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Pinch-off of a viscous suspension thread

Published online by Cambridge University Press:  03 August 2018

Joris Château ,
Élisabeth Guazzelli Open the ORCID record for Élisabeth Guazzelli [Opens in a new window]  and
Henri Lhuissier Open the ORCID record for Henri Lhuissier [Opens in a new window]
Joris Château
Affiliation:
Aix Marseille Univ, CNRS, IUSTI, 13453 Marseille, France
Élisabeth Guazzelli
Affiliation:
Aix Marseille Univ, CNRS, IUSTI, 13453 Marseille, France
Henri Lhuissier*
Affiliation:
Aix Marseille Univ, CNRS, IUSTI, 13453 Marseille, France
*
†Email address for correspondence: [email protected]
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Abstract

The pinch-off of a capillary thread is studied at large Ohnesorge number for non-Brownian, neutrally buoyant, mono-disperse, rigid, spherical particles suspended in a Newtonian liquid with viscosity $\unicode[STIX]{x1D702}_{0}$ and surface tension $\unicode[STIX]{x1D70E}$. Reproducible pinch-off dynamics is obtained by letting a drop coalesce with a bath. The bridge shape and time evolution of the neck diameter, $h_{\mathit{min}}$, are studied for varied particle size $d$, volume fraction $\unicode[STIX]{x1D719}$ and liquid contact angle $\unicode[STIX]{x1D703}$. Two successive regimes are identified: (i) a first effective-viscous-fluid regime which only depends upon $\unicode[STIX]{x1D719}$ and (ii) a subsequent discrete regime, depending both on $d$ and $\unicode[STIX]{x1D719}$, in which the thinning localises at the neck and accelerates continuously. In the first regime, the suspension behaves as an effective viscous fluid and the dynamics is solely characterised by the effective viscosity of the suspension, $\unicode[STIX]{x1D702}_{e}\sim -\unicode[STIX]{x1D70E}/{\dot{h}}_{\mathit{min}}$, which agrees closely with the steady shear viscosity measured in a conventional rheometer and diverges as $(\unicode[STIX]{x1D719}_{c}-\unicode[STIX]{x1D719})^{-2}$ at the same critical particle volume fraction, $\unicode[STIX]{x1D719}_{c}$. For $\unicode[STIX]{x1D719}\gtrsim 35\,\%$, the thinning rate is found to increase by a factor of order one when the flow becomes purely extensional, suggesting non-Newtonian effects. The discrete regime is observed from a transition neck diameter, $h_{\mathit{min}}\equiv h^{\ast }\sim d\,(\unicode[STIX]{x1D719}_{c}-\unicode[STIX]{x1D719})^{-1/3}$, down to $h_{\mathit{min}}\approx d$, where the thinning rate recovers the value obtained for the pure interstitial fluid, $\unicode[STIX]{x1D70E}/\unicode[STIX]{x1D702}_{0}$, and lasts $t^{\ast }\sim \unicode[STIX]{x1D702}_{e}h^{\ast }/\unicode[STIX]{x1D70E}$.

JFM classification

Drops and Bubbles: Breakup/coalescence Interfacial Flows (free surface): Capillary flows Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , pp. 178 - 198
Copyright
© 2018 Cambridge University Press 

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Château et al. supplementary movie 1

Pinch-off of a capillary bridge of a suspension of particles with a diameter d = 10 micrometers and a particle volume fraction phi = 48%, suspended in pure PEG (close to 2500 times as viscous as water). In order to compensate for the continuously increasing rates of deformation at the bridge neck, the time in the movies is increasingly slowed down as pinching proceeds. The duration, t_0 - t, remaining before the pinch-off is indicated at the top. The width of the image is 4.45 mm.

Download Château et al. supplementary movie 1(Video)
Video 1.4 MB

Château et al. supplementary movie 2

Pinch-off of a capillary bridge of a suspension of particles with a diameter d = 135 micrometers and a particle volume fraction phi = 50%, suspended in pure PEG (close to 2500 times as viscous as water). In order to compensate for the continuously increasing rates of deformation at the bridge neck, the time in the movies is increasingly slowed down as pinching proceeds. The duration, t_0 - t, remaining before the pinch-off is indicated at the top. The width of the image is 4.45 mm.

Download Château et al. supplementary movie 2(Video)
Video 1.6 MB