5.3 Wetting Phenomena and Contact Angles
5.3 Wetting Phenomena and Chapter 5: Solid-Liquid-Vapor Phenomena Contact Angles and Interfacial Heat and Mass Transfer 5.3 Wetting Phenomena and Contact Angles 5.3.1 Equilibrium and Apparent Contact Angles Contact angle on a smooth, insoluble, homogenous surface σ− σ cosθ = sv sl (5.38) σ lv θ For a rough surface, the contact angle rough is related to the contact angle on a smooth surface θ by θ = γ θ cos rough cos (5.39)
Where γ is always greater than 1
Transport Phenomena in Multiphase Systems by A. Faghri & Y. Zhang 1 5.3 Wetting Phenomena and Chapter 5: Solid-Liquid-Vapor Phenomena Contact Angles and Interfacial Heat and Mass Transfer Table 5.1 Minimum wetting contact angle (The upper and lower values are for advancing and receding liquid front respectively) Acetone Water Ethanol R-113 Aluminum 73/34 Beryllium 25/11 63/7 0/0 Brass 82/35 18/8 Copper 84/33 15/7 Nickel 16/7 79/34 16/7 Silver 63/38 14/7 Steel 14/6 72/40 19/8 16/5 Titanium 73/40 18/8
Transport Phenomena in Multiphase Systems by A. Faghri & Y. Zhang 2 5.3 Wetting Phenomena and Chapter 5: Solid-Liquid-Vapor Phenomena Contact Angles and Interfacial Heat and Mass Transfer 5.3.2 Wettability and Adsorption
Depending on the contact angle, liquids can be classified as nonwetting, partially wetting, or completely wetting. When a small amount of liquid is brought into contact with an initially-dry solid surface, the liquid behaves in one of two ways: (1) if the liquid does not wet the solid it may break up into small droplets, or (2) if the liquid wets the solid it may spread over the solid surface and form a thin liquid film.
Transport Phenomena in Multiphase Systems by A. Faghri & Y. Zhang 3 5.3 Wetting Phenomena and Chapter 5: Solid-Liquid-Vapor Phenomena Contact Angles and Interfacial Heat and Mass Transfer
Figure 5.7 Drop of liquid on a planar surface.
Transport Phenomena in Multiphase Systems by A. Faghri & Y. Zhang 4 5.3 Wetting Phenomena and Chapter 5: Solid-Liquid-Vapor Phenomena Contact Angles and Interfacial Heat and Mass Transfer Wettability can be attributed to a strong intermolecular attractive force near the interface between the solid and liquid. The thermodynamic definition of surface tension, eq. (2.144), establishes that there is a significant decrease in the surface free energy per unit area in a wetting liquid. Spreading of a liquid on a solid surface can be described by the spreading coefficient Sp, defined as = σ − σ − σ Sps sv v s (5.40) Substituting eq. (5.38) into (5.40) = −σ − θ Spls l v (1 cos ) (5.41) For a partially-wetting liquid ( 0 o ≤ θ ≤ 90 o ), cosθ ≤ 1
Transport Phenomena in Multiphase Systems by A. Faghri & Y. Zhang 5 5.3 Wetting Phenomena and Chapter 5: Solid-Liquid-Vapor Phenomena Contact Angles and Interfacial Heat and Mass Transfer
Figure 5.8 Schematic of apparent contact angle θ
Transport Phenomena in Multiphase Systems by A. Faghri & Y. Zhang 6 5.3 Wetting Phenomena and Chapter 5: Solid-Liquid-Vapor Phenomena Contact Angles and Interfacial Heat and Mass Transfer
Surface pressure of the absorbed material on the solid surface p =σ − σ s sv sv, a (5.42) Young’s equation can be rewritten σ θ= σ − − σ lvcos ( svp s ) s l (5.43)
For tubes with a very small radii of curvature, RI and R are the same II r RR= = (5.44) I II cosθ Substituting eq. (5.44) into eq. (5.10) 2σ (p− p ) = p = cosθ (5.45) vl c cap, c r
Transport Phenomena in Multiphase Systems by A. Faghri & Y. Zhang 7 5.3 Wetting Phenomena and Chapter 5: Solid-Liquid-Vapor Phenomena Contact Angles and Interfacial Heat and Mass Transfer
Figure 5.9 Capillary phenomenon in an open tube
Transport Phenomena in Multiphase Systems by A. Faghri & Y. Zhang 8 5.3 Wetting Phenomena and Chapter 5: Solid-Liquid-Vapor Phenomena Contact Angles and Interfacial Heat and Mass Transfer The pressure at the flat surface a is related to vapor pressure by = + ρ pa p v v gH (5.46) The pressure at point b inside the tube must be equal to that at point a. = +ρ − = pb p vl gH p cap, c p a (5.47) Combining eqs. (5.45-5.47) 2σ cosθ (5.48) = (ρ − ρ )gH r v
Transport Phenomena in Multiphase Systems by A. Faghri & Y. Zhang 9 5.3 Wetting Phenomena and Chapter 5: Solid-Liquid-Vapor Phenomena Contact Angles and Interfacial Heat and Mass Transfer Example 5.3 A 0.25-mm-diameter tube is placed vertically in a pool of water as shown in Fig. 5.7. The density of water is 1000 kg/m3 and its surface tension is 0.06 N/m. It is assumed that the water can completely wet the tube. Find the capillary rise.
Transport Phenomena in Multiphase Systems by A. Faghri & Y. Zhang 10 5.3 Wetting Phenomena and Chapter 5: Solid-Liquid-Vapor Phenomena Contact Angles and Interfacial Heat and Mass Transfer Solution: Since the water can completely wet the tube, the contact angle is Considering that the density of the vapor is much less than that of the liquid, eq. (5.48) can be simplified as 2σ B ρ gH r l Therefore, the capillary rise is 2σ 2× 0.06 H = = =0.098m = 98mm ρ × × × − 3 l gr 1000 9.8 0.125 10
Transport Phenomena in Multiphase Systems by A. Faghri & Y. Zhang 11