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Register a new userJamming in sheared foams and emulsions, explained by critical instability of the films between neighboring bubbles and drops
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Added by
Konstantin Golemanov
Publication date
2009
fields
Physics
and research's language is
English
Authors
N. D. Denkov
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Phenomenon of foam and emulsion jamming at low shear rates is explained by considering the dynamics of thinning in the transient film, formed between the neighboring bubbles and drops. After gradually thinning down to a critical thickness, these films undergo instability transition and thin stepwise, forming the so-called black films, which are only several nanometers thick and, thereby, lead to stronger adhesion between the dispersed particles. Theoretical analysis shows that such film thickness instability occurs only if the contact time between the bubbles/drops in sheared foam/emulsion is sufficiently long, which corresponds to sufficiently low (critical) rate of shear. Explicit expression for this critical rate is proposed and compared to experimental data.
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In a recent letter (Denkov et al., Phys. Rev. Lett., vol. 100 (2008) p. 138301) we calculated theoretically the macroscopic viscous stress of steadily sheared foam/emulsion from the energy dissipated inside the transient planar films, formed between neighboring bubbles/drops in the shear flow. The model predicts that the viscous stress in these systems should be a proportional to Ca^1/2, where Ca is the capillary number and n = 1/2 is the power-law index. In the current paper we explain in detail our model and develop it further in several aspects: First, we extend the model to account for the effects of viscous friction in the curved meniscus regions, surrounding the planar films, on the dynamics of film formation and on the total viscous stress. Second, we consider the effects of surface forces (electrostatic, van der Waals, etc.) acting between the surfaces of the neighboring bubbles/drops and show that these forces could be important in emulsions, due to the relatively small thickness of emulsion films (often comparable to the range of action of the surface forces). Third, additional consideration is made for bubbles/drops exhibiting high surface viscosity, for which we demonstrate an additional contribution to the macroscopic viscous stress, created by the surface dissipation of energy. The new upgraded model predicts that the energy dissipation at the bubble/drop surface leads to power-law index n < 1/2, whereas the contribution of the surface forces leads to n > 1/2, which explains the rich variety of foam/emulsion behaviors observed upon steady shear. Various comparisons are made between model predictions and experimental results for both foams and emulsions, and a very good agreement is found.
In the absence of coalescence, coarsening of emulsions (and foams) is controlled by molecular diffusion of dispersed phase between droplets/bubbles. Studies of dilute emulsions have shown how the osmotic pressure of a trapped species within droplets can ``osmotically stabilise the emulsion. Webster and Cates (Langmuir, 1998, 14, 2068-2079) gave rigorous criteria for osmotic stabilisation of mono- and polydisperse emulsions, in the dilute regime. We consider here whether analogous criteria exist for the osmotic stabilisation of mono- and polydisperse concentrated emulsions and foams, and suggest that the pressure differences driving coarsening are small compared to the mean Laplace pressure. An exact calculation confirms this for a monodisperse 2D model, finding a bubbles pressure as P_i = P + Pi + P_i^G, with P, Pi the atmospheric and osmotic pressures, and P_i^G a ``geometric pressure that reduces to the Laplace pressure only for a spherical bubble. For Princens 2D emulsion model, P_i^G is only 5% larger in the dry limit than the dilute limit. We conclude that osmotic stabilisation of dense systems typically requires a pressure of trapped molecules in each droplet that is comparable to the Laplace pressures the same droplets would have if spherical, as opposed to the much larger Laplace pressures present in the system. We study coarsening of foams and concentrated emulsions when there is insufficient of the trapped species present. Rate-limiting mechanisms are considered, their applicability and associated droplet growth rates discussed. In a concentrated foam or emulsion, a finite yield threshold for droplet rearrangement may be enough to prevent coarsening of the remainder.
The drainage of particulate foams is studied under conditions where the particles are not trapped individually by constrictions of the interstitial pore space. The drainage velocity decreases continuously as the particle volume fraction $phi_{p}$ increases. The suspensions jam - and therefore drainage stops - for values $phi_{p}^{*}$ which reveal a strong effect of the particle size. In accounting for the particular geometry of the foam, we show that $phi_{p}^{*}$ accounts for unusual confinement effects when the particles pack into the foam network. We model quantitatively the overall behavior of the suspension - from flow to jamming - by taking into account explicitly the divergence of its effective viscosity at $phi_{p}^{*}$. Beyond the scope of drainage, the reported jamming transition is expected to have a deep significance for all aspects related to particulate foams, from aging to mechanical properties.
We study the rheological properties of a granular suspension subject to constant shear stress by constant volume molecular dynamics simulations. We derive the system `flow diagram in the volume fraction/stress plane $(phi,F)$: at low $phi$ the flow is disordered, with the viscosity obeying a Bagnold-like scaling only at small $F$ and diverging as the jamming point is approached; if the shear stress is strong enough, at higher $phi$ an ordered flow regime is found, the order/disorder transition being marked by a sharp drop of the viscosity. A broad jamming region is also observed where, in analogy with the glassy region of thermal systems, slow dynamics followed by kinetic arrest occurs when the ordering transition is prevented.
A variety of complex fluids consist in soft, round objects (foams, emulsions, assemblies of copolymer micelles or of multilamellar vesicles -- also known as onions). Their dense packing induces a slight deviation from their prefered circular or spherical shape. As a frustrated assembly of interacting bodies, such a material evolves from one conformation to another through a succession of discrete, topological events driven by finite external forces. As a result, the material exhibits a finite yield threshold. The individual objects usually evolve spontaneously (colloidal diffusion, object coalescence, molecular diffusion), and the material properties under low or vanishing stress may alter with time, a phenomenon known as aging. We neglect such effects to address the simpler behaviour of (uncommon) immortal fluids: we construct a minimal, fully tensorial, rheological model, equivalent to the (scalar) Bingham model. Importantly, the model consistently describes the ability of such soft materials to deform substantially in the elastic regime (be it compressible or not) before they undergo (incompressible) plastic creep -- or viscous flow under even higher stresses.
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