A first application of a cleaning material is made to a surface of a substrate. The cleaning material includes one or more viscoelastic materials for entrapping contaminants present on the surface of the substrate. A first application of a rinsing fluid is made to the surface of the substrate so as to rinse the cleaning material from the surface of the substrate. The first application of the rinsing fluid is also performed to leave a residual thin film of the rinsing fluid on the surface of the substrate. A second application of the cleaning material is made to the surface of the substrate having the residual thin film of rinsing fluid present thereon. A second application of the rinsing fluid is then made to the surface of the substrate so as to rinse the cleaning material from the surface of the substrate.