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Gravity-driven flow of Herschel–Bulkley fluid in a fracture and in a 2D porous medium

Published online by Cambridge University Press:  16 May 2017

V. Di Federico Open the ORCID record for V. Di Federico [Opens in a new window] ,
S. Longo Open the ORCID record for S. Longo [Opens in a new window] ,
S. E. King Open the ORCID record for S. E. King [Opens in a new window] ,
L. Chiapponi Open the ORCID record for L. Chiapponi [Opens in a new window] ,
D. Petrolo Open the ORCID record for D. Petrolo [Opens in a new window]  and
V. Ciriello
V. Di Federico*
Affiliation:
Dipartimento di Ingegneria Civile, Chimica, Ambientale e dei Materiali (DICAM), Università di Bologna, Viale Risorgimento, 2, 40136 Bologna, Italy
S. Longo
Affiliation:
Dipartimento di Ingegneria e Architettura (DIA), Università di Parma, Parco Area delle Scienze, 181/A, 43124 Parma, Italy
S. E. King
Affiliation:
School of Mathematics, University of Edinburgh, Edinburgh, EH9 3FD, UK
L. Chiapponi
Affiliation:
Dipartimento di Ingegneria e Architettura (DIA), Università di Parma, Parco Area delle Scienze, 181/A, 43124 Parma, Italy
D. Petrolo
Affiliation:
Dipartimento di Ingegneria e Architettura (DIA), Università di Parma, Parco Area delle Scienze, 181/A, 43124 Parma, Italy
V. Ciriello
Affiliation:
Dipartimento di Ingegneria Civile, Chimica, Ambientale e dei Materiali (DICAM), Università di Bologna, Viale Risorgimento, 2, 40136 Bologna, Italy
*
†Email address for correspondence: [email protected]
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Abstract

New analytical models are introduced to describe the motion of a Herschel–Bulkley fluid slumping under gravity in a narrow fracture and in a porous medium. A useful self-similar solution can be derived for a fluid injection rate that scales as time $t$; an expansion technique is adopted for a generic injection rate that is power law in time. Experiments in a Hele-Shaw cell and in a narrow channel filled with glass ballotini confirm the theoretical model within the experimental uncertainty.

JFM classification

Geophysical and Geological Flows: Gravity currents Low-Reynolds-number flows: Hele-Shaw flows Non-Newtonian Flows: Non-Newtonian Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 821 , 25 June 2017 , pp. 59 - 84
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Copyright
© 2017 Cambridge University Press 

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