Imperial College London
Alternate

ProfessorRichardCraster

Faculty of Natural Sciences

Dean of the Faculty of Natural Sciences
 
 
 
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Contact

 

+44 (0)20 7594 8554r.craster Website

 
 
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Assistant

 

Miss Hannah Cline +44 (0)20 7594 1934

 
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Location

 

3.05Faculty BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Balmforth:2017:10.1017/jfm.2016.878,
author = {Balmforth, NJ and Craster, RV and Hewitt, DR and Hormozi, S and Maleki, A},
doi = {10.1017/jfm.2016.878},
journal = {Journal of Fluid Mechanics},
pages = {929--954},
title = {Viscoplastic boundary layers},
url = {http://dx.doi.org/10.1017/jfm.2016.878},
volume = {813},
year = {2017}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - In the limit of a large yield stress, or equivalently at the initiation of motion, viscoplasticflows can develop narrow boundary layers that provide either surfaces of failure betweenrigid  plugs,  the  lubrication  between  plugged  flow  and  a  wall,  or  buffers  for  regions  ofpredominantly plastic deformation. (Oldroyd 1947,Proc. Camb. Phil. Soc.43, 383 - 395)presented the first theoretical discussion of these viscoplastic boundary layers, offeringan  asymptotic  reduction  of  the  governing  equations  and  a  discussion  of  some  modelflow  problems.  However,  the  complicated  nonlinear  form  of  Oldroyd’s  boundary-layerequations  has  evidently  precluded  further  discussion  of  them.  In  the  current  paper,we revisit Oldroyd’s viscoplastic boundary-layer analysis and his canonical examples ofa  jet-like  intrusion  and  flow  past  a  thin  plate.  We  also  consider  flow  down  channelswith  either  sudden  expansions  or  wavy  walls.  In  all  these  examples,  we  verify  thatviscoplastic boundary layers form as envisioned by Oldroyd. For each example, we extractthe dependence of the boundary-layer thickness and flow profiles on the dimensionlessyield-stress parameter (Bingham number). We find that, while Oldroyd’s boundary-layertheory  applies  to  free  viscoplastic  shear  layers,  it  does  not  apply  when  the  boundarylayer  is  adjacent  to  a  wall,  as  has  been  observed  previously  for  two-dimensional  flowaround circular obstructions. Instead, the boundary-layer thickness scales in a differentfashion with the Bingham number, as suggested by classical solutions for plane-parallelflows, lubrication theory and, for flow around a plate, by (Piau 2002,J. Non-NewtonianFluid Mech.102, 193 - 218); we rationalize this second scaling and provide an alternativeboundary-layer theory.
AU  - Balmforth,NJ
AU  - Craster,RV
AU  - Hewitt,DR
AU  - Hormozi,S
AU  - Maleki,A
DO  - 10.1017/jfm.2016.878
EP  - 954
PY  - 2017///
SN  - 1469-7645
SP  - 929
TI  - Viscoplastic boundary layers
T2  - Journal of Fluid Mechanics
UR  - http://dx.doi.org/10.1017/jfm.2016.878
UR  - http://hdl.handle.net/10044/1/43813
VL  - 813
ER  -
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