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Using a squeegee on a layer of viscous or viscoplastic fluid
Phys. Rev. Fluids 7, 104101 – Published 13 October, 2022
DOI: https://doi.org/10.1103/PhysRevFluids.7.104101
Abstract
We use lubrication theory to study the bow wave ahead of a squeegee as it moves steadily over a horizontal layer of fluid. If the squeegee is infinitely long with a small gap at its base then the motion is two dimensional and we obtain an analytic prediction for the flow thickness. For a relatively long straight squeegee on a layer of viscous fluid with no gap, we deploy a two-dimensional approximation, which enables the flow thickness in the bow wave to be determined relative to the thickness at the squeegee. The analysis is completed by balancing the flux into the bow wave with the transverse flux perpendicular to the squeegee associated with hydrostatic pressure gradients. The simple method is adapted to squeegees that are angled to the direction of translation. For a layer of viscoplastic fluid that has a relatively high yield stress, the bow wave is quasiplugged and this observation enables a different flux balance to be used to determine the flow thickness. The predictions are compared favorably to numerical results.
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References (15)
- H. R. Dietterich, K. V. Cashman, A. C. Rust, and E. Lev, Diverting lava flows in the lab, Nat. Geosci. 8, 494 (2015).
- A. Ross, S. Wilson, and B. Duffy, Blade coating of a power-law fluid, Phys. Fluids 11, 958 (1999).
- G. S. White, C. J. W. Breward, P. D. Howell, and R. J. S. Young, A model for the screen-printing of Newtonian fluids, J. Eng. Math. 54, 49 (2006).
- M. Taroni, C. J. W. Breward, P. D. Howell, J. M. Oliver, and R. J. S. Young, The screen printing of a power-law fluid, J. Eng. Math. 73, 93 (2012).
- E. M. Hinton, A. J. Hogg, and H. E. Huppert, Viscous free-surface flows past cylinders, Phys. Rev. Fluids 5, 084101 (2020).
- A. Sauret, N. J. Balmforth, C. P. Caulfield, and J. N. McElwaine, Bulldozing of granular material, J. Fluid Mech. 748, 143 (2014).
- H. K. Moffatt, Viscous and resistive eddies near a sharp corner, J. Fluid Mech. 18, 1 (1964).
- B. W. Thompson, Secondary flow in a Hele-Shaw cell, J. Fluid Mech. 31, 379 (1968).
- D. Davis, J. Suppe, and F. A. Dahlen, Mechanics of fold-and-thrust belts and accretionary wedges, J. Geophys. Res. B 88, 1153 (1983).
- T. V. Ball, C. E. Penney, J. N. Neufeld, and A. C. Copley, Controls on the geometry and evolution of thin-skinned fold-thrust belts, and applications to the Makran accretionary prism and Indo–Burman ranges, Geophys. J. Int. 218, 247 (2019).
- S. Puleo, Dark Tide; The Great Molasses Flood of 1919 (Beacon Press, Boston, 2010).
- G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, UK, 1973).
- E. M. Hinton, A. J. Hogg, and H. E. Huppert, Shallow free-surface Stokes flow around a corner, Philos. Trans. R. Soc. A 378, 20190515 (2020).
- N. J. Balmforth and R. V. Craster, A consistent thin-layer theory for Bingham plastics, J. Non-Newtonian Fluid Mech. 84, 65 (1999).
- N. J. Balmforth, A. S. Burbidge, R. V. Craster, J. Salzig, and A. Shen, Visco-plastic models of isothermal lava domes, J. Fluid Mech. 403, 37 (2000).
