It is usually believed that wall slip contributes small effects to macroscopic flow characteristics. Here we demonstrate that this is not the case for the thermocapillary migration of a long bubble in a slippery tube. We show that a fraction of the wall slip, with the slip length λ much smaller than the tube radius R, can make the bubble migrate much faster than without wall slip. This speedup effect occurs in the strongslip regime where the film thickness b is smaller than λ when the Marangoni number S=τTR=σ0 .(1) is below the critical value S* ∼ .( λ=R)1/2, where τT is the driving thermal stress and σ0 is the surface tension. The resulting bubble migration speed is found to be Ub ∼(σ0/μ)S3 (λ/R) which can be more than a hundred times faster than the no-slip result Ub ∼ (σ/Mu;)S5 (Wilson, J. Eng. Math., vol. 29, 1995, pp. 205-217; Mazouchi & Homsy, Phys. Fluids, vol. 12, 2000, pp. 542-549), with μ being the fluid viscosity. The change from the fifth power law to the cubic one also indicates a transition from the no-slip state to the strong-slip state, albeit the film thickness always scales as b ∼ RS 2. The formal lubrication analysis and numerical results confirm the above findings. Our results in different slip regimes are shown to be equivalent to those for the Bretherton problem (Liao, Li & Wei, Phys. Rev. Lett., vol. 111, 2013, 136001). Extension to polygonal tubes and connection to experiments are also made. It is found that the slight discrepancy between experiment (Lajeunesse & Homsy, Phys. Fluids, vol. 15, 2003, pp. 308-314) and theory (Mazouchi & Homsy, Phys. Fluids, vol. 13, 2001, pp. 1594-1600) can be interpreted by including wall slip effects.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering