  We investigate the evolution of binary fractions in star clusters using
N-body models of up to 100000 stars. Primordial binary frequencies in these
models range from 5% to 50%. Simulations are performed with the NBODY4 code and
include a full mass spectrum of stars, stellar evolution, binary evolution and
the tidal field of the Galaxy. We find that the overall binary fraction of a
cluster almost always remains close to the primordial value, except at late
times when a cluster is near dissolution. A critical exception occurs in the
central regions where we observe a marked increase in binary fraction with time
-- a simulation starting with 100000 stars and 5% binaries reached a core
binary frequency as high as 40% at the end of the core-collapse phase
(occurring at 16 Gyr with ~20000 stars remaining). Binaries are destroyed in
the core by a variety of processes as a cluster evolves, but the combination of
mass-segregation and creation of new binaries in exchange interactions produces
the observed increase in relative number. We also find that binaries are cycled
into and out of cluster cores in a manner that is analogous to convection in
stars. For models of 100000 stars we show that the evolution of the core-radius
up to the end of the initial phase of core-collapse is not affected by the
exact value of the primordial binary frequency (for frequencies of 10% or
less). We discuss the ramifications of our results for the likely primordial
binary content of globular clusters.
