[M-IS21] Geophysical fluid dynamics-Transfield approach to geoscience

[MIS21-02] Rheology of bubble suspensions in unsteady shear flows

*Kohei Ohie¹, Yuji Tasaka¹, Yuichi Murai¹ (1.Hokkaido University)

Keywords:Rheology, Viscoelasticity, Bubble suspension, Magma

Bubbly flows are ubiquitous in industry and nature. The dispersed bubbles change the original rheological properties and modify, for example, the eruption pattern of volcanoes. In this study, the viscoelasticity of a dilute bubble suspension is elucidated based on the constitutive equation proposed by Frankel and Acrivos. Nondimentionalization of the equation reveals that the bubble suspension rheology is systematized by three parameters, volume fraction, capillary number Ca, and dynamic capillary number Cd. The non-dimensional parameters Ca and Cd indicate the deformability of the suspended bubble in a Newtonian medium and the unsteadiness of the bubble deformation. The relative viscosity and phase of viscoelasticity were comprehensively investigated according to the volume fraction, Ca, and Cd. It was revealed that the viscosity increase or decrease depends on whether Ca or Cd exceeds a common critical value, 0.65. It also turned out that the phase of viscoelasticity takes the minimum value at Ca << 1 and Cd = O(1). This means that the bubble suspension has the most prominent viscoelasticity when the time scale of the shear deformation is as same as the relaxation time of the suspended bubble and when the bubbles keep in a spherical shape.