Understanding the dynamics particle-laden films is vital for numerous applications both in nature and in engineering. However, the complexity of having an evolving free interface along with an underlying microstructure makes these flows difficult to simulate, making mathematical modelling a necessary tool. In absence of particles, the stability of a gravity-driven thin film has been extensively studied. Yih (1963) in his pioneering study carried out a linear stability analysis and identified a long wavelength instability in a falling film. Subsequently Benney (1966) performed an expansion in wave amplitude and derived a nonlinear wave equation describing the evolution of the film height that reproduced the linear stability findings as a limiting case. The presence of particles alters the rheology of the fluid with the non-uniformity of particle concentration altering the local shear viscosity leading to a coupling with the momentum balance. Using a Benney-like amplitude expansion, a set of coupled nonlinear equations are derived describing the evolution of film height and particle concentration. The modified Benney equation is solved numerically and the threshold of instability is calculated. However, the Benney equation is known to have a finite time blowup beyond the stability threshold (Pumir et al. 1983). This is countered using a weighted residual approach in conjunction with the lubrication approximation. To access disturbances of finite wavelength, the governing equations are linearised to obtain a generalized Orr-Sommerfeld system of equations. The predictions of linear stability analysis are then compared with the results from the nonlinear long wave theories.