Research interests

In my research, I use mathematical modelling and lab experiments to uncover the science behind a broad range of flow phenomena in industrial, environmental and geophysical fluid mechanics. In most projects, I work in collaboration with PGR students and post-docs in my group, colleagues in Manchester and collaborators from around the world. We carry out mathematical modelling either analytically or numerically, depending how far progress can be made using pen and paper. We do experiments in the lab of the Manchester Centre for Nonlinear Dynamics, a few minutes walk from the Department of Mathematics, where I usually work.

Research areas:
  • The fluid mechanics of cleaning and decontamination
    This multidisciplinary topic lies at the border between fluid mechanics, engineering and chemistry. It has many practical applications: from cleaning in dishwashers to the decontamination of toxic chemicals.
  • Drag reduction with flows over superhydrophobic surfaces
    In this topic, we're looking at how superhydrophobic surfaces can reduce the drag of solid surfaces when flowing into a liquid, for instance a ship or a submarine, or when a liquid flows against a solid such as in pipelines. We've studied both slow viscous flows (low Reynolds number flows for the experts) and fast turbulent flows (high Reynolds numbers). Recently, we've been particularly interested in how surfactants (molecules found in soap for instance) affect the drag reducing performance of a superhydrophobic surface.
  • Surfactant-driven flow dynamics in confined geometries
    Flows can be driven by surfactants (small molecules found in soap for instance) under the so-called Marangoni force. This force can be quite powerful and lead to unexpected behaviours such as flows solving a maze, or intriguing mathematical singularities at contact lines.
  • Dispersion and mixing in turbulent jets, plumes and fountains
    Here, we've analyze the fundamental properties of these canonical turbulent flows. They have applications ranging from large geophysical flows such as volcanic eruptions to industrial processes in chemical reactors, or oil refinement, mechanical ventilation and even oil spills in the ocean.

The fluid mechanics of cleaning and decontamination

Cleaning and decontamination processes at surfaces can use mechanical forces to remove alien materials on a surface. However, these can lead to high consumption in water, detergents and energy. In this project we investigate a more environmentally friendly process, which relies on a slow dissolution process.

We have investigated various scenarios for the decontamination of a droplet on a substrate,  which is submerged in a liquid film. The decontamination occurs through a convective mass transfer. We have studied the case where the droplet lies on a flat impermeable substrate, or when it is confined between two walls in the transverse direction, or when it lies on a porous substrate.

Through analytical, numerical and experimental investigation, we have found how the mass transfer or cleaning rate evolves depending on the geometry and the Péclet number.
Left: gravity-driven film flow over a droplet (blue) to start a convective mass transfer at surface. Right: typical profile of advection-diffusion boundary layer found above a drop in a shear flow.
- Etzold, M. A., Fortune, G. T., Landel, J. R. Dalziel, S. B. (2022) "Droplet absorption and spreading into thin layers of polymer hydrogels". Under review. (ArXiv)
- Landel, J. R., Wilson, D. I. (2021) "The fluid mechanics of cleaning and decontamination of surfaces". Annual Review of Fluid Mechanics 53, 147-171.
- Etzold, M. A., Landel, J. R., Dalziel, S. B. (2022) "Three-dimensional advective–diffusive boundary layers in open channels with parallel and inclined walls". International Journal of Heat and Mass Transfer 153, 119504. (Author accepted manuscript)
- Landel, J. R., Thomas, A. L., McEvoy, H. and Dalziel, S. B. (2016) "Convective mass transfer from a submerged drop in a thin falling film". Journal of Fluid Mechanics 789, 630-668. doi (arXiv)
- Landel, J. R., McEvoy, H. and Dalziel, S. B. (2015) "Cleaning of viscous drops on a flat inclined surface using gravity-driven film flows". Food and Bioproducts Processing 93, 310-317. doi (pdf)

Drag reduction with flows over superhydrophobic surfaces

Superhydrophobic surfaces (SHSs) have the property of repelling water from their surface to an astonishing degree. Known in nature as the ‘lotus leaf effect’, water rolls on the lotus leaf as near-perfect beads, instead of spreading over the leaf. Owing to a combination of micro-texture and chemistry, water droplets mostly stand above air bubbles trapped in the micro-texture. This is known as the Cassie-Baxter or fakir state!

