Temperature measurements and heating effects

In this section I will briefly discuss heating effects in the fibre trap and elucidate different temperature measurement methods.

The local trap temperature in the experiment can be probed just like the viscosity via the Brownian motion of the trapped sphere by determining the diffusion coefficientDif f, from [81, 82] and from the Stokes-Einstein relation [83, 84]: TDif f = Dif f ∗6πηrsphere kb ← hz2i= P n∆z2 n = 2Dif f∆t (5.14)

hz2i = Mean square dis- placement

n = number of discrete data points

The temperature calculation presented here evolves from the mean square displacement (MSD) of a particle that is bombarded by fluid molecules, in this case for one dimension along the z-axis. Dif f indicates the Brownian thermal induced diffusivity or diffusion coefficient [82]. In the experiment no agreement was achieved between the approximated trap temperature of 273K and the determined one TDif f = 1417K.

Here I suspect that the sampling of the spheres motion via the video analysis is not accurate enough to produce a meaningful result. For this reason the trap temperature has been either approximated by measuring with a ther- mocouple or via measurements with an infrared (IR) camera for the heated sample cell.

To give the sample medium a set temperature, heating elements were incor- porated into the trap, this enhances the Brownian motion and decreases the integration time due to the enhanced Brownian movement of the spheres. The temperature9 _{was measured with an IR camera as shown in figure 5.10.}

Figure 5.10: Temperature gradient in the sample area. Here the heated top coverslip is imaged via an IR camera and shown in an false colour plot. The two fibers (F1 and F2) are shown in the picture to elucidate the geometry. The actual sample cell made up by the v-groove 10×5mm spans over the marked area in the picture. A gradient of≈5◦Cis measured over the sample area. However no convective currents were observed in the analysed data. The images shows a homogeneous temperature of≈62◦_C

at the sample area.

With this method the temperature was determined prior to every experimen- tal realisation, where the sample was additionally heated.

Heating of the sample cell also changes the refractive index of the host medium; here a correction of nh = n20

◦

h − 0.013 for a temperature from

20 to 50◦C via the formulanh(T) =n20 ◦

h −0.00045(T −20) where T is in ◦_C

from [85] is used for the theoretical simulations.

5.2. THEORETICAL MODEL

Additional heating in the sample cell can lead to convective roles in the host medium, which can induce perturbations to the Brownian motion trajectory of the trapped sphere. As the temperature shown in figure 5.10 is homoge- neous over the trapping area perturbations from heat convection are unlikely. Such non Brownian perturbations can easily be spotted as they lead to slant- ing of the Gaussian distribution of the sampled position data, especially in the direction of the flow channel parallel to the two fibre ends (along the x-axis). However these effects were not observed in the experimental data (see figure 5.7 (right - above) where a Gaussian shape is maintained). Convective rolls can also be induced due to local heating from the optical field particularly when the sample area is at room temperature. To inves- tigate the absorption and subsequent heating of the laser radiation and the Koehler illumination a drop of DI water was placed on a coverslip. After 30 minutes the temperature was measured with the IR camera (with a sensitiv- ity of ±0.1◦ C) see figure 5.11.

Figure 5.11: Absorption heating of a drop of DI water by 110mW of 1070nmlight emerging from a single mode fibre. Left: Picture shows the direction of the single mode fibre, the drop of DI-water is shown in the center of the picture in black at a temperature of 17.4◦C. Right: after 30 minutes the water at the vicinity of the fibre has reached a temperature of about 19◦C.

100mW of laser power launched from one single mode fibre into the DI wa- ter host medium changed the temperature by ≈ 1.6◦C = 1.6K. In units of

kbT this is only 1.6×1.38×10−23J/K10. For the subsequent measurements

this heating effect was treated as minor and not implied in the calculations of the trap stiffness. In some experiments D2O was used with a even lower

absorption coefficient than water.

In addition, no heating effects were observed from the Koehler illumination of the setup, here the water droplet showed no temperature change after 30

10_Wherek

minutes of illumination under experimental conditions (without laser). Heating effects of the laser can have effects on the sample medium viscos- ity and on the measured trap stiffness and were found by [80] to be of the order of 2%11 _{at 100mW for a single beam gradient tweezers with a high}

NA (NA=1.3) for spheres in water. Contrary to my experiment, the heating effects in water are of the order of ≈ 0.8K and differ by a factor of 2 to my findings for two diverging beams with NA=0.14. My results are closer to the findings by [86] of ≈1.0−1.5K (here for all experiments wavelength and laser power are comparable). Still for the lower NA used in in the fibre trap experiment one would expect a lower heating effect as those reported by [80, 86]. Due to the different geometry dual beam versus single beam trap a direct comparison seems not feasible at this stage.

In addition [80] found that the absorption effects of the spheres are minor, so the absorption of the host medium (water) is prominent.

In conclusion more accurate measurements need to be undertaken to draw quantitative conclusions from the experiment. At the present stage the exact temperature can only be approximated and used as a rough verification of the experimentally determined viscosity, via comparison to the temperature given in figure 5.9.