A brief description of the mathematical model of Amon and Denson and its application to intumescent coatings A brief introduction to the Amon and Denson theory have proposed a mathematic model to describe how spherical bubbles in a polymer liquid will expand when the interior pressure inside the bubbles is increased. Refer to Figure 1, which shows uniformly distributed bubbles of radius R, within a viscous polymer liquid that has a viscosity µ. Each bubble has an envelope of radius on conservation of mass “S”. Based and momentum, have obtained the following equation to describe the expansion ratio of the bubbles: (1) where and are the radius of the bubble and the outer shell respectively at time t, with initial values of and is the viscosity of the surrounding liquid and is the bubble respectively, η σ surface tension. By conservation of volume, (2) The outer shell radius is calculated at each time step. The initial outer shell radius is calculated by using the nucleation density, i.e. the number of nucleation sites per volume, N/V. (3) All nucleated cells are uniformly distributed and each cell has of volume at . The initial outer shell radius, is significantly greater than the initial bubble radius . Figure 1 shows a schematic representation of the cell model.
A brief description of the mathematical model of Amon and Denson and its application to intumescent coatings A brief introduction to the Amon and Denson theory have proposed a mathematic model to describe how spherical bubbles in a polymer liquid will expand when the interior pressure inside the bubbles is increased. Refer to Figure 1, which shows uniformly distributed bubbles of radius R, within a viscous polymer liquid that has a viscosity µ. Each bubble has an envelope of radius “S”. Based on conservation of mass and momentum, have obtained the following equation to describe the expansion ratio of the bubbles: (1) where and are the radius of the bubble and the outer shell respectively at time t, with initial values of and respectively, η is the viscosity of the surrounding liquid and σ is the bubble surface tension. By conservation of volume, (2) The outer shell radius is calculated at each time step. The initial outer shell radius is calculated by using the nucleation density, i.e. the number of nucleation sites per volume, N/V. (3) All nucleated cells are uniformly distributed and each cell has of volume at . The initial outer shell radius, is significantly greater than the initial bubble radius . Figure 1 shows a schematic representation of the cell model.
with_Burak_theory.docx