This observation has recently inspired scientists to cover the external surface of ships, submarines or the internal surface of pipelines with SHSs in order to decrease their drag. As drag or friction between air and water is significantly less than between water and solid, SHSs have the potential to reduce considerably the energy used in maritime transport or pipe flows. However, laboratory experiments conducted in the past ten years have found inconsistent results, with many studies reporting significantly decreased performance compared with theoretical and numerical predictions.

With collaborators from the University of Cambridge and the University of California  Santa-Barbara, we have shown that surfactants, organic molecules naturally present in our environment, are the most likely cause for the decreased performance of SHSs. As even minute concentrations of surfactants can severely reduce the SHS performance, the impact of our discovery is important for many applications and could guide the design of future SHSs. We are also investigating the impact of turbulent flows on the drag reducing properties of the superhydrophobic surface.
- Luzzatto-Fegiz P., Tomlinson, S. D., Egan, R., Gibou, F., Jensen, O. E., Landel, J. R. (2022) "Mechanisms of turbulent drag reduction for superhydrophobic surfaces across large Reynolds numbers". Under review.
- Temprano-Coleto F., Smith, S. M., Peaudecerf F. J., Landel, J. R., Gibou, F., Luzzatto-Fegiz P. (2022) "Slip on three-dimensional surfactant-contaminated superhydrophobic gratings". Under review. (ArXiv)
- Egan R., Guittet A., Temprano-Coleto F., Isaac T., Peaudecerf F. J., Landel J. R., Luzzatto-Fegiz P., Burstedde C., Gibou R., (2021) "Direct numerical simulation of incompressible flows on parallel octree grids". Journal of Computational Physics 428, 110084. (Preview online)
- Landel, J. R., Peaudecerf, F. J., Temprano-Coleto, F. , Gibou, F., Goldstein, R. E., Luzzatto-Fegiz, P. (2019) "A theory for the slip and drag of superhydrophobic surfaces with surfactant". Journal of Fluid Mechanics 883, A18. (ArXiv)
- Peaudecerf, F. J., Landel, J. R., Goldstein, R. E., Luzzatto-Fegiz, P. (2017) "Traces of surfactants can severely limit the drag reduction of superhydrophobic surfaces". Proceedings of the National Academy of Sciences of the United States of America. doi (full text and SI)

Surfactant-driven flow dynamics in confined geometries

In an experiment, we have showed that surfactants can solve a maze. This fun kitchen-top experiment reveals the impact that surfactant, invisible molecules found in soap and detergent, can have at a normal human scale. This is due to the strong surface-tension forces disturbed by the surfactants at the air-liquid interface.

In our experiments, we found that a few drops of surfactants deposited at the surface of a maze filled with milk can indeed find the exit! The main mechanism for this strange behaviour is due to the fact that there are already pre-existing surfactants at the surface of the milk. When we add more surfactants the surfactant molecules push each other to try to find an equilibrium, which is when the surfactant concentration is uniform. The surfactants already present are compressed in dead end channels of the maze, preventing the added surfactants to penetrate these false routes, whilst allowing them to penetrate in the much larger exit of the maze.

In another research project, we have shown that as the surfactants compress near a wall, they induce a singularity which manifests in the pressure and shear forces in the liquid. The pressure diverges whilst the shear forces oscillate.
Picture
Surfactants solving a maze.
Picture
Vorticity contours of a Stokes flow in a cavity, with surfactant spreading at the top surface. The vorticity is multivalued at the top corners, indicating a singularity
- Mcnair R., Jensen O. E., Landel J. R. (2021) "Surfactant spreading in a two-dimensional cavity and emergent contact-line singularities". Journal of Fluid Mechanics, 930,  A15. (Author accepted manuscript)
- Temprano-Coleto, F. , Peaudecerf, F. J., Landel, J. R., Gibou, F., Luzzatto-Fegiz, P. (2018) "Soap opera in the maze: Geometry matters in Marangoni flows". Physical Review Fluids 3, 100507. (Author accepted manuscript)

