A mechanism for intermittency in spatial distribution of small inertial particles advected by a turbulent incompressible fluid flow is discussed. The mechanism is related to self-excitation (i.e., exponential growth without an external source) of fluctuations of concentration of small particles in a turbulent fluid flow. The effect is caused by the inertia of particles which results in a divergent velocity field of particles. An equation for the high-order correlation functions of concentration of small inertial particles is derived. It is shown that the growth rates of the higher moments of particle concentration are higher than those of the lower moments, i.e., particle spatial distribution is intermittent. Similar phenomena occur for noninertial admixtures advected by divergent turbulent velocity field.