Deformation of bubbles in a highly viscous pipe flow

The rheology of bubble-bearing magma is important in volcanic conduit flow. Its rheological properties strongly depend on the deformation of bubbles in highly viscous liquid. Here we conduct an experimental investigation on the deformation of bubbles in a Stokes pipe flow, in which the shear rate is non-uniform. The deformation of the bubbles in various shear rates is observed by high-speed photography. The deformed shape is classified using the capillary number, Ca, the ratio of viscous shear stress that promotes bubble deformation to surface tension that resist deformation. We find that the length of the elongated bubbles due to shear at Ca>1 is smaller than that in a simple shear field whose capillary numbers are equal to each other. In such a case, the bubbles have an asymmetric shape like the section of a two-dimensional airfoil with camber. Implication to the effective viscosity of the suspensions with such a wing-shaped bubble is briefly discussed.