Complex viscosity of dilute capsule suspensions: a numerical study

Abstract

In this paper, we apply an oscillating shear flow to a dilute capsule suspension and report its viscoelastic properties. We analyze the complex viscosity under different capillary numbers and viscosity ratios, which is a viscosity contrast inside and outside the capsules. For all viscosity ratios, the real part of complex viscosity η′ monotonically decreases with the frequency of the applied oscillating shear, while the imaginary part η′′ shows the maximum value at an intermediate frequency. In general, the capsule with a larger viscosity ratio gives larger η′, while that of smaller viscosity ratio gives larger η′′. At high frequencies, the capsule that has higher (lower) inner viscosity contributes to increase (decrease) the viscosity of the solutions. In order to separately discuss the contributions of the membrane elasticity and internal fluid viscosity, we analyse the first term and second term of the particle stress tensor. The first term, which is called elastic stress in this paper, represents particle stress that arises from the capsule deformation. The amplitude of elastic stress is nearly constant at low frequencies, while it is inversely proportional to the applied frequency at high frequencies. The phase of elastic stress shifts from the shear to strain phases when the frequency increases. These tendencies of elastic stress do not depend on the viscosity ratio, and the qualitative trends are the same for all viscosity ratios. The second term, which is called viscous stress in this paper, represents particle stress that arises from the viscosity ratio, and the trend is drastically different by the viscosity ratio. The viscous stress contributes to increase (decrease) the viscosity and decrease (increase) the elasticity, when the capsule inner viscosity is higher (lower). Finally, we evaluate the effect of the capillary number. At low frequencies, both the capillary number and viscosity ratio are important factors for the rheology. On the other hand, the viscosity ratio becomes the only governing factor at high frequencies because the membrane elasticity has a negligible effect.

Keywords

• capsule
• rheology
• complex viscosity
• stokes flow
• boundary element method