We consider planar flow involving two viscous fluids in a porous medium. One fluid is injected through a line source at the origin and moves radially outwards, pushing the second, ambient fluid outwards. There is an interface between the two fluids and if the inner injected fluid is of lower viscosity, the interface is unstable to small disturbances and radially directed unstable Saffman–Taylor fingers are produced. A linearized theory is presented and is compared with nonlinear results obtained using a numerical spectral method. An additional theory is also discussed, in which the sharp interface is replaced with a narrow diffuse interfacial region. We show that the nonlinear results are in close agreement with the linearized theory for small-amplitude disturbances at early times, but that large-amplitude fingers develop at later times and can even detach completely from the initial injection region.

Bernoulli pads can create a significant normal force on an object without contact. The radial outflow which creates this force also imposes a significant shear force on the object. Better understanding this shear force can improve pad designs in order to mitigate material deformation and damage, or allow the pads to be used as shear-based cleaning implements. Here, we use computational fluid dynamics to explore the parameter space and show a power-law relationship between the fluid power at the pad inlet and the maximum shear stress. These simulations are validated by a particle tracking velocimetry experiment. A relationship between the maximum shear stress and the inlet Reynolds number is provided, and some implications of the observed scaling relationships are explored.