A floating prolate spheroid

The equilibrium position of a spherical or prolate spheroidal particle resembling a needle floating at the interface between two immiscible fluids is discussed. A three-dimensional meniscus attached to an a priori unknown contact line at a specified contact angle is established around the particle, imparting to the particle a capillary force due to surface tension that is balanced by the buoyancy force and the particle weight. An accurate numerical solution for a floating sphere is obtained by solving a boundary-value problem, and the results are compared favorably with an approximate solution where the effect of the particle surface curvature is ignored and the elevation of the contact line is computed using an analytical solution for the meniscus attached to an inclined flat plate. The approximate formulation is applied locally around the nearly planar elliptical contact line of a prolate spheroid to derive a nonlinear algebraic equation governing the position of the particle center and the mean elevation of the contact line. The effect of the fluid and particle densities, contact angle, and capillary length is discussed, and the shape of the contact line is reconstructed and displayed from the local solution.

Graphical abstractIllustration of a contact line developing around a floating spheroidal particle with aspect ratio c/b = 5, drawn as a heavy line. The rectangular frame marks the position of the undisturbed interface.Figure optionsDownload full-size imageDownload high-quality image (75 K)Download as PowerPoint slideHighlights► Developed an efficient method for estimating the equilibrium position of a floating elongated particle. ► Demonstrated the effect of physical and geometrical parameters on the particle floating angle. ► Reconstructed the shape of the three-phase contact line.