Dispersion and mixing in turbulent jets, plumes and fountains

Sinuous instability of confined turbulent jets

The study of quasi-two-dimensional turbulent jets is relevant to chemical reactors, the coking process in oil refinement, as well as shallow rivers flowing into lakes or oceans. In the event of a spillage of pollutants into a river, it is critical to understand how these agents disperse with the flow in order to assess damage to the environment. For such flows, characteristic streamwise and cross-stream dimensions can be much larger than the fluid-layer thickness, and so the flow develops in a confined environment. When the distance away from the discharge location is larger than ten times the fluid-layer thickness, the flow is referred to as a quasi-two-dimensional jet.

From experimental observations using dyed jets (see top right fig.) and particle image velocimetry (see bottom right fig.), we find that the structure of a quasi-two-dimensional jet consists of a high-speed mean- dering core with large counter-rotating eddies developing on alternate sides of the core. The core and eddy structure is self-similar with distance from the discharge location. The Gaussianity of the cross-stream distribution of the time-averaged velocity is due, in part, to the sinuous instability of the core.

Resolving analytically the advection-diffusion equation in the flow, we found that if a finite quantity of pollutants is spilled in the river, more than 50% will travel faster and farther due to the strong dispersive interaction of the eddies and the sinuous core.
Picture
Pictures of a steady quasi-two-dimensional turbulent jet revealed by dye injection.
Picture
Sinuous instability of a confined jet. Left: Passive tracers (shown as streaks) in a confined turbulent momentum jet; middle: corresponding velocity field (arrows) and vorticity field (background) measured using particle image velocimetry; right: schematic of the self-similar unstable sinuous core and alternating side vortices.
- Landel, J. R., Caulfield, C. P., Woods, A. W. (2012) "Meandering due to large eddies and the statistically self-similar dynamics of quasi-two-dimensional jets". Journal of Fluid Mechanics 692, 347-368. doi (pdf)
- Landel, J. R., Caulfield, C. P., Woods, A. W. (2012) "Streamwise dispersion and mixing in quasi-two-dimensional steady turbulent jets". Journal of Fluid Mechanics 711, 212-258. doi (pdf)

Physics of an oil spill in deep seas

In the event of an oil leak at the bottom of the ocean, a multiphase hydrocarbon plume rises through the ocean layer, and then forms an oil slick at the surface (see top picture). In 2010, the accident that destroyed the Deep Water Horizon platform in the Gulf of Mexico, led to the largest oil spill in deep seas (1260 m depth). The consequences of the oil spill were disastrous for the environment and the local economies along the Gulf affected by the oil spill.

As part of the Consortium for Advanced Research on the Transport of Hydrocarbon in the Environment (CARTHE), we study the physics of the oil plume as it rises from the bottom of the ocean to the surface. The turbulent plume is constituted of different phases: oil droplets, gas bubbles, water and potentially some dispersant. One of the key factor determining the quantity of oil and gas reaching the surface, and subsequently the impact of the oil spill, is related to the dilution of the plume by entrainment of sea water. A turbulent plume entrains ambient water through a complex turbulent process.

In the case of an oil plume rising in the ocean, the plume dynamics is affected by multiple environmental factors, such as: the stratification of the ocean, the presence of currents, the Earth rotation, the use of dispersant, the physical and chemical properties of the oil and gas mixture. Since 2015, we have conducted experiments in the GK Batchelor Laboratory at DAMTP, University of Cambridge, to understand the impact of these factors on the plume dynamics.
In particular, the experiments conducted by Daria Frank have shown that the Earth rotation can induce a precession of large scale plumes in a homogeneous environment (see bottom picture). This precession can lead to enhanced dispersion of the plume in the environment, thus increasing the dilution of the plume. Our results suggest that this precession could occur for ash clouds from long volcanic eruption or oil plumes from a deep water oil leak, such as the Deep Water Horizon 2010 oil leak.
- Frank D., Landel J. R., Dalziel S. B., Linden P. F., (2020) "Effects of background rotation on the dynamics of multiphase plumes". Journal of Fluid Mechanics 915, A2. (Open access link)
- Frank, D., Landel, J. R., Dalziel, S. B., Linden, P. F. (2017) "Anticyclonic precession of a plume in a rotating environment". Geophysical Research Letters. doi
- See also interview by Tom Rocks Maths and FYFD: YouTube video.

