Fluidization and wall slip of soft glassy materials by controlled surface roughness

Ladislav Derzsi, Daniele Filippi, Giampaolo Mistura, Matteo Pierno, Matteo Lulli, Mauro Sbragaglia, Massimo Bernaschi, and Piotr Garstecki

Phys. Rev. E 95, 052602 – Published 4 May 2017

Abstract

We present a comprehensive study of concentrated emulsions flowing in microfluidic channels, one wall of which is patterned with micron-size equally spaced grooves oriented perpendicularly to the flow direction. We find a scaling law describing the roughness-induced fluidization as a function of the density of the grooves, thus fluidization can be predicted and quantitatively regulated. This suggests common scenarios for droplet trapping and release, potentially applicable for other jammed systems as well. Numerical simulations confirm these views and provide a direct link between fluidization and the spatial distribution of plastic rearrangements.

Received 7 November 2016
Revised 8 February 2017

DOI:https://doi.org/10.1103/PhysRevE.95.052602

Physics Subject Headings (PhySH)

Emulsions Glassy systems

Lattice-Boltzmann methods

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ladislav Derzsi^1,*, Daniele Filippi¹, Giampaolo Mistura¹, Matteo Pierno^1,†, Matteo Lulli², Mauro Sbragaglia^2,‡, Massimo Bernaschi³, and Piotr Garstecki⁴

¹Dipartimento di Fisica e Astronomia “G. Galilei”–DFA and Sezione CNISM, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
²Dipartimento di Fisica, Università di Roma “Tor Vergata” and INFN, Via della Ricerca Scientifica, 1, 00133 Roma, Italy
³Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini, 9, 00185 Roma, Italy
⁴Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland

^*ladislav.derzsi@unipd.it
^†matteo.pierno@unipd.it
^‡sbragaglia@roma2.infn.it

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Issue

Vol. 95, Iss. 5 — May 2017

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Images

Figure 1
(a) Experimental setup used for flow visualization of dense emulsions. The flow is driven by a pressure drop $Δ p = p_{IN} - p_{OUT}$ through a microfluidic channel of height $H$ , one wall of which is patterned with a controlled roughness. Snapshots with a black background show the trajectories of fluorescent nanoparticles suspended in the continuous phase of the emulsion, flowing at different channel height $z$ : close to the rough wall (bottom snapshot), in the center of the channel (middle snapshot, corresponding to the plug region), and close to the smooth wall (top snapshot). Flow profiles $v_{flow} (z)$ are reported either at fixed roughness for different pressure drops (b) or at fixed pressure drop for different surface roughness (c). In the latter case the slip velocity on the rough wall $v_{rough}$ has been subtracted. Numerical values of the slip velocities at the rough walls (determined by fitting the last three to four data points of the PTV measurement in proximity of the walls) are 0.17, 0.17, and 0.20 mm/s for geometries $g / d = 3.15$ ; $w / d = 1.68$ , 3.15, and 7.89, respectively.
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Figure 2
Flow profiles and rate of plastic rearrangements $Γ$ , Eq. (1), from numerical simulations based on the lattice Boltzmann methods. (a) Velocity profiles and the associated $Γ$ for a fixed roughness and increasing pressure drop $Δ p$ . Data at fixed $Δ p$ for different roughness are also displayed (b). Slip velocities at the rough walls are negligible for geometry $g / d = 3$ ; $w / d = 1$ , while they are $10^{- 4}$ and $2.5 \times 10^{- 4}$ for geometries $g / d = 3$ ; $w / d = 3$ and $w / d = 8$ , respectively. Rearrangements are identified by comparing the Delaunay triangulations of two consecutive configurations (c). (d) We report the spatial distribution of $Γ$ in a Couette geometry (see Sec. 2b), highlighting the properties of a sheared layer close to smooth and rough walls. The distance from the wall shown in units of the mean droplet diameter. Data are reported in lattice Boltzmann units (lbu).
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Figure 3
(a) Stress profiles for symmetric channels with smooth walls on both sides ( $z \pm H / 2$ ) and for asymmetric channels with a smooth wall from one side ( $z = - H / 2$ ) and a rough wall on the other side ( $z = + H / 2$ ). The flow is driven by the same pressure drop. (b),(c) Velocity and fluidity profiles for a Couette geometry (see Sec. 2b) obtained by applying a constant wall velocity $u_{w}$ at the wall in $z = - H / 2$ for the two channel configurations used in (a). For the asymmetric channel configuration, the wall fluidity is enhanced in contact with the rough wall [26, 32] and the measured fluidity profile matches the theoretical prediction [22, 23] [solid line, see Eq. (3)]. The inset of (c) reports the stress profile as a function of the distance from the wall in $z = + H / 2$ . Notice that in the Couette geometry the stress is spatially constant and the constant is found to be larger in the asymmetric channel configuration. Data are reported in lattice Boltzmann units (lbu).
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Figure 4
(a) Difference of the slip velocities (2) as a function of the roughness periodicity $λ = w + g$ for different pressure drops $Δ p$ and different gaps $g$ . Dashed lines are guides for the eyes with slope $- 1$ . (b) Difference of the slip velocities, normalized by the maximum (plug) velocity $v_{plug}$ , as a function of the wall roughness periodicity $λ$ in units of the mean droplet diameter $d$ . Dashed line is a guide for the eyes with slope $- 1$ . Inset shows the dependence of $v_{plug}$ with $Δ p$ .
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Figure 5
Lattice Boltzmann simulation results for the increase of the rate of plastic rearrangements induced by the rough wall, $Γ_{TOT}$ (see text for details). $Γ_{TOT}$ is plotted as a function of the slip variation $Δ v_{slip}$ (2). Dashed-dotted line is a guide for the eyes with slope 1. Inset reports the slip variation as a function of the dimensionless period $λ / d$ . Dashed line is a guide for the eyes with slope $- 1$ . Data are reported in lattice Boltzmann units (lbu).
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