© 2018 American Institute of Mathematical Sciences. All rights reserved. We prove the existence of solutions for a coupled system modeling the flow of a suspension of fluid and negatively buoyant non-colloidal particles in the thin film limit. The equations take the form of a fourth-order nonlinear degenerate parabolic equation for the film height h coupled to a second-order degenerate parabolic equation for the particle density ψ. We prove the existence of physically relevant solutions, which satisfy the uniform bounds 0≤6 ψ/h≤1 and h > 0.