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Pinch-off of a viscous suspension thread

  • Joris Château (a1), Élisabeth Guazzelli (a1) and Henri Lhuissier (a1)

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 $t^{\ast }\sim \unicode[STIX]{x1D702}_{e}h^{\ast }/\unicode[STIX]{x1D70E}$ .

Copyright

Corresponding author

Email address for correspondence: henri.lhuissier@univ-amu.fr

References

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