# Staff Directory

## Dr Philip Trevelyan

#### Contact Details

- Faculty of Computing, Engineering and Science
- Lecturer in Mathematics
- philip.trevelyan@southwales.ac.uk
- (01443) 4 82275
- G733
- Treforest

## Qualifications

PhD Applied Mathematics, Leeds (1996-1999).

BA (Hons) 2.1 Mathematics, Oxford (1993-1996).

## Experience

Lecturer, Mathematics, Glamorgan/South Wales (2010-now).

Post-Doctoral Research Associate positions:

Chemically Driven Instabilities, Nonlinear Physical Chemistry Unit, Brussels (2006-2010).

Reactive Thin Films, Chemical Engineering, Imperial College London (2004-2006).

Heated Thin Films, Chemical Engineering, Leeds (2002-2004).

Thin Films, Chemistry Department, Leeds (1999-2002).

## Responsibilities

Third Year Tutor

Co-supervising 1 PhD student

Supervising 3 final year project students and 1 MMath project student

MS3S29 – Final Year Project Organiser

MS3S20 – Partial Differential Equations

MS2S04 – Further Calculus (first half)

MS1S461 – Mathematics and Statistics for Computing

AM2H41 – Engineering Mathematics 2

AM0S01 – Foundations of Mathematics

Other roles: internal registers and fire warden.

## Publications

Journal Publications

1. M.J.A. Choudhury, P.M.J. Trevelyan and G.P. Boswell, A mathematical model of nutrient influence on fungal competition, submitted to Journal of Theoretical Biology.

2. M.J.A. Choudhury, P.M.J. Trevelyan and G.P. Boswell, Determining the kinematic properties of an advancing front using a decomposition method, IAENG, 46, 578-584, (2016).

3. V. Loodts, P.M.J. Trevelyan, L. Rongy, A. De Wit, Density profiles around A+B→C reaction-diffusion fronts in partially miscible systems: A general classification, Phys. Rev. E. 94, 043115, (2016).

4. P.M.J. Trevelyan, C. Almarcha and A. De Wit, Buoyancy-driven instabilities around miscible A+B→C reaction fronts: A general classification, Phys. Rev. E. 91, 023001, (2015).

5. J. Gandhi and P.M.J. Trevelyan, Onset conditions for a Rayleigh-Taylor instability with step function density profiles, J. Engng. Math. 86, 31-48, (2014).

6. C. Almarcha, P. M. J. Trevelyan, P. Grosﬁls and A. De Wit, Thermal effects on the diffusive layer convection instability of an exothermic acid-base reaction front, Phys. Rev. E. 88, 033009, (2013).

7. J. Carballido-Landeira, P.M.J. Trevelyan, C. Almarcha and A. De Wit, Mixed-mode instability of a miscible interface due to coupling between Rayleigh-Taylor and double-diffusive convection modes, Phys. Fluids. 25, 024107, (2013).

8. L.A. Riolfo, Y. Nagatsu, S. Iwata, R. Maes, P.M.J. Trevelyan and A. De Wit, Experimental evidence of reaction-driven miscible viscous fingering, Phys. Rev. E., 85, 015304, (2012).

9. P.M.J. Trevelyan, A. Pereira and S. Kalliadasis, Dynamics of a reactive thin film, Math. Model. Nat. Phenom., 7, 99-145, (2012).

10. P.M.J. Trevelyan, Approximating the large time asymptotic reaction zone solution for fractional order kinetics AnBm, Discrete and Continuous Dynamical Systems – Series S, 5, 219-234, (2012).

11. S. Kuster, L.A. Riolfo, A. Zalts, C. El Hasi, C. Almarcha, P.M.J. Trevelyan, A. De Wit and A. D’Onofrio, Differential diffusion effects on buoyancy-driven instabilities of acid-base fronts: the case of a color indicator, J. Phys. Chem. Chem. Phys., 13, 17295-17303 (2011).

