The onset of heterogeneity in the pinch-off of suspension drops

Abstract

Significance The pinch-off of a liquid drop extruded from a nozzle is a canonical situation that involves a series of self-similar regimes ending in a finite-time singularity. This configuration allows for exploring capillary flows over a large range of scales. In the case of suspension drops, the presence of particles breaks the self-similarity by introducing a length scale that can be much larger than the particle diameter. This length scale is a signature of the heterogeneities and delimitates a regime, in which a continuum approach of a suspension can be used from a regime where the discrete nature of the particles is involved.

Particulate suspension coating of capillary tubes

“…with η f the viscosity of the interstitial fluid, φ the volume fraction of the suspension, and φm = 0.59 the maximal packing fraction for the particles and fluid used. 22,34 In the thick film regime, the thickness of the suspension film coating the inner wall of the capillary tube should be given by: 26,27 h R = 1.34 Ca…”

“…In this situation, we define the effective capillary number based on the viscosity of the suspension:The effective viscosity of the suspension can be estimated through different models such as, for instance, the Maron–Pierce correlation: 46 with η f the viscosity of the interstitial fluid, ϕ the volume fraction of the suspension, and ϕ m = 0.59 the maximal packing fraction for the particles and fluid used. 22,34…”

“…15,16 When solid particles are dispersed in a liquid, the usual interfacial dynamics and rheological approaches used to describe capillary flows can often fail when the lengthscale of the capillary object, here the liquid film, becomes comparable to the diameter of the particles. This peculiar dynamics of suspension has been considered in various configurations such as the formation of droplets, [17][18][19][20][21][22] the stability of jets, 23 the fragmentation of suspension sheets, 24 the motion of contact lines, 25 and during the formation of thin films. 26 The challenge arises from the fact that for capillary flows of suspensions, in addition to the film thickness h, an additional lengthscale enters into the problem: the particle diameter d. This complexity when using a suspension of non-Brownian particles dispersed in non-volatile liquids has been considered during the formation of a thin film of suspension in a dip-coating process.…”

Breakup of particle-laden droplets in airflow

“…(2012), Château, Guazzelli & Lhuissier (2018), Rubio-Rubio et al. (2018), Thievenaz & Sauret (2022) and Thievenaz, Rajesh & Sauret (2021). Similarly, for the breakup of suspension jets, the heterogeneity of the particles affects the shape and the breakup length of the jets (Roche, Kellay & Stone 2011; Château & Lhuissier 2019).…”

Transition to the viscoelastic regime in the thinning of polymer solutions

“…The break-up corresponds to a finite-time singularity. 13,14 In many industrial applications, the liquid is not a homogeneous Newtonian fluid but often contains particles, solutes, cells, or other components. At certain length and time scales, these components interact with the flow and sometimes influence capillary flows dramatically.…”