Hydrodynamics of subphase entrainment during Langmuir–Blodgett film deposition

The phenomenon of subphase entrainment that accompanies Langmuir–Blodgett film deposition is examined in terms of the hydrodynamics of dip coating coupled with mass transport of the depositing monolayer. The governing equations for film thickness and for concentration of the monolayer material have been derived based on the lubrication approximation theory for steady-state conditions, subject to viscous, surface tension, gravity, intermolecular and Marangoni forces. The equations have been solved by numerical methods. In the absence of the monolayer, the model reduces to various forms of the case of substrate withdrawal from a pure liquid — the well known dip coating problem. Effect of several parameters related to material properties and operating conditions have been examined. We consider two mechanisms for subphase entrainment: the flow driven by the motion of the solid substrate, and Marangoni driven flow caused by surface tension gradient due to surface concentration gradient. Attractive van der Waals forces and Marangoni flow are responsible for thickening of the entrained subphase film. Gravity drainage and repulsive van der Waals forces thin the entrained subphase film. The entrained subphase film thickness measurement is done by using a dual channel spectrometer in conjunction with a software to obtain thickness from spectral information. Our numerical results are in good agreement with the extent of entrainment predicted by the model.