Closed-Form Expressions for Contact Angle Hysteresis: Capillary Bridges between Parallel Platens
Abstract
:1. Introduction
2. Theory
2.1. The Toroidal Approximation
2.2. Contact Angle Hysteresis
- 1)
- When the platen moves downwards and the gap decreases, initially, the contact line remains stationary until the contact angle equals the advancing contact angle (see Figure 5a). This is known as pinning.
- 2)
- If the gap decreases further, the contact angle remains at the advancing angle and the contact line expands (see Figure 5b). This is known as slipping.
- 3)
- When the gap increases, the contact angle first decreases while the contact line remains constant (pins—see Figure 5c).
- 4)
- When the contact angle reaches the receding angle, provided the gap is still increasing, it will remain at that angle while the contact line declines (slips—see Figure 5d). And so on.
- State initial conditions
- We need to know four things: gap, initial contact angle, contact line radius, and volume.
- Gap is a design/experimental parameter and is known, equilibrium (and dynamic for later) contact angle is a fluid property and can be found easily beforehand.
- The volume or the contact line radius needs to be measured. The other can be calculated using Equations (6) or (8), respectively. However, they only need to be measured once. The values can then be used throughout the calculation.
- Change the gap
- It is assumed that subsequent motion will be continuous and no relaxation towards equilibrium conditions is observed.
- The change in geometry depends on the direction the upper platen is moved.
- If it is moving upwards, initially, the receding contact angle will be lower than the equilibrium contact angle. Here, the contact line radius (given) will stay constant until the instantaneous contact angle (given by Equation (16)) equals the receding contact angle. If the motion continues to increase, the contact angle stays constant and the contact line radius changes according to Equation (8).
- Change the direction
- At this point, the contact angle equals the receding contact angle and the contact line radius is known. Decreasing the gap, the contact line radius will remain constant and the contact angle will increase, as in Equation (16), until it reaches the advancing contact angle. Decreasing the gap further will mean the contact angle stays at the advancing angle and the contact line radius changes.
2.3. Linearization and Applicability to Squeeze Flow Rheometry
3. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
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Bowen, J.; Cheneler, D. Closed-Form Expressions for Contact Angle Hysteresis: Capillary Bridges between Parallel Platens. Colloids Interfaces 2020, 4, 13. https://doi.org/10.3390/colloids4010013
Bowen J, Cheneler D. Closed-Form Expressions for Contact Angle Hysteresis: Capillary Bridges between Parallel Platens. Colloids and Interfaces. 2020; 4(1):13. https://doi.org/10.3390/colloids4010013
Chicago/Turabian StyleBowen, James, and David Cheneler. 2020. "Closed-Form Expressions for Contact Angle Hysteresis: Capillary Bridges between Parallel Platens" Colloids and Interfaces 4, no. 1: 13. https://doi.org/10.3390/colloids4010013
APA StyleBowen, J., & Cheneler, D. (2020). Closed-Form Expressions for Contact Angle Hysteresis: Capillary Bridges between Parallel Platens. Colloids and Interfaces, 4(1), 13. https://doi.org/10.3390/colloids4010013