Viscous fingering on soft substrates
Lead Research Organisation:
University of Manchester
Department Name: Physics and Astronomy
Abstract
The research proposed here is motivated by recent striking observations of the viscous fingering instability on soft substrates. This instability readily develops if a viscous fluid is displaced by a less viscous fluid in a narrow gap between rigid plates, and typically results in complex highly branched patterns of fingers on the interface between the two fluids. Viscous fingering has been of long-standing research interest because it serves as an archetype for front-propagating pattern-forming phenomena, as diverse as the growth of bacterial colonies and the propagation of flame fronts. We find that this instability can be manipulated by replacing the bottom bounding plate with a soft substrate. Firstly, we observe that the instability can be delayed, so that the interface remains axisymmetric for injection rates at which the pattern in the corresponding rigid system already exhibits nonlinear growth. This is similar to other systems in which the fluid flow interacts with a compliant boundary, for example, with thin elastic membranes, although soft substrates deform differently compared to those. Secondly, the thickness and the stiffness of the soft substrate can be tuned to change the structure of the fingers that do develop once the circular interface becomes unstable to non-axisymmetric perturbations. The resulting patterns range from the highly branched fingering observed in rigid systems to the stubby fingers that develop on the meniscus between two cylinders co-rotating with the same speed. Thus, the instability is strongly influenced by the deformation of the soft substrate, which in turn deforms in response to the two-phase flow, and is likely to have viscoelastic properties. We propose to employ a combination of experimental, theoretical and computational approaches to fully-characterise the complex fluid-structure interactions that lead to these novel phenomena.
Planned Impact
1. The UK fluid mechanics and the soft matter communities will benefit from the PDRA's scientific training, which meets the requirements of the IRMS 2010 for fluid mechanics in combining numerical and analytical research with experiments. This individual will work in an inter- and intradisciplinary research environment of high quality, obtaining skills and scientific expertise well-suited for employment in both academia and industry.
2. The project will also benefit a more general scientific community in academia and industry as it will involve further development of the open-source library oomph-lib, making the codes developed for this project available for re-use in many other applications. The library is regularly used
in industry-driven projects, e.g. by Thales Underwater Ltd., Mondelez International Inc. and Cambridge Display Technology Ltd. who were/are involved in EPSRC-funded KTA projects conducted at the MCND. Following the approach taken in all previous studies that utilised oomph-lib, the
newly developed parts of the packages will be augmented by detailed tutorials and made available at http://www.oomph-lib.org.
3. The subject of the proposal lends itself to the type of public engagements that the PI is involved in on a regular basis, such as outreach activities organised by ScienceGrrl, or the Big Bang Fair. By demonstrating the comparisons between the experimental and theoretical results of this research, the PI will be able to show the power of mathematical modelling in a real-world problem. Further expansion of the outreach activities is already planned, as explained in the "Pathways to Impact" document.
2. The project will also benefit a more general scientific community in academia and industry as it will involve further development of the open-source library oomph-lib, making the codes developed for this project available for re-use in many other applications. The library is regularly used
in industry-driven projects, e.g. by Thales Underwater Ltd., Mondelez International Inc. and Cambridge Display Technology Ltd. who were/are involved in EPSRC-funded KTA projects conducted at the MCND. Following the approach taken in all previous studies that utilised oomph-lib, the
newly developed parts of the packages will be augmented by detailed tutorials and made available at http://www.oomph-lib.org.
3. The subject of the proposal lends itself to the type of public engagements that the PI is involved in on a regular basis, such as outreach activities organised by ScienceGrrl, or the Big Bang Fair. By demonstrating the comparisons between the experimental and theoretical results of this research, the PI will be able to show the power of mathematical modelling in a real-world problem. Further expansion of the outreach activities is already planned, as explained in the "Pathways to Impact" document.
People |
ORCID iD |
Draga Pihler-Puzovic (Principal Investigator) |
Publications
Box F
(2020)
Hard auxetic metamaterials
in Extreme Mechanics Letters
Box F
(2020)
Flow-induced choking of a compliant Hele-Shaw cell.
