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I am an applied mathematician and fluid dynamicist, and I am interested in using mathematics to model and understand physical processes in the world around us. I am particularly interested in the mechanics of rheologically complex materials, flow through porous and deformable media, and the behaviour of granular suspensions, and in geophsyical, industrial and biological applications of these problems.

I am an Associate Professor of Applied Mathematics and Fluid Mechanics in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge, and a Fellow and Director of Studies in Mathematics at Corpus Christi College, Cambridge.

Research interests

Research areas in which I have worked and topics of current interest include:

  • Non-Newtonian fluid mechanics and dynamics of 'structured' fluids: geophysical applications (mud flows, magmatic systems, mud volcanism); industrial applications (mine tailings, batch processing, cleaning)

  • Viscoplasticity: channel and displacement flows; viscoplastic boundary layers; locomotion through viscoplastic fluids (swimming in mud and worm locomotion)

  • Flows of two-phase suspensionss and granular media

  • Clogging and jamming: blood flow and sickle-cell disease; granular patterns in displacement flows

  • Poro-elasticity and flow through/of deformable media: applications in geophysics (subsidence, sub-glacial till, liquefaction) and industry (pulp and paper, insulation)

  • Thixotropy and liquefaction

  • Convection in porous media: impact of heterogeneity; plume dynamics; dissolution and CO2 sequestration; astrophysical convection and internal heat

  • Mixing in porous media; viscous fingering

  • Glaciological probelems: till mechanics; water transport

  • Geological convective problems: hydrological circulation, mid-ocean ridge dynamics, magma chambers

If you are interested in studying for a PhD or holding a postdoctoral position working with me, please get in touch. There is an ever-changing list of interesting problems to work on!

Current lecturing

Mathematics Part III: Non-Newtonian Fluid Mechanics (16 lectures, Michaelmas)

NST IA: Mathematical Methods II 'A' course (24 lectures, Lent)

Publications

  1. Balmforth, N.J. and Hewitt, D.R. The implications of a fluid yield stress, Journal of Fluid Mechanics (Perspectives), 2025 1011, P1

  2. Hewitt, D.R. and Balmforth, N.J. Stokes layers in complex fluids, Journal of Non-Newtonian Fluid Mechanics, 2024 334, 105328

  3. Hewitt, D.R. Swimming in viscoplastic fluids, Rheologica Acta, 2024 DOI: 10.1007/s00397-024-01466-8

  4. Pecnik Bambic, M., Araujo, N.A.M., Walker, B.J., Hewitt, D.R., Pei, Q.X, Ni, R., and Volpe, G. Optimal face-to-face coupling for fast self-folding kirigami, Soft Matter, 2024 DOI: 10.1039/d3sm01474f

  5. Warburton K.L.P., Hewitt D.R., Meyer C.R. and Neufeld J.A. A shallow approximation for ice streams sliding over strong beds, Journal of Glaciology, 2023 1-12

  6. Hinton, E.M., Hewitt, D.R. and Hogg, A.J. Obstructed free-surface viscoplastic flow on an inclined plane, Journal of Fluid Mechanics, 2023 964, A35

  7. Hogan, K., Warburton, K.L.P., Graham, A.G.C., Neufeld, J.A., Hewitt, D.R., Dowdeswell, J.A. and Larter, R.D. Towards modelling of corrugation ridges at ice-sheet grounding lines, The Cryosphere, 2023 17, 2645-2664

  8. Warburton, K.L.P., Hewitt, D.R. and Neufeld, J.A. Shear dilation of subglacial till results in time-dependent sliding laws, Proceedings of the Royal Society A , 2023 479 (20220536)

  9. Hewitt, D.R. Clogged Corners (a Focus on Fluids article), Journal of Fluid Mechanics, 2022 948 (F1) [pdf]

  10. Paterson, D.T., Eaves, T.S., Hewitt, D.R., Balmforth, N.J. and Martinez, D.M. One-dimensional compression of a saturated elastoviscoplastic medium, Physical Review Fluids, 2022 7 (054303) [pdf]

  11. Hewitt, D.R. Evolution of convection in a layered porous medium, Journal of Fluid Mechanics, 2022 941 (A56) [pdf]

  12. Nijjer, J.S., Hewitt, D.R., and Neufeld, J.A.. Horizontal miscible displacements through porous media: the interplay between viscous fingering and gravity segregation, Journal of Fluid Mechanics, 2022 935 (A14) [pdf]

