Study on stretching liquid bridges with symmetric and asymmetric surface wettability

The breakup process of stretching liquid bridges between plates is crucial for liquid transfer in printing technology. In the present study, the liquid bridges stretched by two parallel flat plates were simulated by using many-body dissipative particle dynamics, in which the competition between slip velocity of contact lines and thinning velocity of liquid bridges was focused on, and it shows that this competition plays a key role in determining the breakup behaviors of liquid bridges and the liquid transfer ratio between the two plates. The influences of surface wettability, plate stretching velocity, and liquid Oh number on the breakup process were discussed. The simulated results show that both poorer surface wettability and larger stretching velocity help to increase slip velocity and enable the liquid bridge to slip off the surfaces. For the case with hydrophilic surface and small plate stretching velocity, thinning velocity dominates the breakup process and the pinch-off occurs approximately at the middle part of the liquid bridge. For cases with asymmetric surface wettability, the liquid transfer ratio depends only on the asymmetry of surface wettability for smaller plate stretching velocity and larger Oh number. However, this phenomenon no longer occurs if the stretching velocity is increasing, where slip of the contact line becomes important. The shift of minimal radius for liquid bridges with asymmetric stretching velocities is also investigated, and it was found that the shift moment is only related to the surface wettability, regardless of the plate stretching velocity. Moreover, it shows that the formation of satellite drops depends on the sequential order of the appearance of the liquid bridge slipping off the surface and the breakup of the filament. The present work provides some insight to better understand the rupture mechanism of stretching liquid bridges, and may help to improve printing technology.

Figure 1

The relation between attractive coefficient A and Oh number with repulsive coefficient B fixed at 25.

Figure 2

Schematic diagram of a stretching liquid bridge between two flat plates.

Figure 3

The comparison of liquid bridge profiles between theoretical predictions and simulation results. (a) hydrophilic surface with $\theta ={30}^{\circ }$. (b) Hydrophobic surface with $\theta ={100}^{\circ }$.

Figure 4

The comparison of liquid bridge profiles with asymmetric wettability, where ${\theta }_{\mathrm{upper}}={30}^{\circ }$ and ${\theta }_{\mathrm{lower}}={55}^{\circ }$.

Figure 5

Variation of the minimum radius of the thread versus time with the power law of the three flows, i.e., potential flow (2/3), inertial-viscous flow (1.0), and stochastic flow (0.418).

Figure 6

Minimum radius versus the distance between the plates with different Re.

Figure 7

Variation of minimum radius with H for different surface wettability.

Figure 8

$Z_{\mathrm{r},\min }$ versus breakup time with different $\theta$ and $\mathrm{Re}=1.22$.

Figure 9

The variation of the position of the rupture point with Re for different plate wettabilities.

Figure 10

The variation of $Z_{\mathrm{r},\min }$ with time for $\mathrm{Re}=1.22$ and 1.46.

Figure 11

The radius Г of the contact line varying with the liquid bridge length.

Figure 12

The evolution of the slip velocity of the contact line and the thinning velocity of the midpoint with $\mathrm{Re}=1.22$ and 1.46.

Figure 13

The average velocity of slipping and thinning varying with Re on the surface of $\theta ={70}^{\circ }$.

Figure 14

The average velocities of slipping and thinning varying with $\theta$ for $\mathrm{Re}=1.22$.

Figure 15

The average velocities of slipping and thinning varying with Re on the surface of $\theta ={70}^{\circ }$ for $\mathrm{Oh}=0.9$.

Figure 16

The contour of the critical liquid bridge length L for different stretching velocities and surface wettability. (a) $\mathrm{Oh}=0.3$; (b) $\mathrm{Oh}=0.9$.

Figure 17

The radius Г of the contact line on the upper plate varying with the liquid bridge length.

Figure 18

The contour of the critical liquid bridge length on asymmetric wettability surfaces for different Re. (a) $\mathrm{Re}=0.49$; (b) $\mathrm{Re}=1.95$.

Figure 19

(a) The liquid transfer $\mathrm{\Phi }$ varying with different surface wettability on the upper plate for $\mathrm{Re}=1.22$. (b) $\mathrm{\Phi }$ varying with Re for the contact angle on the upper plate, $\theta ={70}^{\circ }$.

Figure 20

The contour of $\mathrm{\Phi }$ with different surface wettability and Re under asymmetric surface wettability. (a) $\mathrm{Oh}=0.3$; (b) $\mathrm{Oh}=0.9$.

Figure 21

The evolution of the position of the contact lines on the upper surface (solid lines) and on the lower surface (dashed lines) with different Re for $\theta ={55}^{\circ }$.

Figure 22

The variation of the position of minimum radius versus breakup time. (a) The influences of Re for $\theta ={55}^{\circ }$; (b) the influences of surface wettability for $\mathrm{Re}=2.44$.

Figure 23

The contours of the critical liquid bridge length for asymmetric stretching velocities. (a) $\mathrm{Oh}=0.3$; (b) $\mathrm{Oh}=0.9$. (c) The snapshots of stretching liquid bridges in regions A and B.

Figure 24

The contour of $\mathrm{\Phi }$ for different surface wettability and Re with asymmetric stretching velocities. (a) $\mathrm{Oh}=0.3$; (b) $\mathrm{Oh}=0.9$.