Impinging jets and draining patterns

Impininging jets are important in many industrial cleaning processes, whether performed manually or using a cleaning in place system. In our daily life, dishwashers use impinging jets to clean the surface of dishes, plates and cutleries.  It is also a well-known daily preoccupation of half of the world's population!

To clean efficiently it is important to understand how the velocity and the shear stresses evolve in the flow. As can be seen in the two pictures on the left, showing an impinging jet at low impact speed (top) and one at high speed (bottom), there are different regions in the flow.

Close to the impinging point, a thin layer of very high speed radial flow exists. In this region, the flow has intense shear and soil on the surface can be removed through mechanical forces. The limit of this region is characterised by a film jump.

Beyond the radial flow zone, flow at the top is pulled down by gravity and forms thick ropes at the edge of the draining flow region. In the interior of the draining flow region, the film is relatively thin. Our PIV measurements show a uniform velocity profile in this region.

As can be seen in the figures, the film surface is very unstable to long waves, which are two-dimensional at low speed and three-dimensional at high speed.

In the draining region, cleaning of soil attached to the surface is not performed mechanically due to the low shear. Instead, a slower dissolution process can occur. If soap is used, detachment of soil can also occur by changes in the adhesion properties.
Picture
Jet impinging on a vertical surface at low Reynolds number (front view).
Picture
Jet impinging on a vertical surface at high Reynolds number (front view).
- Aouad, W., Landel, J. R., Dalziel, S. B., Davidson, J. F., Wilson, D. I. (2016) "Particle image velocimetry and modelling of horizontal coherent liquid jets impinging on and draining down a vertical wall". Experimental Thermal and Fluid Science 74, 429-443. doi (pdf)

Crowned cap bubbles

 How big can air bubbles in water be? How fast do these large bubbles rise? These were the questions that motivated this experimental study, which eventually led to the discovery of a new kind of bubble. Our study was motivated by issues arising from the sequestration of carbon dioxide, one of the main greenhouse gas, in underground reservoirs at the bottom of the ocean. In case of a leak of carbon dioxide (CO2), we need to know the size of the fastest bubbles which can form, in order to determine whether the bubble will reach the ocean surface before  its gas is entirely dissolved in the water or not. The latter being undesirable as effectively releasing the CO2 into the atmosphere.

In experiments conducted at the GK Batchelor Laboratory (DAMTP, University of Cambridge), we found that under some circumstances, releasing a large volume of air in water could lead to two very different kinds of bubbles. The first kind is the well-known spherical cap bubble, with a top spherical part and flat bottom (see figure on the top right). The second kind corresponds to a multi-part bubble, with a large lenticular bubble on top, and a crown of smaller bubbles trapped in its wake (see figure at the bottom right).

The most surprising discovery about the second bubble, or crowned cap bubble, is that for the same total volume of air, the crowned cap bubble rises 5% faster than the spherical cap bubble.  It had always been assumed that the air volume of large bubbles was the main parameter determining their speed. Here we found that through a different organisation of the air, the bubble can decrease its drag and therefore rise slightly faster.
Picture
Spherical cap bubble (base diameter: 10 cm).
Picture
Crowned cap bubble: a multipart bubbles with a large lenticular bubble on top (base diameter: 15 cm) and a toroidal crown of smaller bubbles in its wake.
- Landel, J. R., Cossu, C., Caulfield, C. P. (2008) "Spherical cap bubbles with a toroidal bubbly wake". Physics of Fluids 20: 122101. doi (pdf) Paper in the Physics of Fluids top 20 (Dec 2008, Jan 2009).