A mathematical model for droplet separation by surface tension using contact cantilevers -- applications to {\it{in situ}} diagnosis and treatment

TL;DR

This paper develops an exact mathematical model describing the shape and parameters of a liquid meniscus formed by a cantilever device, enabling simultaneous diagnosis and treatment in biomedical applications.

Contribution

It provides an exact analytical characterization of the meniscus shape and extremal parameters based on surface tension and density, facilitating combined diagnosis and treatment.

Findings

Explicit formulas for meniscus shape and extremal parameters

Relationship between surface tension, density, and meniscus characteristics

Potential for integrated diagnosis and treatment procedures

Abstract

This work provides an exact mathematical characterization of the meniscus formed by a liquid of density $\rho$ (model for tumor tissue) when probed with a cantilever device, operating by gravity (acceleration $g$) and with surface tension coefficient $\sigma$ (material-dependent for the specific choice of liquid and cantilever). The shape and extremal parameters (maximum height $\mathcal{H}$, break-off volume $\mathcal{V}$) of the meniscus formed, as functions of $\sigma, \rho$, are found by an exact analysis. Having knowledge of the explicit relationship between these parameters allows to perform in one procedure both diagnosis and treatment.