12. C. Almarcha, Y. R’Honi, Y. De Decker, P. M. J. Trevelyan, K. Eckert, and A. De Wit, Convective mixing induced by acid-base reactions, J. Phys. Chem. B., 115, 9739-9744, (2011).

13. P.M.J. Trevelyan, C. Almarcha and A. De Wit, Buoyancy-driven instabilities of miscible two-layer stratifications in porous media and Hele-Shaw cells, J. Fluid Mech., 670, 38-65, (2011).

14. M. Mishra, P.M.J. Trevelyan, C. Almarcha and A. De Wit, Influence of double diffusive effects on miscible viscous fingering, Phys. Rev. Lett., 105, 204501 (2010).

15. S.H. Hejazi, P.M.J. Trevelyan, J. Azaiez and A. De Wit, Viscous fingering of a miscible reactive A+B→C interface: A linear stability analysis, J. Fluid Mech., 652, 501-528 (2010).

16. L. Rongy, P.M.J. Trevelyan and A. De Wit, Influence of buoyancy-driven convection on the dynamics of A+B→C reaction fronts in horizontal solution layers, Chem. Eng. Sci., 65, 2382-2391 (2010).

17. C. Almarcha, P.M.J. Trevelyan, L.A. Riolfo, A. Zalts, C. El Hasi, A. D’Onofrio and A. De Wit, Active role of a color indicator in buoyancy-driven instabilities of chemical fronts, J. Phys. Chem. Lett., 1, 752-757 (2010).

18. C. Almarcha, P.M.J. Trevelyan, P. Grosfils and A. De Wit, Chemically Driven Hydrodynamic Instabilities, Phys. Rev. Lett., 104, 044501 (2010).

19. P.M.J. Trevelyan, Analytical small time asymptotic properties of A+B→C fronts, Phys. Rev. E, 80, 046118 (2009).

20. C. Ruyer-Quil, P.M.J. Trevelyan, F. Giorgiutti-Dauphine, C. Duprat and S. Kalliadasis, Film flows down a fiber: Modeling and influence of streamwise viscous diffusion, Eur. Phys. J. Special Topics, 166, 89-92 (2009).

21. A. Pereira, P.M.J. Trevelyan, U. Thiele and S. Kalliadasis, Interfacial instabilities driven by chemical reactions, Eur. Phys. J. Special Topics, 166, 121-125 (2009).

22. P.M.J. Trevelyan, Higher-order large-time asymptotics for a reaction of the form nA+mB→C, Phys. Rev. E, 79, 016105 (2009).

23. L. Rongy, P.M.J. Trevelyan and A. De Wit, Dynamics of A+B→C reaction fronts in the presence of buoyancy-driven convection, Phys. Rev. Lett., 101, 084503 (2008).

24. P.M.J. Trevelyan, D.E. Strier and A. De Wit, Analytical asymptotic solutions of nA+mB→C reaction-diffusion equations in two-layer systems: A general study, Phys. Rev. E, 78, 026122 (2008).

25. C. Ruyer-Quil, P.M.J. Trevelyan, F. Giorgiutti-Dauphine, C. Duprat and S. Kalliadasis, Modelling film flows down a fibre, J. Fluid Mech., 603, 431-462 (2008).

26. P.M.J. Trevelyan, B. Scheid, C. Ruyer-Quil and S. Kalliadasis, Heated falling films, J. Fluid Mech., 592, 295-334 (2007).

27. A. Pereira, P.M.J. Trevelyan, U. Thiele and S. Kalliadasis, Thin Films in the Presence of Chemical Reactions, Fluid Dyn. Mater. Process., 3, 303-316 (2007).

28. A. Pereira, P.M.J. Trevelyan, U. Thiele and S. Kalliadasis, Dynamics of a horizontal thin liquid film in the presence of reactive surfactants, Phys. Fluids, 19, 112102 (2007).

29. A. Pereira, P.M.J. Trevelyan, U. Thiele and S. Kalliadasis, Interfacial hydrodynamic waves driven by chemical reactions, J. Engng. Math., 59, 207-220 (2007).

