  The long range attractive force between two hydrophobic surfaces immersed in
water is observed to decrease exponentially with their separation -- this
distance-dependence of effective force is known as the hydrophobic force law
(HFL). We explore the microscopic origin of HFL by studying distance-dependent
attraction between two parallel rods immersed in 2D Mercedes Benz model of
water. This model is found to exhibit a well-defined HFL. Although the
phenomenon is conventionally explained by density-dependent theories, we
identify orientation, rather than density, as the relevant order parameter. The
range of density variation is noticeably shorter than that of orientational
heterogeneity. The latter is comparable to the observed distances of
hydrophobic force. At large separation, attraction between the rods arises
primarily from a destructive interference among the inwardly propagating
oppositely oriented heterogeneity generated in water by the two rods. As the
rods are brought closer, the interference increases leading to a decrease in
heterogeneity and concomitant decrease in free energy of the system, giving
rise to the effective attraction. We notice formation of hexagonal ice-like
structures at the onset of attractive region which suggests that metastable
free energy minimum may play a role in the origin of HFL.
