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Optimal rigid brush for fluid capture

Published online by Cambridge University Press:  07 July 2025

Basile Radisson Open the ORCID record for Basile Radisson [Opens in a new window] ,
Hadrien Bense Open the ORCID record for Hadrien Bense [Opens in a new window] ,
Lucie Domino Open the ORCID record for Lucie Domino [Opens in a new window] ,
Hoa-Ai Béatrice Hua Open the ORCID record for Hoa-Ai Béatrice Hua [Opens in a new window] ,
Emmanuel Siéfert Open the ORCID record for Emmanuel Siéfert [Opens in a new window]  and
Fabian Brau Open the ORCID record for Fabian Brau [Opens in a new window]
Basile Radisson
Affiliation:
Nonlinear Physical Chemistry Unit, CP231, Université libre de Bruxelles (ULB), 1050 Bruxelles, Belgium
Hadrien Bense
Affiliation:
Nonlinear Physical Chemistry Unit, CP231, Université libre de Bruxelles (ULB), 1050 Bruxelles, Belgium
Lucie Domino
Affiliation:
Nonlinear Physical Chemistry Unit, CP231, Université libre de Bruxelles (ULB), 1050 Bruxelles, Belgium
Hoa-Ai Béatrice Hua
Affiliation:
Nonlinear Physical Chemistry Unit, CP231, Université libre de Bruxelles (ULB), 1050 Bruxelles, Belgium
Emmanuel Siéfert
Affiliation:
Nonlinear Physical Chemistry Unit, CP231, Université libre de Bruxelles (ULB), 1050 Bruxelles, Belgium
Fabian Brau*
Affiliation:
Nonlinear Physical Chemistry Unit, CP231, Université libre de Bruxelles (ULB), 1050 Bruxelles, Belgium
*
Corresponding author: Fabian Brau, fabian.brau@ulb.be
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Abstract

Assemblies of slender structures forming brushes are common in daily life from sweepers to pastry brushes and paintbrushes. These types of porous objects can easily trap liquid in their interstices when removed from a liquid bath. This property is exploited to transport liquids in many applications, ranging from painting, dip-coating and brush-coating to the capture of nectar by bees, bats and honeyeaters. Rationalising the viscous entrainment flow beyond simple scaling laws is complex due to the multiscale structure and the multidirectional flow. Here, we provide an analytical model, together with precision experiments with ideal rigid brushes, to fully characterise the flow through this anisotropic porous medium as it is withdrawn from a liquid bath. We show that the amount of liquid entrained by a brush varies non-monotonically during the withdrawal at low speed, is highly sensitive to the different parameters at play and is very well described by the model without any fitting parameter. Finally, an optimal brush geometry maximising the amount of liquid captured at a given retraction speed is derived from the model and experimentally validated. These optimal designs open routes towards efficient liquid-manipulating devices.

JFM classification

Low-Reynolds-number flows: Porous media

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 1014 , 10 July 2025 , A29
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© The Author(s), 2025. Published by Cambridge University Press

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Supplementary material: File

Radisson et al. supplementary movie 1

Retraction of a brush (D = 17 mm, R = 0.5 mm, d = 2.0 mm) at various speeds (V = 4, 8, 16, 32 mm/min) from a bath of silicon oil (μ = 0.97 Pa s, initial immersion depth L0 = 16 mm), the frame rate being adjusted to synchronize the retractions.
Download Radisson et al. supplementary movie 1(File)
File 6.5 MB
Supplementary material: File

Radisson et al. supplementary movie 2

Retraction of a brush (D = 16 mm, R = 0.3 mm, d = 1.5 mm) at various speeds (V = 2, 8, 32, 128 mm/min) from a bath of silicon oil (μ = 0.97 Pa s, initial immersion depth L0 = 7 mm), the frame rate being adjusted to synchronize the retractions.
Download Radisson et al. supplementary movie 2(File)
File 7.6 MB
Supplementary material: File

Radisson et al. supplementary movie 3

Retraction of a brush (D = 17 mm, R = 0.5 mm, d = 2.0 mm) at various initial immersion depths (L0 = 6, 11, 16 mm) from a bath of silicon oil (μ = 0.97 Pa s, retraction speed V = 32 mm/min), the frame rate being adjusted to synchronize the retractions.
Download Radisson et al. supplementary movie 3(File)
File 4.9 MB
Supplementary material: File

Radisson et al. supplementary movie 4

Withdrawing of brushes of various rod radii (R = 0.4, 0.5, 0.6, 0.7 mm) but with the same distance between the rod centers d = 1.8 mm, diameter D = 16 mm and immersion depth L0 = 10 mm at constant speed V = 100 mm/min from a silicon oil bath (μ = 0.97 Pa s). The movie stops when the brushes have been displacement by a distance L0.
Download Radisson et al. supplementary movie 4(File)
File 2.7 MB
Supplementary material: File

Radisson et al. supplementary movie 5

Withdrawing of two parallel plates (d = 1.58 mm, W = 75 mm) immersed at a depth L0 = 42.8 mm at constant speed V = 1000 mm/min from a silicon oil bath (μ = 0.097 Pa s).
Download Radisson et al. supplementary movie 5(File)
File 1.9 MB