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

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.