:
“Comparing various thixotropic models and their performance in predicting flow behaviour of treated tailings”, published in the proceedings of Paste 2023, Banff, Canada.
“Exploring the role of time-dependency in tailings deposition flows”, published in the proceedings of the
26th International Conference on Paste, Thickened and Filtered Tailings (Paste 2024),
pages 257–270.
From Fundamental Rheology to Predictive Flow Modelling
My work bridges fundamental rheological behaviour and practical
numerical modelling of complex, time-dependent materials. At the
fundamental level, the focus is on understanding how shear,
deformation history and periods of rest influence material structure,
viscosity, yield behaviour and flow resistance.
These physical processes are incorporated into computational models
through constitutive relations and structural-evolution equations
coupled directly to the governing flow equations. This allows the
material properties to evolve dynamically during transport,
deposition, rest and remobilisation, rather than being represented
by fixed or purely instantaneous rheological parameters.
The broader value of this modelling approach lies in:
Understanding structural breakdown under shear
Representing structural recovery during periods of rest
Quantifying shear-history and time-dependent effects
Comparing alternative thixotropic constitutive formulations
Coupling structural evolution with free-surface flow dynamics
Investigating changes in viscosity and yield behaviour during flow
Improving prediction of spreading, runout and deposition
Studying stopping, resting and subsequent remobilisation
Evaluating when conventional time-independent rheological formulations are insufficient
Developing more physically based models for treated tailings and other complex sediment-rich materials
Material structure → Shear and deformation history →
Structural breakdown and recovery → Evolving rheology →
Coupled flow simulation → Spreading and deposition →
Predictive thixotropic modelling
Overall Rheology and Thixotropy Expertise
My expertise spans the complete modelling chain for non-Newtonian
and thixotropic flows, from understanding the underlying material
physics and constitutive behaviour to developing coupled numerical
models for time-dependent flow, free-surface evolution and deposition.
Material structure → Rheological behaviour →
Structural breakdown and recovery →
Constitutive modelling → Coupled flow equations →
Free-surface dynamics → Deposition and remobilisation
This combination enables me to investigate complex fluids
from the evolution of their internal material structure to
their large-scale flow, spreading, stopping and deposition
behaviour.
A central theme of my work is that the rheological properties
of a thixotropic material cannot always be regarded as fixed.
The material continuously evolves as it is sheared, transported,
deposited and allowed to rest. Its present flow behaviour can
therefore depend strongly on its previous deformation history.
My work integrates
rheological physics, constitutive modelling, computational fluid dynamics and numerical-method development
to represent this history-dependent behaviour directly within
flow simulations. This provides a more physically based framework
for investigating treated tailings and other complex materials
whose properties evolve during motion and rest.