  The problem of demixing in the Asakura-Oosawa colloid-polymer model is
considered. The critical constants are computed using truncated virial
expansions up to fifth order. While the exact analytical results for the second
and third virial coefficients are known for any size ratio, analytical results
for the fourth virial coefficient are provided here, and fifth virial
coefficients are obtained numerically for particular size ratios using standard
Monte Carlo techniques. We have computed the critical constants by successively
considering the truncated virial series up to the second, third, fourth, and
fifth virial coefficients. The results for the critical colloid and (reservoir)
polymer packing fractions are compared with those that follow from available
Monte Carlo simulations in the grand canonical ensemble. Limitations and
perspectives of this approach are pointed out.