30. S. Saprykin, P.M.J. Trevelyan, R. Koopmans and S. Kalliadasis, Free-surface thin-film flows over uniformly heated topography, Phys. Rev. E, 75, 026306 (2007).

31. P.M.J. Trevelyan and S. Kalliadasis, Wave dynamics on a thin liquid film falling down a heated wall, J. Engng. Math., 50, 177-208 (2004).

32. P.M.J. Trevelyan and S. Kalliadasis, Dynamics of a reactive falling film at large Peclet numbers. I Long-wave approximation, Phys. Fluids, 16, 3191-3208 (2004).

33. P.M.J. Trevelyan and S. Kalliadasis, Dynamics of a reactive falling film at large Peclet numbers. II Nonlinear waves far from criticality: Integral-boundary-layer approximation, Phys. Fluids, 16, 3209-3226 (2004).

34. P.M.J. Trevelyan, S. Kalliadasis, J.H. Merkin and S.K. Scott, Dynamics of a vertically falling film in the presence of a first-order chemical reaction, Phys. Fluids, 14, 2402-2421 (2002).

35. P.M.J. Trevelyan, S. Kalliadasis, J.H. Merkin and S.K. Scott, Mass transport enhancement in regions bounded by rigid walls, J. Engng. Math., 42, 45-64 (2002).

36. P.M.J. Trevelyan, S. Kalliadasis, J.H. Merkin and S.K. Scott, Circulation and reaction enhancement of mass transport in a cavity, Chem. Eng. Sci., 56, 5177-5188 (2001).

37. P.M.J. Trevelyan, L. Elliott and D.B. Ingham, A numerical method for Schwarz-Christoffel conformal transformation with application to potential flow in channels with oblique sub-channels, CMES-Comp. Model. Eng., 1, 117-122 (2000).

38. L.M. Conroy, P.M.J. Trevelyan and D.B. Ingham, An analytical, numerical, and experimental comparison of the fluid velocity in the vicinity of an open tank with one and two lateral exhaust slot hoods and a uniform crossdraft, Ann. Occup. Hyg., 44, 407-419 (2000).

39. P.M.J. Trevelyan, L. Elliott and D.B. Ingham, Potential flow in a semi-infinite channel with multiple sub-channels using the Schwarz-Christoffel transformation, Comput. Meth. Appl. Mech. Eng., 189, 341-359 (2000).

Conference Proceedings / Extended Abstracts

40. P.M.J. Trevelyan, D.E. Strier and A. De Wit, Asymptotic reaction-diffusion profiles in two-layer systems, Mathematics in Chemical Kinetics and Engineering. (Ghent, Belgium, February 2009).

41. A. Pereira, P.M.J. Trevelyan and S. Kalliadasis, Hydrodynamics of reactive thin films, Proc. 22nd Int. Cong. Theo. Appl. Mech., paper 1132. (Adelaide, Australia, August 2008).

42. S. Kalliadasis and P.M.J. Trevelyan, Dynamics of a reactive falling film at large Peclet numbers, Proc. 21st Int. Cong. Theo. Appl. Mech., paper FM14_L10220 (Warsaw, Poland, August 2004).

43. Toth, Boissonade, Scott, Westerhoff, Jonnalagadda, Gaspar, Trevelyan, Showalter, Snita, Marek, Mayama, Dewel, Simon, Sorensen, Epstein, Satnoianu, Harrison, Merkin, Hemming, Hantz, Noszticzius, Miller, Hauser, Sielewiesiuk, General discussion, Faraday Discussions, 2002, 120, 407-419. (Manchester, UK, September 2001).

44. P.M.J. Trevelyan, D.B. Ingham and L. Elliott, The effects of ventilation and sash handles on the flow in fume cupboards, Proc. Prog. Modern Vent.: 6th Int. Sym. Vent. Contam. Contr. Ventilation 2000, 2000, 2, 80-83. (Helsinki, Finland, June 2000).

