In this paper we use non-Gaussian hydrodynamics to study the magnetic response of a flux-line liquid in the mixed state of a type-II superconductor. Both the derivation of our model, which goes beyond conventional Gaussian flux liquid hydrodynamics, and its relationship to other approaches used in the literature are discussed. We focus on the response to a transverse tilting field which is controlled by the tilt modulus, c44, of the flux array. We show that interaction effects can enhance c44 even in infinitely thick clean materials. This enhancement can be interpreted as the appearance of a disentangled flux-liquid fraction. In contrast to earlier work, our theory incorporates the nonlocality of the intervortex interaction in the field direction. This nonlocality is crucial for obtaining a nonvanishing renormalization of the tilt modulus in the thermodynamic limit of thick samples
