Modelling the rheology of anisotropic particles adsorbed on a two-dimensional fluid interface
Luo, A.M. ; Sagis, L.M.C. ; Oettinger, H.C. ; Michele, C. de; Ilg, P. - \ 2015
Soft Matter 11 (2015). - ISSN 1744-683X - p. 4383 - 4395.
complex fluids - capillary interactions - constitutive equation - general formalism - liquid-crystals - dynamics - thermodynamics - emulsions
We present a general approach based on nonequilibrium thermodynamics for bridging the gap between a well-defined microscopic model and the macroscopic rheology of particle-stabilised interfaces. Our approach is illustrated by starting with a microscopic model of hard ellipsoids confined to a planar surface, which is intended to simply represent a particle-stabilised fluid-fluid interface. More complex microscopic models can be readily handled using the methods outlined in this paper. From the aforementioned microscopic starting point, we obtain the macroscopic, constitutive equations using a combination of systematic coarse-graining, computer experiments and Hamiltonian dynamics. Exemplary numerical solutions of the constitutive equations are given for a variety of experimentally relevant flow situations to explore the rheological behaviour of our model. In particular, we calculate the shear and dilatational moduli of the interface over a wide range of surface coverages, ranging from the dilute isotropic regime, to the concentrated nematic regime.
Nonequilibrium thermodynamics of nucleation
Schweizer, M. ; Sagis, L.M.C. - \ 2014
Journal of Chemical Physics 141 (2014). - ISSN 0021-9606 - 13 p.
homogeneous nucleation - inhomogeneous-media - general formalism - complex fluids - systems - clusters - dynamics - temperature - interface - equations
We present a novel approach to nucleation processes based on the GENERIC framework (general equation for the nonequilibrium reversible-irreversible coupling). Solely based on the GENERIC structure of time-evolution equations and thermodynamic consistency arguments of exchange processes between a metastable phase and a nucleating phase, we derive the fundamental dynamics for this phenomenon, based on continuous Fokker-Planck equations. We are readily able to treat non-isothermal nucleation even when the nucleating cores cannot be attributed intensive thermodynamic properties. In addition, we capture the dynamics of the time-dependent metastable phase being continuously expelled from the nucleating phase, and keep rigorous track of the volume corrections to the dynamics. Within our framework the definition of a thermodynamic nuclei temperature is manifest. For the special case of nucleation of a gas phase towards its vapor-liquid coexistence, we illustrate that our approach is capable of reproducing recent literature results obtained by more microscopic considerations for the suppression of the nucleation rate due to nonisothermal effects.
Normal stresses in surface shear experiments
Sagis, L.M.C. - \ 2013
The European Physical Journal. Special Topics 222 (2013)1. - ISSN 1951-6355 - p. 99 - 103.
in-water emulsions - interfacial permeability - general formalism - bending rigidity - complex fluids - dynamics - viscoelasticity - thermodynamics - liquid/liquid - gas/liquid
When viscoelastic bulk phases are sheared, the deformation of the sample induces not only shear stresses, but also normal stresses. This is a well known and well understood effect, that leads to phenomena such as rod climbing, when such phases are stirred with an overhead stirrer, or to die swell in extrusion. Viscoelastic interfaces share many commonalities with viscoelastic bulk phases, with respect to their response to deformations. There is however little experimental evidence that shear deformations of interfaces can induce in-plane normal stresses (not to be confused with stresses normal to the interface). Theoretical models for the stress-deformation behavior of complex fluid-fluid interfaces subjected to shear, predict the existence of in-plane normal stresses. In this paper we suggest methods to confirm the existence of such stresses experimentally.
Does size matter? Elasticity of compressed suspensions of colloidal- and granular-scale
Menut, P. ; Seiffert, S. ; Sprakel, J.H.B. ; Weitz, D.A. - \ 2012
Soft Matter 8 (2012)1. - ISSN 1744-683X - p. 156 - 164.
complex fluids - rheology - emulsions - pastes - viscoelasticity - particles - glasses - slip
We investigate the mechanics of dense packing of very small, colloidal-scale, and larger, granular-scale microgel particles. At low particle concentration, thermally induced Brownian motion of the particles is important for the colloidal-scale systems; in contrast, such Brownian motion is irrelevant at particle packing fractions beyond jamming. As a consequence, colloidal and granular systems behave very similarly under these conditions. At sufficiently high compression of the microgel particles, their polymeric nature sets the scale of the osmotic pressure and shear modulus of the whole packing, in direct analogy with macroscopic, continuous polymer gels. This observation suggests that the particulate nature of microgels is inconsequential for their linear elasticity in a highly packed state. In contrast, the particulate nature of the microgels does become essential when the packed suspensions are forced to yield and flow; here, the differences between colloidal- and granular-scale particles are marked.
