CBET-EPSRC: Analysis and Optical Control of Surfactant Effects for Increased Lubrication of Liquid Flows in the Cassie State
Lead Research Organisation:
Imperial College London
Department Name: Mathematics
Abstract
Superhydrophobic surfaces (SH surfaces, or SHS) are a special breed of surfaces, arising in natural settings or increasingly in man-made synthetic situations, which are unusually slippery. In nature, superhydrophobicity manifests itself as the so-called "lotus-leaf effect": water beads up on a lotus leaf and readily slips off. This slippery feature can be supremely useful in a rich panoply of engineering applications, including direct attempts to emulate this effect in man-made superhydrophobic coatings, or using the effect to promote easier passage of fluids in driven flows (drag reduction). It has been proposed recently, however, that these attractive drag reduction properties in driven flows can quickly be compromised by the presence of surfactants, or impurities in the fluids that quickly aggregate at the fluid surfaces, even in trace amounts. This means that their presence is virtually unavoidable. It is therefore critical to assess the extent of this impediment, whether it can be mitigated, and even whether the deliberate addition of surfactants can be leveraged to attain desired objectives, such as enhanced drag reduction, flow stabilisation, or even mass transport. This is the topic of our proposal.
The main goals of this proposal are to (a) quantitatively assess the extent to which the slip properties of a surface are compromised by the presence of surfactants for internal channel flows in the laminar flow regime; (b) study whether a possible "remobilisation" of interfaces already studied in the context of surfactant-laden bubbles can play a useful role in drag reduction involving superhydrophobic surfaces; (c) explore, both theoretically and experimentally, how a special class of surfactants deliberately added to the fluid, and controllable (or "tunable") by external light stimuli, can affect the slip properties of superhydrophobic surfaces; (d) explore how the stability of laminar flows over SHS is affected by the presence of surfactant, both soluble and insoluble, and whether incipient instabilities can be controlled by light actuation; (e) examine, both theoretically and experimentally, mass/particle transport using Marangoni stresses associated with light-actuated surfactants as a propulsion mechanism.
While light-actuated surfactants have been studied before, the novelty of our proposal lies in their deployment in the setting of superhydrophobic surfaces and their use as a control mechanism both for sustained drag reduction, elimination of instability, and as a mechanism for strategic mass transfer. The fundamental insights from our proposed work packages will have broad implications for a variety of applications of SHS ranging from drag reduction and self-cleaning surfaces to controllable drug delivery in emerging healthcare technologies.
The main goals of this proposal are to (a) quantitatively assess the extent to which the slip properties of a surface are compromised by the presence of surfactants for internal channel flows in the laminar flow regime; (b) study whether a possible "remobilisation" of interfaces already studied in the context of surfactant-laden bubbles can play a useful role in drag reduction involving superhydrophobic surfaces; (c) explore, both theoretically and experimentally, how a special class of surfactants deliberately added to the fluid, and controllable (or "tunable") by external light stimuli, can affect the slip properties of superhydrophobic surfaces; (d) explore how the stability of laminar flows over SHS is affected by the presence of surfactant, both soluble and insoluble, and whether incipient instabilities can be controlled by light actuation; (e) examine, both theoretically and experimentally, mass/particle transport using Marangoni stresses associated with light-actuated surfactants as a propulsion mechanism.
While light-actuated surfactants have been studied before, the novelty of our proposal lies in their deployment in the setting of superhydrophobic surfaces and their use as a control mechanism both for sustained drag reduction, elimination of instability, and as a mechanism for strategic mass transfer. The fundamental insights from our proposed work packages will have broad implications for a variety of applications of SHS ranging from drag reduction and self-cleaning surfaces to controllable drug delivery in emerging healthcare technologies.
