  We demonstrate that the law of the rectilinear coexistence diameter in
two-dimensional (2D) mixtures of non-spherical colloids and non-adsorbing
polymers is violated. Upon approach of the critical point, the diameter shows
logarithmic singular behavior governed by a term t ln(t), with t the relative
distance from the critical point. No sign of a term t^2b could be detected,
with b the critical exponent of the order parameter, indicating a very weak or
absent Yang-Yang anomaly. Our analysis thus reveals that non-spherical particle
shape alone is not sufficient for the formation of a pronounced Yang-Yang
anomaly in the critical behavior of fluids.
