  We propose a mesoscopic model of binary fluid mixtures with tunable viscosity
ratio based on a two-range pseudo-potential lattice Boltzmann method, for the
simulation of soft flowing systems. In addition to the short range repulsive
interaction between species in the classical single-range model, a competing
mechanism between the short-range attractive and mid-range repulsive
interactions is imposed within each species. Besides extending the range of
attainable surface tension as compared with the single-range model, the
proposed scheme is also shown to achieve a positive disjoining pressure,
independently of the viscosity ratio. The latter property is crucial for many
microfluidic applications involving a collection of disperse droplets with a
different viscosity from the continuum phase. As a preliminary application, the
relative effective viscosity of a pressure-driven emulsion in a planar channel
is computed.
