A numerical model is presented for predicting the instability and breakup of liquid jets of Newtonian fluid driven by thermo-capillary perturbations. The model uses a one-dimensional slender-jet approximation to obtain the equations of motion in the form of a set of coupled nonlinear partial differential equations (PDEs). These equations are solved using the method-of-lines (MOL), wherein the PDEs are transformed to a system of ordinary differential equations (ODEs) for the nodal values of the jet variables on a uniform staggered grid. The model predicts instability and satellite formation in infinite threads of fluid and continuous jets that emanate from an orifice. The model is validated using established computational data, as well as axisymmetric, volume of fluid (VOF) computational fluid dynamic (CFD) simulations. The key advantages of the model are its ease of implementation and speed of computation that is several orders of magnitude faster than the VOF CFD simulations. The model enables rapid parametric analysis of jet breakup and satellite formation as a function of jet dimensions, modulation parameters, and fluid rheology.
The model also incorporates post break-up behavior by providing methods for the fission of the jet into discrete ligaments and drop. Each separate ligament is assigned its own computational domain that is passed to the ODE solver in lockstep. Furthermore, some drops merge downstream as a results of their velocity differentials at the point of break-up; the model implements drop merging by blending discrete computational domains into one, using cubic interpolation and third-order polynomials to create a liquid bridge between the two. The study of merging behavior has application in the field of inkjet printing, wherein the thermal pulse to the surface of a jet is modulated to create different drop volumes. The model reveals that larger than usual drops do not spontaneously form at the end of the filament; they first break into smaller pieces which coalesce downstream.