  The dynamics of neutrally buoyant particles transported by a turbulent flow
is investigated for spherical particles with radii of the order of the
Kolmogorov dissipative scale or larger. The pseudo-penalisation spectral method
that has been proposed by Pasquetti et al. (2008) is adapted to integrate
numerically the simultaneous dynamics of the particle and of the fluid. Such a
method gives a unique handle on the limit of validity of point-particle
approximations, which are generally used in applicative situations. Analytical
predictions based on such models are compared to result of very well resolved
direct numerical simulations. Evidence is obtained that Faxen corrections give
dominant finite-size corrections to velocity and acceleration fluctuations for
particle diameters up to four times the Kolmogorov scale. The dynamics of
particles with larger diameters is dominated by inertial-range physics, and is
consistent with predictions obtained from dimensional analysis.
