Yield stress fluids applications

Yield stress fluids are ubiquitous. For the past 25+ years we’ve studied hydrodynamic instabilities, multi-fluid flows, bubbles, particles and droplets, numerical methods, displacement and dispersion in different guises.

Hydrodynamic instabilities in visco-plastic fluids:

Topics include:

  • Developing the methodology for linear stability in yield stress fluids, treating the yield surface perturbation correctly.
  • Energy stability methods for nonlinear stability
  • Some weakly nonlinear stability work
  • Various approximation method to derive bounds for stability
  • Plane Poiseuille flow, Hagen-Poiseuille flow
  • Taylor-Couette flow
  • Rayleigh-Bénard flow and natural convection flows
  • Rayleigh-Taylor configurations (see plug cementing and exchange flows)
  • Experimental studies of Hagen-Poiseuille flow and empirical rules for transition
  • Numerous studies of multi-layer flow stability.
  • Exposing the relationship between the yield limit and energy stability for internal flows
  • Use of energy stability for thermal switching
  • Pulsed plumes in natural convection with localized heating
  • Energy stability for the stopping of settling particles

Displacement flows, dispersion and mixing with generalised Newtonian fluids

The majority of this work has been in conjunction with the study of well cementing flows

Visco-plastic lubrication flows

This theme has arisen from the observation that by retaining unyielded fluid at an interface, it is possible to eliminate interfacial instability. The question then is how to configure useful flows that exploit this feature?

  • We have achieved stable multi-layer shear flows at high Re by placing an unyielded layer at the interface.
  • In a lab-scale dedicated multi-layer flow loop we have run various experimental designs using clear lab fluids (typically weighted Carbopol, xanthan or glycerin solutions, some viscoelastic fluids), mostly to establish proof of concept.
  • For core-annular flows we have a wide range of experimental flows showing flow stability, including using visco-elastic core fluids
  • We have proven results for linear and nonlinear stability of these flows.
  • We have studied start-up and development lengths
  • With special configurations we can achieve linearly stable flows at infinite Re!
  • We have developed methods for how to engineer hydrodynamically stable core-annular oil-water flows, by using an emulsion of the oil and water as a visco-plastic skin to maintain stability.
  • We have worked on controlling the shape of core fluids, stably frozen in after controlled oscillation. This is used in the above method to provide a hydrodynamic lift force that counters buoyancy of the core.
  • We are looking at applications in food industry, polymer processing, paper coating, oil and gas.

Bubbles, droplets and particles

Stability of bubbles droplets and particles in yield stress fluids is vitally important for many industrial applications, e.g. slurry, foam and emulsion stability. Stability characteristics are also useful in separation techniques for particles. Some of the topics here include the following.

  • Using controlled oscillation of multi-layer flows to produce shaped droplet encapsulation, with the novelty of larger scale droplets avoiding capillary length-scale restrictions
  • We have defined the yield limit clearly for bubbles, droplets and particles.
  • We have determined the yield limits for 2D and axisymmetric particles, droplets and bubbles
  • We have shown that isolated particles in a yield stress fluid will stop in a finite time (hence distance) if the yield number is sufficiently high
  • This principle has been exploited in novel particle separation techniques
  • Associated with the yield limit is a yielded envelope, at the onset of motion. The yield envelope is not unique to the particle, meaning that there can be a form of cloaking, where the particle shape cannot be detected from the motion.
  • We have developed numerical methods for attaining the yield limit, using either mobility or resistance formulations, and a direct method for computing.
  • We have compared 2D planar flows with slipline methods from plasticity theory: they are not exactly the same.
  • We have explored the yield limit of pairs of bubbles and particles, as well as randomised suspensions (bubbly liquids), all in 2D planar geometries
  • We have devised experimental methods to explore the yield limit in gels such as Carbopol. These experiments reveal considerable elastic deformation before the bubbles start to move. We are studying this onset more deeply.
  • We have devised experiments for the onset of motion of clouds of bubbles. These show a range of behaviours ranging from isolated bubble release, through mobilization of bubble chains/arrays to a bursting phenomenon.
  • We have performed experiments with 2-3 bubbles to explore coaleschence, effects on bubble release, etc
  • We have performed numerous experiments on bubble rising in yield stress fluids. These agree with similar experiments of other authors, showing typically a pointed tail attributed to viscoelasticity.
  • When we inject/release multiple bubbles, they tend to follow the path of previous bubbles, but are smaller and move faster. This indicates that the pathway of the first bubble also creates some form of “damage” to the gel.
  • Other experiments have purposefully damaged the gel of introduced e.g. a water layer. Bubbles released appear to be attracted towards the rheologically weaker layer of fluid. We are studying this phenomena more closely, using experiments and computation.
  • We have performed both simulations and experiments to study the passage of bubbles through different layers of fluid. This leads to a change in bubble shape typically and interesting transients crossing the interface.
  • The above studies reveal an interesting tunneling phenomena.
  • Passage through the interface also reveals different patterns of entrainment, e.g. of the lower fluid into the upper in the wake of the bubble.
  • We are studying entrainment in yield stress fluids more deeply.

Restarting waxy crude oil pipelines

This was an active collaboration with colleagues from IFP and from PUC-Rio.

  • We identified 3 regimes for start-up, dominated by friction, compressibility and/or acoustic propagation. Most of these timescales for start-up are anyway fast compared with the actual displacement times
  • We also computed compressible displacement flows, using axisymmetric (2D) and reduced models.
  • The effects of thixotropy have been explored
  • Sometimes it is possible to restart pipelines below the incompressible pressure limit, combining thixotropic and compressible effects
  • We studied these effect using a reduced model, to try to derive semi-analytical predictions of start-up
  • We performed a number of start-up flow experiments, using both Carbopol and laponite as working fluids.

Mathematical Modelling of Industrial Processes

Various processes have attracted our attention over the years. Some of this work is undertaken as consulting activity and not all involves yield stress fluids.

  • Spray-forming of Aluminium billets
  • Well control
  • Czrochalski crystal growth
  • Image processing using nonlinear diffusion filters
  • Injection molding
  • Oilfield cementing
  • Waxy crude oil pipelining
  • Pile grouting
  • Sand control/gravel packing
  • Fracturing flows
  • Fouling
  • Solidification of alloys
  • Fiber flows in pulp and paper processing
  • Different process-related hydrodynamic stabilities
  • Geothermal wells