Thermal diffusion by Brownian-motion-induced fluid stress

The Ludwig-Soret effect, the migration of a species due to a temperature gradient, has been extensively studied without a complete picture of its cause emerging. Here we investigate the dynamics of DNA and spherical particles subjected to a thermal gradient using a combination of Brownian dynamics and the lattice Boltzmann method. We observe that the DNA molecules will migrate to colder regions of the channel, an observation also made in experiments. In fact, the thermal diffusion coefficient found agrees quantitatively with the experimentally measured value. We also observe that the thermal diffusion coefficient decreases as the radius of the studied spherical particles increases. Furthermore, we observe that the thermal-fluctuation–fluid-momentum-flux coupling induces a gradient in the stress which leads to thermal migration in both systems.

Figure 1

Number fraction $n∕n_{total}$ where $n$ is the number of beads whose center of mass is between $y-0.25$ and $y+0.25$ and $n_{total}$ is the total number of beads, as a function of height for $\lambda$-DNA subjected to different temperature gradients. Data are averaged over the final 40 time steps of five simulations started from different random initial conditions. Shown is the average of the two mirror-image halves of the periodic system.

Figure 2

Number fraction $n∕n_{total}$ where $n$ is the number of beads whose center of mass is between $y-0.25$ and $y+0.25$ and $n_{total}$ is the total number of beads, as a function of height at different times for $\lambda$-DNA with $\mathrm{\Delta }T=4\mathrm{K}$. Data are averaged over ten time steps of five simulations started from different random initial conditions. Shown is the average of the two mirror-image halves of the periodic system.

Figure 3

Stress in the $y$ direction across the channel for $\lambda$-DNA. Data are averaged over the final 40 time steps of five simulations started from different random initial conditions. Shown is the average of the two mirror-image halves of the periodic system.

Figure 4

Number fraction $n∕n_{total}$ where $n$ is the number of beads whose center of mass is between $y-0.25$ and $y+0.25$ and $n_{total}$ is the total number of beads, as a function of height for spherical particles of different diameter with $\mathrm{\Delta }T=4\mathrm{K}$. Data are averaged over the final 40 time steps of five simulations started from different random initial conditions. Shown is the average of the two mirror-image halves of the periodic system.

Figure 5

Stress in the $y$ direction across the channel for spherical particles of different diameter. Data are averaged over the final 40 time steps of five simulations started from different random initial conditions. Shown is the average of the two mirror-image halves of the periodic system.