Maximal liquid bridges between horizontal cylinders

What is it about?

We present an analysis on two−dimensional liquid bridges trapped between solid cylinders that support the forces of surface tension and hydrostatic pressure. We determine the shapes of such liquid bridges using an exact analytical solution to the Laplace−Young equation and analyze the maximum trapping capacity (the cross sectional area of the largest liquid bridge produced) for a given inter−cylinder distance and contact angle. Our results show that the maximum trapping capacity and the meniscus slope angle of the largest liquid bridge are linearly related to the inter−cylinder distance when the cylinder radius is small compared to the capillary length. In this regime of small cylinders, the largest amount of liquid can be trapped when the inter−cylinder distance is approximately twice the capillary length. We additionally derive several approximate solutions to the Laplace-Young equation that analytically verify these relationships.

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Why is it important?

We present exact and approximate solutions to the Laplace-Young equation. These solutions can be extended to determine the capillary trapping of fluids in several two−dimensional geometries. An example is the equilibrium of fluid ganglia or stringers trapped in a solid matrix