The spreading dynamics of surfactant molecules on a thin fluid layer is of both fundamental and practical interest. A mathematical model formulated by Gaver and Grotberg [J Fluid Mech 235:399–414, 1992] describing the spreading of a single layer of insoluble surfactant has become widely accepted, and several experiments on axisymmetric spreading have confirmed its predictions for both the heigh...

This article provides a theoretical junction between two different mathematical models dedicated to the reflectance and the transmittance of diffusing layers. The KubelkaMunk model proposes a continuous description of scattering and absorption for two opposite diffuse fluxes in a homogenous layer (continuous 2-flux model). On the other hand, Kubelka’s layering model describes the multiple refle...

This paper provides a theoretical connection between two different mathematical models dedicated to the reflectance and the transmittance of diffusing layers. The Kubelka–Munk model proposes a continuous description of scattering and absorption for two opposite diffuse fluxes in a homogeneous layer (continuous two-flux model). On the other hand, Kubelka’s layering model describes the multiple r...

Abstract: Interface between matrix/coating or coating/coating in fact represents a very complicate 6 thin interfacial layer. So interface model is necessary to avoid the difficulty on considering such a 7 complicate thin layer in analysis. Classic interface model and cohesive model have been widely used 8 in stress analysis of coating materials, though they cannot represent the effect of very t...

This study investigated the effects of temperature on drying behavior and kinetic features lily scales. A series experiments were carried out at 65, 75, 85 °C to dry scales in a laboratory air-ventilated oven dryer. Drying was found significantly affect times rates. The rate curves suggested that process occurred entirely within descending period. During simulation kinetics, Page Logarithmic mo...