Thermocapillary migration of an odd viscous droplet on a uniformly heated surface: A lattice Boltzmann study

TL;DR

This study investigates the spontaneous thermocapillary migration of an odd viscous droplet on a uniformly heated surface using a phase-field lattice Boltzmann framework that couples Allen–Cahn phase-field dynamics with Navier–Stokes flow including an antisymmetric (odd) viscous stress. The authors show that the odd viscosity converts tangential Marangoni stresses into asymmetric normal stresses at the interface, driving directional motion with the direction set by the sign of $\eta_o$ and the speed increasing with the contact angle and $|\eta_o|$ while decreasing with viscosity ratio. On inclined substrates, the odd-viscosity–induced force can oppose or aid gravity, yielding uphill migration in some cases and showcasing a tunable actuation mechanism. The work advances understanding of thermocapillary transport in nonconventional fluids and suggests design principles for microfluidic devices leveraging odd viscosity. Potential extensions to three-dimensional geometries are highlighted for future exploration.

Abstract

In this study, the thermocapillary actuation behavior of an odd viscous droplet on a uniformly heated surface is numerically investigated using a phase-field-based lattice Boltzmann method. The numerical results reveal that unlike a conventional viscous droplet that remains stationary on a uniformly heated surface, the presence of odd viscosity converts tangential Marangoni stresses into asymmetric normal stresses along the interface, thereby inducing spontaneous droplet motion. Specifically, when the odd viscosity coefficient is positive (negative), the droplet migrates toward the right (left). Additionally, due to the enhanced interfacial temperature gradient, the droplet migration velocity consistently increases with the contact angle. Further, it is observed that the droplet's migration velocity decreases with an increasing viscosity ratio between the surrounding fluid and the droplet. Finally, as the droplet is placed on an inclined surface, its migration direction and velocity are governed by the interaction between gravity and the odd viscosity-induced force, and in certain cases, the droplet can even climb upward against gravity.

Figures (15)

• Figure 1: Schematic of a droplet on a uniformly heated inclined solid substrate, where the bottom wall is maintained at a constant temperature $T_H$, the top wall is maintained at a constant temperature $T_L$, and the side walls are adiabatic.
• Figure 2: The flow field (the left plane) and the temperature field (the right plane) surrounding the moving droplet at the contact angle $\theta=120^\circ$, (a) the numerical results reported by Liu et al.Liu JCP2015, (b) the present data, in which the red lines are $\phi = 0$, the blue lines with arrows are the velocity vectors, and the black lines with arrows are the streamlines.
• Figure 3: Time evolution of the $x$-coordinate of droplet centroid at various contact angles.
• Figure 4: Snapshots of the displacement process for different odd viscosity coefficients: (a) $\eta =-3.0$, (b) $\eta = 0$, (c) $\eta = 3.0$. In each row, images from left to right correspond to dimensionless times $t^*=0, 4.73, 9.47$, respectively.
• Figure 5: The relationship between centroid position ($x_p$) (normalized by the initial position) and the dimensionless time ($t^*$) at different odd viscosity coefficients.