# The Effect of Length Scale on Flow Properties of Micro, Nano and Macro-Emulsions

Flow properties of a complex fluid depend on not only the characterizations of the components that make up the system but also the interactions between the phases. One of the most significant factors that affect these interactions is the length scale of the dispersed phase. According to Stokes law, the root of complex fluid rheological models, the velocity of a moving particle in a fluid is a function of the viscosity of the fluid and also the size of the moving droplet. The main aim of this research is to understand the crucial elements that define and control the rheological behaviour of complex fluids and thereby provide evidence for proposed modifications of the available rheological models to include parameters that capture the deduced crucial elements. In particular, by adjusting different aspects of Stokes law. The modified models can then be applied to a wider range of complex fluid systems, including emulsions, regardless of the chemicals that form the system. The complex fluids used in this research to develop the above are emulsions with droplets ranging over four orders of magnitude, 10 nm to 100 µm. Within a single base chemical system microemulsions, nanoemulsions and macroemulsions could be formed. The length scale and flow properties of each group were examined and the effect of length scale on rheological properties was investigated. Critical elements there were identified include: • Use of the appropriate viscosity value for the fluid through which the dispersed phase diffuses. It is often assumed that the viscosity of the pure continuous phase fluid can be used as the reference viscosity in the Stokes equation. In a real system the viscosity of the continuous phase can be strongly affected, and thereby defined by, the presence of the dispersed phase itself and the interfacial layer. Hence it is paramount that the appropriate reference viscosity is used. It is noted that the standard assumption is often applicable for highly diluted suspensions that are composed of rigid spheres. However, the research undertaken here demonstrates that this assumption must be reconsidered for more concentrated systems and particularly for emulsions. We recommend that for such systems the viscosity of the pure continuous phase is replaced by the constant viscosity of the sample at a zero shear rate. • Consideration of structural factors that also affect the viscosity. In particular it is often assumed that: 1- the droplets/particles are spherical and non-deformable; and 2- the dispersed phase presents as a single length scale, i.e. the system is a monodisperse system. The inclusion of these assumptions limits dramatically the applicability of the available models to fit and describe the real flow behaviour and thereby does not allow for predictability of behaviours. Typically models have been modified by adding experimental factors rather than explicitly incorporating the above factors into the development of a model. In this work the deviation from these rheological models are explained and correlated to the deviation from spherical structure and monodispersity. • Defining the relative viscosity as the ratio between the sample viscosity and the reference viscosity is common practice in the application of most rheological models. The viscosity of water tends to be taken as the reference viscosity. This leads to no agreement between the well-known rheological models and the experimental data, especially when applied to analysis of microemulsion rheology. In this work, we show that by taking the viscosity of the relevant ternary surfactant solution as the reference viscosity, the existing models can be applicable to microemulsions. This work sheds light on the relationship between the non-Newtonian behaviour of nanoemulsions and their underlying thermodynamic instability. In these systems the Newtonian behaviour is not evident till a shear rate of 100/s is reached. On the other hand the Newtonian viscosity is observed in thermodynamically stable systems, e.g. surfactant solutions and microemulsions, beyond a shear rate of 5/s or less. The Newtonian region also was observed in normal emulsions with narrow size distributions, dilute monodisperse coarse emulsions or dilute normal emulsions prepared in a Warring blender while a short chain alcohol is added to the system. By adding the short chain alcohol to the system not only the densities of the two phases are made similar and the emulsification is eased but also the polydispersity of the final emulsion is decreased. Finally a single model to be applicable to different types of emulsions with droplet sizes over five orders of magnitude was proposed. However the relationship is applicable to the systems with a low degree of polydispersity and once polydispersity is introduced the flow behaviour becomes complicated and the proposed model is not applicable.