in Proceedings of the National Academy of Sciences of the United States of America
Cuttle C
(2020)
Dynamics of front propagation in a compliant channel
in Journal of Fluid Mechanics
Cuttle C
(2021)
The engulfment of aqueous droplets on perfectly wetting oil layers
in Journal of Fluid Mechanics
Jain S
(2023)
Material nonlinearities yield doubly negative holey metamaterials
in Extreme Mechanics Letters
Li H
(2023)
Swelling-induced patterning in soft microchannels
in Soft Matter
Li H
(2023)
Propagation of air fingers into an elastorigid Y-bifurcation
in Physical Review Fluids
Peng G
(2023)
Axisymmetric gas-liquid displacement flow under a confined elastic slab
in Physical Review Fluids
Description | · Development of a design rationale for a fluidic analogue of an electrical fuse which can be engineered into microfluidic devices as a flow limiter. This is based on a novel phenomenon of choking, whereby the elastomer is sheared outwards with the flow and accumulates in a boundary layer near the outlet, which constricts the flow and, above a critical flow rate, `chokes' the flow entirely. · Development and validation of a theoretical framework for understanding and predicting the elastic response of a deformable channel to a pressurised fluid injection. · Observation and explanation (using a theoretical model) of the impact of viscous fingering in a narrow gap between a solid wall and a soft bounded elastomer on the choking phenomenon. |
Exploitation Route | · The findings may be taken forward by scientific and industrial users of microfluidic devices. Microfluidic devices have far-ranging applications in industries as diverse as agriculture , medical diagnostics, pollutant monitoring, fertility treatment, food safety and cancer research. The potential for application by end-users is therefore large. · The research findings may also provide valuable insight into industrial, geophysical flows in confined poro-elastic media with applications in fuel extraction and carbon sequestration. The motion of fluid within the narrow, deformable gap is mathematically analogous to two-dimensional flow in a porous, elastic medium and, as such, this study provides a platform on which to build further knowledge of the elastic response of channels wall, or porous rock formations, to pressurised fluid injections via laboratory-based experiments. |
Sectors | Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology,Other |
URL | https://www.pnas.org/content/117/48/30228 |
Description | Modelling the flow-induced deformation of a soft Hele-Shaw cell |
Organisation | University of Cambridge |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | We have performed physical inspiration and experimental verification for the mathematical modelling of a single-phase flow in a Hele-Shaw cell with an enclosed, compliant boundary. |
Collaborator Contribution | The partner has contributed mathematical modelling to the understanding of a single-phase flow in a Hele-Shaw cell with an enclosed, compliant boundary. |
Impact | To date, this collaboration has resulted in both internal and international conference presentations, at the MCND Winter Seminar Series 2020 and the APS DFD annual meeting 2019 respectively. Disciplines involved: Physics, Applied Mathematics |
Start Year | 2019 |
Description | On Trapping and Escape of Viscous Fingers in a Soft Hele-Shaw Cell |
Organisation | University of Oxford |
Department | Department of Engineering Science |
Country | United Kingdom |
Sector | Academic/University |
PI Contribution | Viscous flow in the narrow gap between a rigid plate and a confined elastic solid has been observed to `choke' at high flow rates, due to the deforming solid making contact with the plate and sealing the gap. The collaboration was focus on investigating the role of viscous fingering instability on the choking process. We have contributed experimental data and theoretical modelling. The main analysis and results interpretation were done by our team. |
Collaborator Contribution | The collaborators have provided experimental data and have contributed to the presentation of results. |
Impact | This multi-disciplinary collaboration has resulted in one paper that was recently submitted to Phys. Rev. Lett. (reference number LQ18021). The finding of the collaboration formed the bases of the invited seminar at the University of Warwick. The work will also be presented at the Biological Fluids & Flows Conference-TJP80-Cambridge (https://sites.google.com/view/tjp80), the BIRS-UBC-O Workshop, "Equilibrium and non-Equilibrium Pattern Formation in Soft Matter: From Elastic Solids to Complex Fluids" (http://www.birs.ca/ubco) - this will be an invited talk - and the EFMC14 - 14th European Fluid Mechanics Conference-Athens (https://euromech.org/conferences/EFMC/EFMC14). |
Start Year | 2021 |
Description | Biological Fluids & Flows Conference-TJP80-Cambridge. |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | The PI will give an invited talk at the Biological Fluids & Flows Conference-TJP80-Cambridge (https://sites.google.com/view/tjp80). |
Year(s) Of Engagement Activity | 2022 |
URL | https://sites.google.com/view/tjp80 |
Description | Conference |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | National |
Primary Audience | Professional Practitioners |
Results and Impact | Conference organised at the Institute of Physics. The event combined invited talks by experts in the field and panel discussions that inspired healthy debate on the future of the field. Feedback received on the event from professionals and members of the public was excellent. |
Year(s) Of Engagement Activity | 2020 |
URL | http://complexity-physics.org/blog/2020/01/23/studying-the-climate-a-challenge-of-complexity-6th-feb... |
Description | Conference Presentation (abstract submitted) |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | Abstract submitted to attend Congress of International Union of Theoretical and Applied Mechanics |
Year(s) Of Engagement Activity | 2020 |
URL | https://www.ictam2020.org/ |
Description | Conference Presentation at APS DFD 2019 |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | Presentation of preliminary research findings at international conference, which was well-received and sparked interesting debate and discussions afterwards. |
Year(s) Of Engagement Activity | 2019 |
URL | http://meetings.aps.org/Meeting/DFD19/Session/H34.9 |
Description | Confernence Presentation |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Regional |
Primary Audience | Professional Practitioners |
Results and Impact | Conference presentation at faculty-wide workshop which sparked fruitful discussion and ideas for future research directions. |
Year(s) Of Engagement Activity | 2020 |
Description | Invited talk at the XIII Summer Workshop in Mathematics of the University of BrasÃlia |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | About 30 people attended the PI's invited talk, which sparked interesting questions and subsequent exchange of ideas via e-mail. |
Year(s) Of Engagement Activity | 2021 |
URL | https://www.mat.unb.br/verao2021/mecanica_en.html |
Description | The PI was invited to take part in BIRS-UBC-O Workshop on "Equilibrium and non-Equilibrium Pattern Formation in Soft Matter: From Elastic Solids to Complex Fluids". |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Professional Practitioners |
Results and Impact | This activity will take part in July of 2022. The PI is invited to participate in the international workshop organised the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) and of the University of British Columbia Okanagan (UBCO), which is aimed for the global scientific community. |
Year(s) Of Engagement Activity | 2022 |
URL | http://www.birs.ca/ubco. |