45. P.M.J. Trevelyan, L. Elliott and D.B. Ingham, Boundary integral approach to determine the potential fluid flow in a channel with multiple sub-channels, Proc. 2nd UK Conf. Bdary. Int. Meth., 291-302. (London, UK, September 1999).

46. P.M.J. Trevelyan, L. Elliott and D.B. Ingham, Boundary integrals applied to potential flow in channels/oblique sub-channels, Proc. 1st Int. Conf. Bdary. Elem. Techs., 341-348. (London, UK, July 1999)

47. P.M.J. Trevelyan, L. Elliott and D.B. Ingham, Effects of a ventilation duct on the performance of a fume cupboard, RoomVent98, 1998, 1, 385-391. (Stockholm, Sweden, June 1998).

48. P.M.J. Trevelyan, L. Elliott and D.B. Ingham, Ventilation near a fume cupboard, Proc. Inst. Chem. Engrs., 1998, paper 140. (Newcastle, UK, April 1998).

## Memberships

Member of IMA, FHEA

## Research

Turbulent and Potential Flow

My PhD was concerned with studying theoretically how to minimise the leakages from a fume cupboard with particular emphasis on the effect of a ventilation duct in the room. By assuming that potential flow was valid in the room, the flow pattern was obtained analytically using conformal mappings with complex potentials. However, a physically more realistic approach was to use the k-epsilon turbulent model for both the fluid flow inside and outside of the fume cupboard.

Thin Films

After my PhD, I began researching surface tension instabilities of thin films coupled to heat and mass. A single long wave equation was analytically derived, but this method failed for moderate Reynolds numbers. Thus, the weighted integral approach was applied to yield two equations for the fluid flow with additional equations for heat and mass. As multiple travelling wave solitary-like solutions exist full time dependent calculations were performed to determine which solution occurs. In the presence of dispersion we found that the travelling wave solutions were born via non-oscillatory dispersive waves (KdV), unlike the more common oscillatory structures found away from onset. The most common type of solitary-like wave structures consist of a flat film with convex waves on top, however, unusually, concave waves can be the most stable form of solution when the size of the nonlinear term associated with dispersion was sufficiently large and negative. One interesting result obtained was that the inclusion of interfacial heat losses can lead to the removal of convex travelling wave solutions when the wall that the thin film is in contact with is heated by a constant flux, however, such travelling wave solutions always exist when the wall is heated to a constant temperature.

Chemically Driven Instabilities

More recently, my research has been directed towards studying how to generate fluid motion by a chemical reaction via changes in the fluid’s physical properties. In particular the way a simple A+B→C chemical reaction can induce buoyancy-driven instabilities was investigated. To determine if, when and where an instability occurs a linear stability analysis was performed. Similarly viscous fingering instabilities have been investigated with particular attention to the case when a more viscous liquid is injected into a less viscous liquid. Due to a simple A+B→C chemical reaction, non-monotonic viscosity profiles can induce an instability, even with equal diffusion coefficients. Again, a linear stability analysis was performed to confirm the instability.

Reaction Diffusion Equations

Large time asymptotic analytical solutions have been obtained for the reaction nA+mB→C in the presence of immiscible liquids. It was found that a reaction front in immiscible liquids could travel in the opposite direction to the same reaction front in two identical miscible liquids. The centre of mass of the product can move in the opposite direction to the centre of mass of the reaction rate. Using a higher-order large time asymptotic expansion, a more accurate representation for the reaction front position was found. A class of reaction fronts were found whose position did not scale with the square root of time. This showed that the reaction A+2B→C was the only reaction of the form nA+mB→C with n and m being positive integers in which a reaction front could move to a non-zero finite distance away from its initial position in the large time asymptotic limit. Further, the small time asymptotic behaviour of the reaction front formed by A+B→C revealed that the centre of mass of the product concentration distribution is initially located at three quarters of the distance of the centre of mass of the reaction rate from the initial position.

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