Splitting a Liquid Jet

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"Splitting of a Liquid Jet"
Srinivas Paruchuri and Michael P. Brenner
Physical Review Letters 98(13) 134502 (2007)

Soft Matter Keywords

dominant balance, liquid jet splitting, Navier Stokes

Figure 1. (a) Schematic showing a jet passing between a forcing element that cause the jet to split into two filaments. (b) Coordinate system for analysis. The analysis will focus on finding the evolution of the thickness h(x) of the jet cross section.
Figure 2. (a) Time evolution of the jet thickness, h(x). (b) Time evolution of the jet velocity, v(x). The inset plots show the minimum thickness, <math>h_{min}</math> scales as <math>(t^*-t)^2</math>, and the maximum velocity, <math>v_{max}</math> scales as <math>(t^*-t)^{-1}</math>.
Figure 3. (a) Collapse of curves in the lamellar region. The simulation curves all collapse nicely to the analytical approximation near the origin. (b) Collapse of the velocity profile onto the analytical similarity solution near the jump region.


Paruchuri and Brenner develop a theoretical explanation for the splitting of a circular cross section liquid jet into two separate filaments. Beginning from Navier Stokes in the limit that jet cross section changes slowly as it moves downstream from the nozzle, they demonstrate that only when sufficiently large tangential stresses are present does the jet split. A full numerical simulation is compared to analytical approximations with full agreement. Looking at the simulation results, the authors find that there are three distinct regions as one passes from the center of the jet to the outside: 1) a lamellar region characterized by a flat thickness profile and linear velocity field, 2) an outer region characterized by a nearly time independent thickness and velocity, and 3) a jump region with a large jump in the velocity field connecting the lamellar and outer regions. Dominant force balances for these regions are proposed and tested against simulation.

Practical Application of Research

in process

Mechanism for Splitting Events


[1] if necessary

written by Donald Aubrecht