An extended rational thermodynamics model for surface excess fluxes
Sagis, L.M.C. - \ 2012
Physica A 391 (2012)4. - ISSN 0378-4371 - p. 979 - 990.
irreversible thermodynamics - general formalism - complex fluids - kinetic-theory - dynamics - fluctuations - interfaces - rheology - bilayers
In this paper, we derive constitutive equations for the surface excess fluxes in multiphase systems, in the context of an extended rational thermodynamics formalism. This formalism allows us to derive Maxwell–Cattaneo type constitutive laws for the surface extra stress tensor, the surface thermal energy flux vector, and the surface mass flux vector, which incorporate a direct coupling to their corresponding bulk fluxes in the adjacent bulk phases. These constitutive laws also incorporate contributions to the time evolution of the surface excess fluxes from spatial inhomogeneities in these flux fields. These phenomenological equations can be used to model the dynamic behavior of complex viscoelastic interfaces in multiphase systems, in the small deformation limit.
Rheology of interfaces stabilized by a 2D suspension of anisotropic particles: a classical irreversible thermodynamics theory
Sagis, L.M.C. - \ 2011
Soft Matter 7 (2011)17. - ISSN 1744-683X - p. 7727 - 7736.
nonequilibrium thermodynamics - superficial viscosity - general formalism - latex-particles - complex fluids - liquid - liquid/liquid - dynamics - viscoelasticity - gas/liquid
Surface rheological properties have a significant impact on the stability of particle-stabilized emulsions and foams. Interfaces stabilized by anisotropic particles display a highly nonlinear surface rheology, even at relatively small deformation rates. The nonlinearity of the response is the result of changes in the microstructure of the interface, induced by the applied deformation. The particles are oriented in the direction of the imposed flow field, and this leads to a decrease in the surface shear viscosity (shear thinning). In this paper we derive nonlinear constitutive equations for the surface stress tensor of an interface stabilized by a mixture of anisotropic particles and low molecular weight surfactants, using the classical irreversible thermodynamics formalism. These equations are valid in the low shear regime, where departures from linear behavior are still small. The effect of the microstructure of the interface on the rheological response is incorporated through the particle orientation tensor Qs. The constitutive equations are able to predict the shear thinning behavior observed experimentally for this type of interface.
GENERIC model for multiphase systems
Sagis, L.M.C. - \ 2010
Advances in Colloid and Interface Science 153 (2010). - ISSN 0001-8686 - p. 58 - 69.
extended irreversible thermodynamics - complex fluids - dynamics - formalism - rheology
GENERIC is a nonequilibrium thermodynamic formalism in which the dynamic behavior of a system is described by a single compact equation involving two types of brackets: a Poisson bracket and a dissipative bracket. This formalism has proved to be a very powerful instrument to model the dynamic behavior of complex bulk phases. In this paper we review the basic principles of the GENERIC formalism, and show how it can be applied to multicomponent multiphase systems with interfaces displaying viscous stress deformation behavior. The generalization of the GENERIC formalism to multiphase systems provides a powerful tool to model nonlinear dynamic behavior of complex interfaces in for example emulsions or foam. Adding several interfacial contributions to the standard two-bracket formulation we derive the conservation laws for mass, momentum, and energy for the bulk phases of the system. We also derive the jump balance equations for the surface mass density, surface momentum, and surface energy. In addition to these balance equations we obtain constitutive equations for the extra stress tensor, energy flux vector, and mass flux vectors in the bulk phase, and the surface extra stress tensor, the surface energy flux vector, and surface mass flux vectors of the interface. The GENERIC formalism also allows us to derive constitutive equations for the transport of mass, momentum, and energy from the bulk phase to the interface. The resulting set of equations is compared to those derived using the rational thermodynamic and classical irreversible thermodynamic formalisms, and is in good agreement with the balance equations derived using these formalisms.
Brownian particles in transient polymer networks
Sprakel, J.H.B. ; Gucht, J. van der; Cohen Stuart, M.A. ; Besseling, N.A.M. - \ 2008
Physical Review. E, Statistical nonlinear, and soft matter physics 77 (2008). - ISSN 1539-3755
viscoelastic properties - associating polymers - complex fluids - microrheology - rheology - dynamics - motion - moduli
We discuss the thermal motion of colloidal particles in transient polymer networks. For particles that are physically bound to the surrounding chains, light-scattering experiments reveal that the submillisecond dynamics changes from diffusive to Rouse-like upon crossing the network formation threshold. Particles that are not bound do not show such a transition. At longer time scales the mean-square displacement (MSD) exhibits a caging plateau and, ultimately, a slow diffusive motion. The slow diffusion at longer time scales can be related to the macroscopic viscosity of the polymer solutions. Expressions that relate the caging plateau to the macroscopic network elasticity are found to fail for the cases presented here. The typical Rouse scaling of the MSD with the square root of time, as found in experiments at short time scales, is explained by developing a bead-spring model of a large colloidal particle connected to several polymer chains. The resulting analytical expressions for the MSD of the colloidal particle are shown to be consistent with experimental findings.
