Elasticity of particle-loaded liquid foams

Abstract

Mixing solid particles with liquid foam is a common process used in industry for manufacturing aerated materials. Desire for improvement of involved industrial processes and optimization of resulting foamed materials stimulates fundamental research on those complex mixtures of grains, bubbles and liquid. In this paper, we generate well-controlled particle-loaded liquid foams and we determine their elastic behavior as a function of particle size (6-3000 μm) and particle volume fraction (0-6%). We focus on both the elastic modulus exhibited by the material at small strain and the strain marking the end of the linear elastic regime. Results reveal the existence of a critical particle-to-bubble size ratio triggering a sharp transition between two well-defined regimes. For small size ratios, the behavior is governed by the mechanical properties of the solid grains, which have been proved to pack in the shape of a foam-embedded granular skeleton. In contrast, bubbles elasticity prevails in the second regime, where isolated large particles contribute only weakly to the rheological behavior of the foamed material. The modeling of elasticity for each regime allows for this transition to be normalized and compared with previously reported particle size-induced effects for foam drainage (Haffner et al. J. Colloid Interface Sci., 2015, 458, 200-208) and solid foam mechanics (Khidas et al., Compos. Sci. Technol., 2015, 119, 62-67). This highlights that rheology and the other properties of particle-loaded foams are subjected to the same size-induced morphological transition.

Yielding of complex liquid foams

“…Equation 6 refers to bubble size as the characteristic size in the transition regime. The bubble size, , is the natural size, but we stress that previous work [21,42]…”

“…Therefore, packed small solid particles and continuous yield stress material induce similar strengthening of foam yield stress. It is interesting to note that such a small confinement pressure was however found to induce extremely large values for bulk elasticity of the granular skeleton [20,21], i.e. P ≈ 150 kPa.…”

“…This value differs from the value measured for the particle-loaded foam, i.e., = *6 $1 &, so the modulus of the reference aqueous foam [32], Note that previous work has demonstrated the validity of eq. 3 for elasticity of foams loaded with large spherical inclusions [21,42]. According to equations 2 and 3, the reduced yield stress writes:…”

“…whipped creams [4], aerated slurries such as cement [1], geopolymer [5] or plaster [6] fresh pastes, colloidal suspension foams [7][8][9][10][11][12][13], granular suspension foams [14][15][16][17][18][19][20][21], emulsion foams [22][23][24][25][26][27][28]. In fact, little is known about rheology of complex liquid foams while such knowledge is crucial for applications.…”

“…Cohen-Addad et al [18] have shown that adding a tiny amount of non-colloidal particles in aqueous foams can enhance drastically their elastic modulus. Gorlier et al [21,20] have revealed the existence of a critical particle-to-bubble size ratio triggering a sharp transition between two well-defined elastic regimes: for small size ratios, the behavior is governed by the mechanical properties of the solid grains, which have been proved to pack in the shape of a foam-embedded granular skeleton. In contrast, bubbles elasticity prevails in the second regime, where isolated large particles contribute only weakly to the rheological behavior of the foamed material.…”