  13. Hewitt, D.R. and Balmforth, N.J. Locomotion with a wavy cylindrical filament in a yield-stress fluid, Journal of Fluid Mechanics, 2022 936 (A17) [pdf]

  14. Doyle S.H., Hubbard B., Christoffersen P., Law R., Hewitt D.R., Neufeld J.A., Schoonman C.M., Chudley T.R., Bougamont M. Water flow through sediments and at the ice-sediment interface beneath Sermeq Kujalleq (Store Glacier), Greenland, Journal of Glaciology, 2021 (1-20) [pdf]

  15. Balmforth, N.J., Craster, R.V. and Hewitt, D.R. Building on Oldroyd's viscoplastic legacy: perspectives and new developments, Journal of Non-Newtonian Fluid Mechanics, 2021 294 (104580) [pdf]

  16. Le Reun, T. and Hewitt, D.R. High-Rayleigh-number convection in porous-fluid layers, Journal of Fluid Mechanics, 2021 920 (A35) [pdf]

  17. Paterson, D.T., Eaves, T.S., Hewitt, D.R., Balmforth, N.J. and Martinez, D.M. On two-phase modeling of dewatering pulp suspensions, AIChE Journal, 2021 67 (e17277) [pdf]

  18. Warburton, K.L.P., Hewitt, D.R. and Neufeld, J.A. Tidal Grounding-Line Migration Modulated by Subglacial Hydrology, Geophysical Research Letters, 2020, 47 (e2020GL089088) [pdf]

  19. Le Reun, T. and Hewitt, D.R. Internally heated porous convection: an idealised model for Enceladus' hydrothermal activity, Journal of Geophysical Research: Planets, 2020, 125 (e2020JE006451) [pdf]

  20. Hewitt, D.R. Vigorous convection in porous media, Proceedings of the Royal Society A (review article) 2020 476 (20200111) [pdf]

  21. Daneshi, M., MacKenzie, J., Balmforth, N.J., Martinez, D.M. and Hewitt, D.R. Obstructed viscoplastic flow in a Hele–Shaw cell, Physical Review Fluids 2020 5 (013301) [pdf]

  22. Warburton, K.L.P., Hewitt, D.R. and Neufeld, J.A. The elastic Landau-Levich problem on a slope, Journal of Fluid Mechanics, 2020 883 (A40) [pdf]

  23. Hewitt, D.R., Peng, G.G., and Lister, J.R. Buoyancy-driven plumes in a layered porous medium, Journal of Fluid Mechanics, 2020 883 (A37) [pdf]

  24. Supekar, R., Hewitt, D.R. and Balmforth, N.J. Translating and squirming cylinders in a viscoplastic fluid, Journal of Fluid Mechanics, 2020 882 (A11) [pdf] (see also Front-cover picture of journal)

  25. Eaves, T.S., Paterson, D.T., Hewitt, D.R., Balmforth, N.J. and Martinez, D.M. Dewatering saturated, networked suspensions with a screw press, Journal of Engineering Mathematics, 2019 doi:10.1007/s10665-019-10029-3 [pdf]

  26. Paterson, D.T., Eaves, T.S., Hewitt, D.R., Balmforth, N.J. and Martinez, D.M. Flow-driven compaction of a fibrous porous medium, Physical Review Fluids, 2019 4 (074306) [pdf]

  27. Nijjer, J.S., Hewitt, D.R., and Neufeld, J.A. Stable and unstable miscible displacements in layered porous media, Journal of Fluid Mechanics, 2019 869 (468-499) [pdf]

  28. Hewitt, D.R., and Balmforth, N.J. Viscoplastic slender-body theory, Journal of Fluid Mechanics, 2018 856 (870-897) [pdf] (see also 'Focus on Fluids' review article Dropping slender-body theory into the mud by Saverio Spagnolie)

  29. Hewitt, D.R., Chini, G.P. and Neufeld, J.A. The influence of a poroelastic till on rapid subglacial flooding and cavity formation, Journal of Fluid Mechanics, 2018 855 (1170-1207) [pdf]

  30. Nijjer, J.S., Hewitt, D.R., and Neufeld, J.A. The dynamics of miscible viscous fingering from onset to shutdown, Journal of Fluid Mechanics, 2018 837 (520-545) [pdf]

