Splitting of a Liquid Jet

We demonstrate that a flowing liquid jet can be controllably split into two separate subfilaments through the application of a sufficiently strong tangential stress to the surface of the jet. In contrast, normal stresses can never split a liquid jet. We apply these results to observations of uncontrolled splitting of jets in electric fields. The experimental realization of controllable jet splitting would provide an entirely novel route for producing small polymeric fibers.

Figure 1

(a) Schematic of the proposed experiment. A liquid jet passes through a forcing element (e.g., an electric capacitor) that stretches out the cross section of the jet. The stretching splits the jets into two subfilaments. Near the splitting event the cross section of the jet stretches from a circle to break into two separate pieces. (b) The dynamics of the splitting is described by deriving equations for evolution of the thickness $h(x,t)$ of the cross section.

Figure 2

Time evolution of the thickness $h(x,t)$ (a) and velocity $v(x,t)$ (b) of the jet cross section, under a tangential stress ${\tau }_0=\gamma /a^2$ and $\mu =0.27\sqrt{\gamma a\rho }$. The inset of (a) shows the minimum thickness vanishes as $h_{\min }\sim (t^{*}-t{)}^2$, while the inset of (b) shows the maximum velocity diverges as $v_{\max }\sim (t^{*}-t{)}^{-1}$.

Figure 3

(a) Collapse of curves in the lamellar region. The dotted line corresponds to the value of $\frac{2}{3}$. The combination $\frac{v(x,t{)}^{2}h(x,t)}{x^2}$ collapses to the dotted line near the origin. (b) Collapse of the velocity profile in the jump region onto the similarity solution. $\xi =(x-x_0)/\ell (t)x_0$ is the position where the velocity is half its maximum.

Figure 4

Scanning electron micrograph of a splitting event from an electrospinning event [13]. The jet radius is originally of order $5\mu \mathrm{m}$, much smaller than the characteristic length scale of the splitting along the fiber. The splitting occurs in a lamellar region as expected from the analysis herein.