Jet instability of a shear-thickening concentrated suspension
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THE EUROPEAN PHYSICAL JOURNAL E
Regular Article
Jet instability of a shear-thickening concentrated suspension Maxime Liard1,2 , Akihiro Sato1 , J´er´emy Sautel1 , Didier Lootens2 , and Pascal H´ebraud1,a 1 2
Universit´e de Strasbourg, IPCMS/CNRS UMR 7504, 23 rue du Loess, 67034 Strasbourg, France Sika Technology AG, Tuffenwies 16, 8048 Z¨ urich, Switzerland Received 23 July 2020 / Received in final form 24 September 2020 / Accepted 12 October 2020 Published online: 16 November 2020 c EDP Sciences / Societ` a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. We investigate the flow of a concentrated suspension of colloidal particles at deformation rates higher than the discontinuous shear-thickening transition shear rate. We show that, under its own weight, a jet of a concentrated enough colloidal suspension, simultaneously flows while it sustains tensile stress and transmits transverse waves. This results in a new flow instability of jets of shear-thickening suspensions: the jet is submitted to rapid transverse oscillations, that we characterize.
1 Introduction Submitted to high strain rates, the flow of concentrated suspensions exhibits a transition towards a strong shearthickening behavior [1–3], both in the colloidal and in the non-colloidal regimes [4]. The deformation rate and the volume fraction at which shear thickening develops depend on the exact nature of the suspension, in particular on the shape and smoothness of the particles [5, 6] and their short-distance interactions [7], being lubrication [8] or friction interactions [9]. Under high shear rates, the suspension strongly shear thickens; at higher shear stresses, the suspension is able to sustain a constant applied stress: it is jammed [10]. Both states have a finite lifetime after the cessation of shear [11]. These behaviors may be rationalized by assuming that a fabric of force chain develops under shear [12] and, that, above some shear rate, becomes dense enough to yield a jammed state [10]. A phenomenological model has been proposed for non-Brownian suspensions [13] in which shear thickening appears as a first-order transition between two Newtonian branches of flow: a lubricated one whose viscosity diverges at some volume fraction and a frictional one whose viscosity diverges at a lower volume fraction. Assuming that particles can make contacts, a stress scale appears above which the lubricated branch of flow is unstable. Depending on the volume fraction of the suspension, the transition leads to a discontinuity in the apparent viscosity, which defines the discontinuous shear transition (DST). This describes well the experimentally measured phase diagram [10]. a
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At the discontinuous shear-thickening transition (DST), the suspension becomes dilatant: a strong normal force develops at or close to the transition. Dilatance is related to the existence of a compression axis under the applied deformation and to the formation of a force network [10, 14]. One may thus expect tha
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