  31. Hewitt, D.R., and Lister, J.R., Stability of columnar convection in a three-dimenional porous medium, Journal of Fluid Mechanics, 2017 829 (89-111) [pdf]

  32. Hewitt, D.R., and Balmforth, N.J., Taylor's swimming sheet in a yield stress fluid, Journal of Fluid Mechanics, 2017 828 (33-56) [pdf]

  33. Kvick, M., Martinez, D.M., Hewitt, D.R., and Balmforth, N.J., Imbibition with swelling: Capillary rise in thin deformable porous media, Physical Review Fluids, 2017 2 (074001) [pdf]

  34. Balmforth, N.J., Craster, R.V., Hewitt, D.R., Hormozi, S., and Maleki, A., Viscoplastic boundary layers, Journal of Fluid Mechanics, 2017 813 (929-954) [pdf]

  35. Liu, Y., Balmforth, N.J., Hormozi, S. and Hewitt, D.R., Two-dimensional viscoplastic dambreaks, Journal of Non-Newtonian Fluid Mechanics, 2016 238 (65-79) [pdf]

  36. Hewitt, D.R., Paterson, D.T., Balmforth, N.J., and Martinez, D.M. Dewatering of fibre suspensions by pressure filtration, Physics of Fluids, 2016 28 (063304). [pdf]

  37. Hewitt, D.R., Nijjer, J.S., Neufeld, J.A., and Worster, M.G. Flow-induced compaction of a deformable porous medium, Physical Review E, 2016 93, 023116 [pdf]

  38. Hewitt, D.R., Balmforth, N.J., Dasani, M., and Martinez, D.M. Obstructed and channelized viscoplastic flow in a Hele-Shaw cell, Journal of Fluid Mechanics, 2016 790 (173-204) [pdf]

  39. Hewitt, D.R., Neufeld, J.A., and Balmforth, N.J. Shallow, gravity-driven flow in a poro-elastic layer, Journal of Fluid Mechanics, 2015 778 (335-360) [pdf]

  40. Hewitt, D.R., Neufeld, J.A., and Lister, J.R. High Rayleigh number convection in a porous medium containing a thin low-permeability layer, Journal of Fluid Mechanics, 2014 756 (844-869) [pdf]

  41. Hewitt, D.R., Neufeld, J.A., and Lister, J.R. High Rayleigh number convection in a three-dimensional porous medium, Journal of Fluid Mechanics, 2014 748 (879-895) [pdf]

  42. Hewitt, D.R., Neufeld, J.A., and Lister, J.R. Stability of columnar convection in a porous medium, Journal of Fluid Mechanics, 2013 737 (205-231) [pdf]

  43. Hewitt, D.R., and Balmforth, N.J. Thixotropic gravity currents, Journal of Fluid Mechanics, 2013 727 (56-82) [pdf]

  44. Hewitt, D.R., Neufeld, J.A., and Lister, J.R. Convective shutdown in a porous medium at high Rayleigh number, Journal of Fluid Mechanics, 2013 719 (551-586) [pdf] (see also 'Focus on Fluids' review article by David Pritchard, and Front-cover picture)

  45. Hewitt, D.R., Neufeld, J.A., and Lister, J.R. Ultimate regime of high Rayleigh number convection in a porous medium, Physical Review Letters, 2012 108 (224503) [pdf]

PhD students past and present

2024 - Jonathan Watts
2023 - Emma Bouckley
2022 - Emily Cook
2021 - Anushka Herale
2018 - 2022 Kasia Warburton
2015 - 2019 Japinder Nijjer

Previously

From 2019-2023 I was a Lecturer and then Associate Professor at UCL; from 2015-2019 I was a Research Fellow and, latterly, Tutor, at Gonville and Caius College, University of Cambridge. Prior to that, I was a Killam Postdoctoral Research Fellow in the Department of Mathematics at the University of British Columbia, Vancouver (2014-2015). I hold a Ph.D. in Applied Mathematics from the University of Cambridge; my PhD thesis, entitled 'High Rayleigh number Convection in a Porous Medium', can be found here.

Contacts

email: D.R.Hewitt 'at' damtp.cam.ac.uk
Office: Room H1.07, Centre for Mathematical Sciences
Address: DAMTP, Centre for Mathematical Sciences,
Wilberforce Road, Cambridge CB3 0WA.
Telephone: 01223 764067