Axisymmetric squeezing dynamics of resin droplet with surface tension and its numerical solution

Abstract

We investigate the 2D axisymmetric quasi-static dynamics of a UV-curable optically clear resin droplet squeezed between two parallel glass walls using a static force. The radial spreading speed and resulting radial spread are examined using an analytical derivation and a numerical discretized approximation including the effect of the surface tension. Under a boundary condition, the vertical downward velocity of the glass wall is determined by the static force and capillary pressure, and a pressure discontinuity occurs across the air-liquid interface. The capillary pressure is estimated from the Young-Laplace equation. A numerical approximate solution is then derived from the governing equations to obtain a discretized set of linear equations to serve as an alternative theoretical solution. A 2D axisymmetric section with a staggered grid is adopted for a pressure-based segregated velocity-pressure coupled solution process using the SIMPLE algorithm. The change in the rheological properties due to the UV-curing effect is then added to the squeezing dynamics solution with an arbitrary initiation time and the power amplitude of the UV curing. According to a few rheological test results for different UV powers, the relationship between the UV energy (calculated using the UV power) and the resin viscosity is confirmed. The numerical solution is validated, and both theoretical solutions are compared with the experimental results of several squeezing tests with and without UV curing.