Paper Number
PO49 

Session
Poster Session

Title
Linear viscoelasticity of a dilute emulsion of drops containing soluble surfactant

Presentation Date and Time
October 11, 2017 (Wednesday) 6:30

Track / Room
Poster Session / Cripple Creek Ballroom

Authors (Click on name to view author profile)

1. Sengupta, Rajarshi (Carnegie Mellon University, Chemical Engineering)
2. Walker, Lynn M. (Carnegie Mellon University, Chemical Engineering)
3. Khair, Aditya S. (Carnegie Mellon University, Chemical Engineering)

Author and Affiliation Lines (in printed abstract book)
Rajarshi Sengupta, Lynn M. Walker, and Aditya S. Khair
Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213

Speaker / Presenter 
Sengupta, Rajarshi

Text of Abstract
The linear viscoelasticity of a dilute emulsion of drops containing soluble surfactant is calculated under a small-amplitude oscillatory shear deformation. It is assumed that the drops remain spherical. At small values of the strain rate, the contribution of surfactant transport by convection in the bulk is small, i.e., the bulk Peclet number (Pe) is small, and the surfactant distribution is linearly coupled to the flow field at O(Pe). Using regular perturbation expansions about Pe, we calculate the complex viscosity of the emulsion upto O(Peφμ₀), where φ is the small volume fraction of the dispersed phase, and μ₀ is the viscosity of the suspending fluid. When soluble surfactants are present in the dispersed phase, their adsorption to the interface may cause a significant decrease in the bulk concentration, a phenomenon that is known as depletion. The impact of depletion is characterized by two parameters: h, which is the ratio of the minimum bulk concentration required to saturate the interface to the initial bulk concentration, and k, which is the ratio of the desorption time scale to the adsorption time scale. From the Fourier inversion of the complex viscosity we calculate the relaxation modulus of the emulsion at different limits of these two parameters, and identify the appropriate time scales for stress relaxation. We show that the relaxation spectrum can be used to extract information about the dynamics of surfactant adsorption and diffusion at fluid-fluid interfaces.