Pis’ma v ZhETF, vol. 110, iss. 11, pp. 757 - 758

Thermophoresis-assisted micro-scale magnus effect in optical traps

M. N. Romodina, N. M. Shchelkunov, E. V. Lyubin, A. A. Fedyanin¹⁾

Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia

Submitted 2 October 2019

Resubmitted 1 November 2019

Accepted 6 November 2019

DOI: 10.1134/S0370274X19230097

Here we report on the experimental evidence of the

transversal force on the laser light power inside the trap

lift force acting on the optically trapped magnetic mi-

is shown in Fig. 1a. As the laser power increases the force

croparticle rotating in a liquid flow. The lift force grows

with the increase of local microparticle temperature,

which is controlled by the trapping laser power. The

correlation between the lift force and the heating of the

microparticle in an optical trap indicates that the ob-

served effect appears due to the thermophoretic forces

that act on the heated microparticle rotated in the liquid

flow. Using numerical simulations we have shown that

the heated microparticle rotating in the flow creates a

temperature gradient around itself. The appearance of

the temperature gradient can be explained by the dis-

placement of the particle from the center of the optical

trap during particle motion. The microparticle under

the thermophoretic force moves in the direction opposite

to the temperature gradient; therefore the force has a

Fig. 1. (Color online) (a) - The thermophoresis-assisted

component perpendicular to the flow. This is what con-

Magnus force dependence on the laser power in the optical

stitutes the thermophoresis-assisted micro-scale Magnus

trap. The oscillation frequency f = 9 Hz, the amplitude

effect.

of the trap oscillation A = 200 nm, and the microparticle

In our experiments, the magnetic microparticle ro-

rotation rate Ω = 50 Hz. (b) - The effective temperature

tated at a rate up to 100 Hz. The trap position oscillated

of the microparticle’s surface as a function of the trapping

with an amplitude of up to 500 nm along the Ox-axis,

laser power

with a frequency range of 2 to 20 Hz, causing linear par-

ticle motion with velocity that did not exceed 60 µm/s.

grows significantly, allowing one to suggest that heat-

For technical details of the experimental setup see [1, 2].

ing plays an important role in the effect. The effective

The Reynolds number is

temperature of the liquid around the trapped magnetic

microparticle grows linearly along with the light power

Re = ρUa/η,

(1)

inside the trap (see Fig. 1b). The studied effect could

arise from the local non-uniform heating and the ap-

where a is the radius of a particle, ρ is the density,

pearance of temperature difference on the opposite sides

and η is the viscosity of the fluid. For translational mo-

of a trapped microparticle. The observed high values of

tion U is the particle velocity, and for rotational motion

the Magnus force can account for thermophoresis, also

U = 2πΩa, where Ω is the frequency of particle rota-

called thermal diffusion, that moves microscopic parti-

tion. Thereby, in our study, the translational Reynolds

cles along temperature gradients [5-7].

number is 10^-4 and the rotational Reynolds number is

Thus, the thermophoresis-assisted Magnus force is

10^-3 orders of magnitude. This is the case of ultra-low

caused by temperature difference on opposite sides of

Reynolds numbers [3, 4].

the microparticle. The difference appears due to the dis-

The absorption of laser radiation leads to heating

placement of the absorbing microparticle from the cen-

of the trapped microparticles. The dependence of the

ter of the optical trap during its motion in the liquid

¹⁾e-mail: fedyanin@nanolab.phys.msu.ru

flow. The temperature distribution around the optically

Письма в ЖЭТФ том 110 вып. 11 - 12

2019

757

758

M. N. Romodina, N. M. Shchelkunov, E. V. Lyubin, A. A. Fedyanin

trapped microparticle rotating in the liquid flow was

The coupling coefficient S_M between the tempera-

obtained by numerical solutions of the heat equation,

ture distribution and the force acting on the particle

solved using the finite element method. To illustrate the

can be estimated using the closest analogue - the equa-

key processes of the studied phenomena, we calculated

tion for the thermophoretic force in the case of a uniform

the temperature distribution. For the particle rotation

temperature gradient:

rate of 50 Hz and the liquid flow speed of 25 µm/s, the

F_thermo = -k_BTS_T ∇T,

(2)

temperature difference is ΔT = 0.12◦C, which corre-

where k_B is the Boltzmann constant, T is the tempera-

sponds to the gradient of 0.04^◦C/µm.

ture of the liquid, and S_T is the is the Soret coefficient.

The calculated dependence of ΔT on the microparti-

We estimated the value of S_M from Eq. (2), substi-

cle’s rotation rate is shown in Fig. 2a. The dependence of

tuting it with S_T and using the experimental data for

F_thermo = 25 fN (see Fig.1a), calculated the value of

∇T = 0.04^◦C/µm (see Fig. 2b) and obtained the value

of S_M ≈ 150 K^-1. While in the case with a uniform

gradient, the coefficient S_T ≈ 18 K^-1 for a similar sys-

tem [8].

There is no generally accepted theoretical framework

for the Soret coefficient [9], but it is known that S_T

strongly depends on the particle-solvent interface, and

therefore has a highly specific surface chemistry, such as

the degree of surface ionization, or the amount of resid-

ual surfactant used in emulsion. Moreover, it strongly

depends on temperature [8]. In the case scrutinized here,

the temperature distribution on the surface of the parti-

cle is strongly non-uniform, and the temperature inside

the particle is much higher than it is on the surface,

which can significantly affect the charge of the particle

and the degree of surface ionization.

This work was supported by the Russian Ministry

of Education and Science (contract #14.W03.31.0008),

the Russian Science Foundation (grant 15-02-00065, ex-

periment, grant 18-72-00247, calculations), the Russian

Foundation for Basic Research (grant 18-32-20217), and

partially supported by MSU Quantum Technology Cen-

ter.

Full text of the paper is published in JETP Letters

journal. DOI: 10.1134/S002136401923005X

1. M. N. Romodina, E. V. Lyubin, and A. A. Fedyanin, Sci.

Rep. 6, 21212 (2016).

Fig. 2. (Color online) The temperature difference between

2. E. V. Lyubin, M. D. Khokhlova, M. N. Skryabina, and

the left and the right sides of the particle, obtained using

numerical simulation: (a) is the dependence on the fre-

A. A. Fedyanin, J. Biomed. Opt. 17, 101510 (2012).

quency of microparticle rotation, inset is the case of high

3. S. I. Rubinow and J. B. Keller, J. Fluid Mech. 11, 447

values of rotation frequency; (b) - is the dependence on

(1961).

laser power

4. Yu. Tsuji, Yo. Morikawa, and O. Mizuno, J. Fluids

Engin. 107, 484 (1985).

ΔT on the microparticle rotation rate grew linearly from

5. T. L. Bergman and F. P. Incropera, Introduction to heat

transfer, John Wiley & Sons, Hoboken, New Jersey

0 to 10³ Hz, which includes the experimentally studied

(2011).

values of microparticle rotation rates. At the frequen-

6. R. Piazza, Soft Matter 4, 1740 (2008).

cies above 3·10⁴ Hz, ΔT decreases because the speed of

7. K. I. Morozov, JETP 88, 944 (1999).

microparticle rotation becomes higher than the speed

8. M. Braibanti, D. Vigolo, and R. Piazza, Phys. Rev. Lett.

of heat transfer to liquid. The dependence on the laser

100, 108303 (2008).

power also grew linearly (Fig. 2b) in accordance with the

9. A. Wurger, C. R. Mecanique 341, 438 (2013).

data for the experimentally measured force (Fig. 1a).

Письма в ЖЭТФ том 110 вып. 11 - 12

2019