Light generated bubble for microparticle propulsion

Light activated motion of micron-sized particles with effective forces in the range of micro-Newtons is hereby proposed and demonstrated. Our investigation shows that this exceptional amount of force results from accumulation of light-generated heat by a micron-sized particle that translates into motion due to a phase transition in the nearby water. High-speed imagery indicates the role of bubble expansion and later collapse in this event. Comparing observations with known models reveals a dynamic behavior controlled by polytropic trapped vapor and the inertia of the surrounding liquid. The potential of the proposed approach is demonstrated by realization of disordered optical media with binary light-activated switching from opacity to high transparency.

Estimating the equivalent force Fig. 1 shows OMF event captured with a regular camera at a rate of 25 frames per second. Knowing the distance the microsphere covered and having an upper bound for the duration of that this translation occurred, a lower bound on the force is obtained from ݉Δ‫ݔ‬ Δ‫ݐ‬ ଶ ⁄ , where ∆x and ∆t and are distance and duration of motion and ݉ ൌ ሺ4ߨ 3 ⁄ ሻߩ‫ݎ‬ ଷ is the mass of the microsphere. Also, the density and radius of the microsphere are given by ρ and r, respectively. In our case r = 20 µm microsphere made almost exclusively from glass, so ρ = 2500 kg/m 3 . From Fig. 1 the beam translated roughly a distance of 400 µm at time no longer than 0.04 s and therefore the lower bound of the force in this case is 21 pN.
Bubble radius and microsphere location expands, collapse, and later vanishes. The yellow circle with the respective cross at its center shows the location of the microsphere at different instances. Finally, the bubble is highlighted with a white circle whose center is indicated by the white cross. It is interesting to note that while the microsphere translates a significantly during the process, the bubble moves only slightly in the opposite direction.
A Larger scope of the microsphere's motion Measurements of the microspheres location after the bubble fully condensates were made with the high speed camera at 500,000 frames per second and shown in Fig.S3. The blue dots in Fig.S3 show location of the microsphere as a function of time, these are also the measurements that gave rise to the inset in Fig. 3. This behavior corresponds to movement of an object in a liquid, with friction force proportional to the object velocity: where ‫ݔ‬ and ‫ݒ‬ are the location and velocity of the microsphere and the double overdot represent the time second derivative of the microspheres location. ܾ ൌ 6ߨߟܽ is the drag force coefficient of a sphere in accordance to Stokes law, where ߟ is viscosity of water and ܽ is the radius of the microsphere. The solution of Eq. (S1) is: where ‫ݒ‬ is the initial velocity (from the moment the bubble vanished), ݉ is the mass and ‫ݐ‬ is the time.
The red line in Fig.S3 shows the trend of Eq. (S1) with ‫ݒ‬ = 0.6 ݉ ‫ݏ‬ ⁄ and room temperature viscosity of . The small disagreement the calculated motion from the measured one could result from the confinement of the two cover slides as well as from a certain amount of spin that the microsphere obtains.

Statistics of bubble expansion
Variation between individual events makes it hard to facilitate a useful comparison of the measured results with the Rayleigh-Plesset model of the dynamics behavior of a spherical bubble. Variations in this case arise from the explosive nature of the phase transition and its sensitivity to imperfection on the surface of the microsphere and the surrounding water. Since our setup would not allow us to repeatedly excite a given microsphere at the exact same location time after time, we have reputedly excited a microsphere and from the dispersion of outcomes we isolated a representative subset that presumably represents similar events. Accordingly, we have chosen two parameters for quantification of a possible outcomes; the maximal radius of the bubble and the duration from initiation until it dissolves back to liquid water. A histogram of 53 OMF events of the same microsphere that are ordered along these two parameters is shown in Fig.S4. The diagonal arrangement indicates correlation between these two merits of the bubble, which is after all expected. Also, the results are approaching a normal 5 distribution that is centered at maximal radius between 96 to 98 µm and duration of 26 to 28 µs. We therefore chose this most probable outcome as our representative subset of events for the analysisthis is the 7 bubble set whose mean radius and deviation are portrayed in Fig. 4.

Duration of heating period and simulation of temperature distribution
Measurements of the heating time were made by capturing a sequence of frames using Ximea MQ003MG-CM camera pushed to 2398 frames per second while heating the microsphere with 140 mW laser until motion was detected. The laser was triggered with a mechanical shutter SHB05 from Thorlabs, USA. These measurements indicated a typical heating time of 3 ms. This heating period is also confirmed from a finite element simulation (COMSOL) of the temperature buildup with time of laser heated microsphere. Simulation parameters were chosen to reproduce as much as possible the realistic conditions: 50 µm glass microsphere covered by 200 nm silver were considered, a 405 nm laser at a power 100 mW with beam waist of 20 µm. A cross section of the temperature distribution on the microsphere and its surroundings after 3ms of heating is shown in Fig.S5. The beam was focused 10 µm to the right of the south pole of the microsphere. Few things are notable in this simulation: First, the water close to the heat source had reached the critical temperature of 650 K by these 3 ms of heatingin agreement with the measurement of the heating period described above. Secondly, simulation shows 6 that the heat is not evenly distributed around the microsphere by that time, in agreement with observation that the bubble always occur where the laser was heating the microsphere.

The pressure difference
The expected pressure difference was obtained from the bubble dynamic calculation described in the manuscript, the result is given in Fig.S6. Figure  7 source, since the microsphere is already shifted from the beam, condensation kicks-in and the bubble dissolves back to liquid.