Bézier Curve Method to Compute Various Meniscus Shapes

Overview

The question of the meniscus shape, or the boundary of a liquid, has long been an unsolved problem in theoretical physics. The problem holds significance because menisci appear in a variety of contexts, from lava lamps to capillary action to membranes. The Young-Laplace equation, a differential equation, determines the meniscus shape. Although numerous works have attempted to solve the equation, or approximate its solution, they all involve complex techniques and tedious computation. This paper demonstrates an elegant solution to the meniscus shape problem using the Bézier curve method: it fits a Bézier curve to the Young-Laplace equation to approximate its solution. T o test the Bézier curve method's viability, this paper uses it to solve four cases of menisci: liquid in a cylindrical tube, against one plate, against two plates, and in a water droplet. In each case, the accuracy and complexity of the Bézier curve method are analyzed, and the results are compared with those of previous works. The Bézier curve is usually used in the field of computer graphics, as opposed to science, and has never been applied to the meniscus shape problem before. The Bézier curve method is a novel, simple, and accurate technique to solve the meniscus shape problem, and the success of the Bézier curve method here suggests that it could also help solve a variety of other scientific problems.

Competition history

• JSHS 2023 Category not listed

Resources

• National JSHS abstract book ↗

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