Publications
Tomlinson S
(2024)
Thermal Resistance of Heated Superhydrophobic Channels With Thermocapillary Stress
in ASME Journal of Heat and Mass Transfer
Rodriguez-Broadbent H
(2024)
Asymptotically exact formulas for channel flows over liquid-infused surfaces
in IMA Journal of Applied Mathematics
Rodriguez-Broadbent H
(2023)
Superhydrophobic surfaces with recirculating interfacial flow due to surfactants are 'effectively' immobilized
in Journal of Fluid Mechanics
Ray P
(2023)
Flow of shear-thinning liquids in channels with superhydrophobic surfaces
in Journal of Non-Newtonian Fluid Mechanics
Miyoshi H
(2024)
Numerical validation of analytical formulas for channel flows over liquid-infused surfaces
in Journal of Engineering Mathematics
Miyoshi H
(2025)
Equivalent local force conditions minimizing the Frank free energy for topological defect equilibria in nematic liquid crystals
in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Miyoshi H
(2022)
Longitudinal flow in superhydrophobic channels with partially invaded grooves
in Journal of Engineering Mathematics
Meng Y
(2024)
Steady Wind-Generated Gravity-Capillary Waves on Viscous Liquid Film Flows
in SIAM Journal on Applied Mathematics
Mayer M
(2024)
Stability of a photosurfactant-laden viscous liquid thread under illumination
in Journal of Fluid Mechanics
Mayer M
(2022)
Superhydrophobic surface immobilisation by insoluble surfactant
in Journal of Fluid Mechanics
| Description | A mathematical model has been constructed and studied that shows how light radiation can affect cis-trans surfactants that in turn affect instabilities. For example, our analysis shows that light can be used to control breakup of liquid jets, a canonical technological example of interfacial instabilities. This was one of the objectives of the award, namely to illustrate the mathematical models in these highly complex physics-chemical hydrodynamic problems. |
| Exploitation Route | The results are useful for industrial processes that are based on flow control on the micro-scale. Light-actuated surfactants have been shown in the work of this award to be viable options for such control via interfacial Marangoni stresses without the need of thermal gradients or other intrusive processes. |
| Sectors | Electronics Energy Manufacturing including Industrial Biotechology |
| Description | Imperial - University of Texas at Austin |
| Organisation | University of Texas at Austin |
| Country | United States |
| Sector | Academic/University |
| PI Contribution | Funds were obtained from Imperial College to run a meeting with our collaborators from UT Austin to explore further funding opportunities as well as evaluate the grant outputs for translational research. The meeting will take place in early May, 2025, before the end of the grant. |
| Collaborator Contribution | The UT Austin group is led by Prof. Vaibhav Bahadur who is an internationally leading researcher in experiments involving superhydrophobic surfaces. Prof. Bahadur's team has contributed discussions on several physical scenarios that can be explored experimentally and that our team will be addressing theoretically. In addition, the UT Austin team is collaborating with co-I Hodes from Tufts on experimental aspects of our project. |
| Impact | No outputs yet, a paper is being drafted. |
| Start Year | 2023 |
| Description | Imperial-Tufts photosurfactants |
| Organisation | Tufts University |
| Country | United States |
| Sector | Academic/University |
| PI Contribution | The team at Imperial has been developing and studying theoretical models to understand the effect of photosurfactants on surface tension driven instabilities. We have identified the mathematical models and have completed work of the underlying hydrodynamic instabilities. Several papers are in preparation and will be submitted shortly. |
| Collaborator Contribution | The Tufts collaborators are working on two aspects: (i) direct numerical simulations of the phenomena using in-house codes (Tufts, Mathematics), (ii) identification of photosurfactants and design of experiments to illustrate proof of concept. |
| Impact | The collaboration is multi-disciplinary. It involves Mathematics at Imperial College with Mechanical Engineering and Mathematics at Tufts University. |
| Start Year | 2022 |
| Title | Carbon Capture System and Methods |
| Description | A novel design of a liquid-infused microchannel to enable carbon capture from flowing gases and the reversed controlled release of the carbon for storage purposes. The US patent is jointly filed between Imperial College, Tufts University, MIT and UT Texas at Austin. Mathematical models have been developed that show encouraging results compared to other technologies such as packed bed columns. A significant amount of work is under way both theoretically and experimentally to prove the concept and move to the next steps. The current award is directly relevant to these carbon capture efforts. |
| IP Reference | PCT/US22/77489 |
| Protection | Patent / Patent application |
| Year Protection Granted | 2022 |
| Licensed | No |
| Impact | No impacts yet |
| Title | SYSTEM AND METHOD FOR IMPROVED HEAT PIPE |
| Description | The present disclosure describes a system and method involving a mechanism for a microfluidic pump that leverages alternating adverse and favorable thermocapillary stresses along menisici in a periodically fully-developed internal flow in a microchannel. The system includes interdigitated hot and cold ridges that are asymmetrically disposed relative to each other. The asymmetrical configuration results in different widths of the menisci which drives the microfluidic pump based on the favorable and adverse thermocapillary stresses. |
| IP Reference | WO2024054862 |
| Protection | Patent / Patent application |
| Year Protection Granted | 2024 |
| Licensed | No |
| Description | School visit (NHEHS, London) |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Schools |
| Results and Impact | A 45 minute talk given to the Year 13 cohort of the Notting Hill and Ealing High School in London. About 20 students attended. The talk used many examples from the general research that the award deals with, and in particular described the mathematics of Marangoni flows and superhydrophobic flows. The talk generated considerable interest by the students who were fascinated by the fact that mathematics can be used in areas that they traditionally thought of as chemistry or physics. |
| Year(s) Of Engagement Activity | 2022 |
| Description | Science Museum, London |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | Regional |
| Primary Audience | Public/other audiences |
| Results and Impact | These workshops arose after an invitation from the Science Museum in South Kensington to give talks at the Ancient Greeks Lates event in March, 2022. These events attract several thousand people and are centred around special exhibitions. I was a science advisor for the special exhibition "Ancient Greeks: Science and Wisdom" which opened in November, 2021 and closed in June, 2022, and was invited by the curator to participate in the flagship Lates event. I gave two talks during the night, each lasting 30 minutes. My topic was mathematics across scales, including aspects on connections between the geometry of the ancient Greeks and advanced engineering technologies such as microfluidics, superhydrophobicity and pathways to solving grand challenges such as carbon capture. The talks were immensely successful and I was delighted to be able to describe some of the goals of the award to a general audience. |
| Year(s) Of Engagement Activity | 2022 |
