Interfacial Dynamics and Rheology of a Crude-Oil Droplet Oscillating in Water at a High Frequency

Abstract

We report investigations of a pendant diluted crude-oil droplet in water that is forced to oscillate at a frequency ω. The droplet interface contains a significant amount of surface-active agents and displays a marked viscoelastic rheology with elastic moduli larger than viscous ones. At a low frequency, fluid viscosity and inertia are negligible, which allows a direct determination of the dilatational interface rheology. At a large frequency, eigenmodes of inertial shape oscillations are excited. By decomposing the interface shape into spherical harmonics, the resonance curves of the inertial modes of the interface are determined, as well as the frequency and damping rate of each mode. These two parameters are of major importance for the prediction of the deformation and breakup of a droplet in any unsteady flow without any prior knowledge of either the chemical composition or the detailed rheological properties of the interface. Then, interfacial rheology is related to interface dynamics by solving the coupled dynamic equations for the two fluids and the interface. It turns out that the rheology of the interface is well described by an equivalent two-dimensional viscoelastic material, the elasticities and viscosities of which depend upon the frequency. A first significant result is that shear and dilatational elasticities are closely connected, as are shear and dilatational viscosities. This implies that intrinsic rheology plays a major role and that compositional rheology is either negligible or strongly coupled to the intrinsic one. A second major result is that, for moderately aged droplets (≤5000 s), the elasticity and viscosity at a high frequency (10−80 Hz) can be extrapolated from low-frequency measurements (≤1 Hz) by a simple power law of the frequency, ω z. The exponent z is related to the loss angle θ loss by a relation found in many previous low-frequency investigations of crude-oil interfaces: z = θ loss /2π. The present work thus extends classic observations obtained at a low frequency to a higher frequency range corresponding to the natural frequency of the droplets, where the droplet shape results from the balance between dynamic pressure and surface stresses and the interface involves simultaneous shear and dilatation. These results bring about serious constraints regarding the modeling of physicochemical underlying mechanisms and provide some insights for the understanding of the structure of crude-oil interfaces.

Impact of Saltwater Environments on the Coalescence of Oil-in-Water Emulsions Stabilized by an Anionic Surfactant

“…The relaxation exponent and the theoretical loss angle have the relationship described in eq for a critical gel. ,, …”

“…Equation was used to calculate the loss angles from the elastic and viscous moduli that are reported in Table . ,, …”

Determination of Interfacial Concentration of a Contaminated Droplet from Shape Oscillation Damping

“…[21], which are recalled in a Supplementary Material [26]. Note that this theory of shape oscillation, also discussed in [27,28], writes the coupling between linearized Navier-Stokes and surfactant transport equations. Two unknown parameters are required to compute ω n;th and β n;th : the surface tension at equilibrium σ eq and the normalized Gibbs elasticity E ¼ −ðΓ eq =σ eq Þð∂σ=∂ΓÞ eq , where subscript "eq" denotes equilibrium values.…”

Assessing the Interfacial Activity of Insoluble Asphaltene Layers: Interfacial Rheology versus Interfacial Tension

“…29 However, currently, there is no consensus on whether the interfacial layers should be viewed as mere dense 2D suspensions or whether they are interfacial gels. 30,31 In the present work, we will compare the interfacial activity and interfacial rheology of different asphaltene fractions as differences in polarity should lead to differences in interfacial forces and potential physical cross-linking. This should provide clarity on whether the interfacial forces and subsequent gelation or mere crowding determines the behavior.…”