Conical Interfaces between Two Immiscible Fluids Induced by an Optical Laser Beam

We demonstrate the existence of conical interface deformations induced by a laser beam that are similar to Taylor cones in the electrical regime. We show that the cone morphology can be manipulated by fluid and laser parameters. A theory is proposed to quantitatively describe these dependences in good agreement with experimental data obtained for different fluid systems with low interfacial tensions. Counterintuitively, the cone angle is proved to be independent of the refractive index contrast at leading order. These results open a new optofluidic route towards optical spraying technology—an analogue of electrospraying—and more generally for the optical shaping of interfaces.

Figure 1

(a) Sketch of the experiment: a laser beam ($\lambda =532\mathrm{nm}$ in vacuum) is focused at the interface with the objective O1 (Olympus x10) and deforms this interface by radiation pressure. Deformation of the interface for $P<P_c$ (Winsor toluene S1b for ${\omega }_0=12.9\mu \mathrm{m}$, $P=1.53\mathrm{W}$). (b) Conical deformation by radiation pressure for $P>P_c$ (Winsor toluene S1b for ${\omega }_0=12.9\mu \mathrm{m}$, $P=1.55\mathrm{W}$). (c) Typical variation of the incident angle ${\alpha }_i$ as a function of the height of deformation for $P<P_C$ and $P>P_C$. Note that the curve for $P>P_c$ exhibits a clear plateau. ${\alpha }_{\mathrm{TR}}$ is the total reflection (TR) incident angle. (d) Light path revealing the total reflection mechanism inside the conical deformation (microemulsion S3). (e)–(g) Conical deformations for various experimental systems: (e) Winsor heptane S2 for ${\omega }_0=12.2\mu \mathrm{m}$, $P=2.25\mathrm{W}$, (f) microemulsion S3e for ${\omega }_0=9.0\mu \mathrm{m}$ and $P=2.89\mathrm{W}$, and (g) jet and drop emission at the tip of the cone for Winsor toluene S1b system with ${\omega }_0=8.8\mu \mathrm{m}$ and $P=1.06\mathrm{W}$.

Figure 2

Semiangle ${\theta }_c$ of the cone for Winsor toluene system S1b as a function of the power $P$ and the beam waist ${\omega }_0$ of the laser. ${\omega }_0(0)$ represents the laser beam waist extrapolated at zero power (see the Supplemental Material [24]). The dashline indicates the total reflection value $\pi /2-{\alpha }_{\mathrm{TR}}$. Inset: Cone semiangle rescaled by $\sqrt{{\omega }_0}$ versus laser power $P$ in log-log scale.

Figure 3

(a) Variation of the $f$ function with the incident angle ${\alpha }_i$ for different relative index contrasts $\delta =2.\mathrm{\Delta }n/(n_1+n_2)$. (b) Variation of the normalized cone angle as a function of the normalized radial position $r/{\omega }_0$ for various liquid systems. The solid line indicates the theoretical prediction $\mathrm{\Phi }(·)$ [see Eq. (6)]. (c) Comparison between a theoretical cone deformation (red line) and an experimental deformation for microemulsion system S3b for $P=0.5\mathrm{W}$ and ${\omega }_0=5.8\mu \mathrm{m}$. (d) Cone angle as a function of $\gamma /n_2$ for various systems and for a given ratio ${\omega }_0/P=4.57\mu \mathrm{m}/\mathrm{W}$. The line indicates the theoretical prediction [Eq. (7)].

Figure 4

Experimental cone angles versus the characteristic cone angle $\sqrt{c{\omega }_0\gamma /P{n}_2}$ for all the investigated experimental systems. The best fit is ${\theta }_c=1.86(c{\omega }_0\gamma /P{n}_2{)}^{0.5}$ whereas the dashed line refers to Eq. (7). Inset: same plot in linear scales.

Figure 5

(a) Theoretical minimal angle of the deformation without gravity effects for various refractive index constrast. (b) Rescaled cone angle ${\theta }^{\mathrm{num}}/{\theta }_c^{*}$ numerically obtained compared with the perturbative result $\theta ={\theta }_c^{*}(1+\nu \chi )$ as a function of the $\chi =Bo/{\theta }_c^{*}$ parameter for $P/P_c=1.35$.