Question

Identify a real-world problem in which the concept of a “thin film” and an "infinite slab" can be applied and turn in a copy of an appropriate problem statement.

Answer 1

Thin gel or slab of air freshener is a common real world application in which the concept of a “thin film” and an "infinite slab" can be observed.

Background

Film theory was proposed by Walter G. Whitman in 1923. It is the simplest theory which explains behaviour of mass transfer coefficient in turbulent flow. When a fluid flows turbulently (forced convection by fan) past a solid surface (air freshener), with mass transfer occurring from the surface to the fluid. In Fig. above, the actual concentration profile is shown by curve while the dotted lines represent concentration profile assumed in Film Theory.

Problem Statement

Consider a thin gel (essential oil in gelatin) or thin solid slab (napthelene) which is 100 mm long and 5 mm thick, placed in a room at 298K and 1 atm. Since infinity is a concept of relative measure; when length is much larger than thickness, it can be considered that diffusion occurs on an infinite slab. A thin film forms over the solid surface such that quantity of solute (A) within the film (C_A2) would be small relative to the amount passing through it (C_A1). The solute diffuses through a film of 0.5 mm thickness. Estimate the rate (mol/ m².s) at which fragrance (i.e, solute, A) enters in air, at steady state.The bulk of air consists of 20 mol% of A and binary diffusivity is 20 mm²/s.