Emulsion droplet deformation and breakup with Lattice Boltzmann model
Sman, R.G.M. van der; Graaf, S. van der - \ 2008
Computer Physics Communications 178 (2008)7. - ISSN 0010-4655 - p. 492 - 504.
immiscible polymer blends - t-shaped microchannel - membrane emulsification - nonuniform system - complex fluids - free energy - flows - simulations - dynamics - computation
In this paper we have performed an extensive study of the effects of various dimensionless numerical parameters used in the Lattice Boltzmann implementation of the diffuse interface model describing deformation and breakup of an emulsion droplet in 2D. Such an extensive study on these parameter is absent in scientific literature of diffuse interface models. We have found that parameters like the dimensionless interface thickness and the Peclet number have to be within certain ranges for correct physical behavior. Outside these ranges droplets either dissolve, show incorrect Laplace pressures, or do not deform to stable shapes at subcritical capillary numbers. Furthermore, we have found that droplet breakup is sensitive to these parameters.
Rouse dynamics of colloids bound to polymer networks
Sprakel, J.H.B. ; Gucht, J. van der; Cohen Stuart, M.A. ; Besseling, N.A.M. - \ 2007
Physical Review Letters 99 (2007)20. - ISSN 0031-9007 - 4 p.
complex fluids - moduli
We present experimental evidence of a transition in the short-time Brownian motion of colloids from diffusive to subdiffusive, Rouse-like. This transition is seen for particles that are bound, through physical adsorption, to transient polymer networks. The characteristic Rouse scaling of the mean square particle displacement with vt, found in the experiments, is rationalized using an analytical bead-spring model of a large particle anchored to a set of polymer chains.
Lattice Boltzmann simulations of droplet formation in a T-shaped microchannel
Graaf, S. van der; Nisisako, T. ; Schroën, C.G.P.H. ; Sman, R.G.M. van der; Boom, R.M. - \ 2006
Langmuir 22 (2006)9. - ISSN 0743-7463 - p. 4144 - 4152.
in-water emulsions - membrane emulsification - numerical-simulation - complex fluids - liquid-gas - model - flows - interface - dynamics - mixture
We investigated the formation of a droplet from a single pore in a glass chip, which is a model system for droplet formation in membrane emulsification. Droplet formation was simulated with the lattice Boltzmann method, a method suitable for modeling on the mesoscale. We validated the lattice Boltzmann code with several benchmarks such as the flow profile in a rectangular channel, droplet deformation between two shearing plates, and a sessile drop on a plate with different wetting conditions. In all cases, the modeling results were in good agreement with the benchmark. A comparison of experimental droplet formation in a microchannel glass chip showed good quantitative agreement with the modeling results. With this code, droplet formation simulations with various interfacial tensions and various flow rates were performed. All resulting droplet sizes could be correlated quantitatively with the capillary number and the fluxes in the system.
Dynamics of reversible supramolecular polymers : independent determination of the dependence of linear viscosity on concentration and chain length by using chain stoppers
Knoben, W. ; Besseling, N.A.M. ; Bouteiller, L. ; Cohen Stuart, M.A. - \ 2005
Physical Chemistry Chemical Physics 7 (2005)11. - ISSN 1463-9076 - p. 2390 - 2398.
living polymers - micellar solutions - complex fluids - relaxation - microrheology - systems - moduli - rheology
The linear viscoelasticity of solutions of a hydrogen bonded reversible supramolecular polymer in the presence of a chain stopper was studied by rheometry and by dynamic light scattering using probe particles. The use of chain stoppers enabled the independent variation of the degree of polymerisation and the monomer concentration, and the effect of both parameters on rheology was investigated. Scaling exponents were obtained for the chain length and concentration dependence of the zero-shear viscosity and the terminal relaxation time, and these were compared to theoretical values. The results indicate that the reversible supramolecular polymer is semiflexible, and that both breaking and reptation of chains contribute to the stress relaxation. The parameters from macroscopic rheometry were compared to microscopic values obtained from probe particle diffusion. The particles probe the macroscopic viscoelastic parameters if their size is large compared to the correlation length in the system and to the (persistence) length of the polymer chains.