2.4 Wetting and contact angle

Wetting phenomena are crucial in colloid science, influencing how liquids interact with solid surfaces. This topic explores the balance of adhesive and cohesive forces at interfaces, which determines whether a liquid will spread or form droplets on a surface.

Contact angle measurement quantifies surface wettability, with Young's equation linking it to interfacial tensions. Understanding these concepts is key for applications like coating, printing, and microfluidics, where controlling liquid-solid interactions is essential for optimal performance.

Wetting phenomena

• Wetting refers to the interaction between a liquid and a solid surface when they come into contact
• The degree of wetting is determined by the balance of adhesive and cohesive forces at the solid-liquid interface
• Understanding wetting phenomena is crucial for controlling and optimizing various processes in colloid science, such as surface coating, printing, and microfluidics

Wetting vs non-wetting

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• Wetting occurs when a liquid spreads over a solid surface, forming a thin, uniform film (water on clean glass)
• Non-wetting happens when a liquid forms discrete droplets on a solid surface, minimizing contact area (mercury on glass)
• The wettability of a surface depends on the relative magnitudes of the adhesive forces between the liquid and solid and the cohesive forces within the liquid

Contact angle

• Contact angle is a quantitative measure of the wettability of a solid surface by a liquid
• Defined as the angle formed between the solid surface and the tangent to the liquid-vapor interface at the point of contact
• Lower contact angles (<90°) indicate better wetting, while higher angles (>90°) suggest poor wetting or non-wetting behavior

Young's equation

• Young's equation describes the equilibrium contact angle in terms of the interfacial tensions between the solid, liquid, and vapor phases: $\gamma_{SV} = \gamma_{SL} + \gamma_{LV} \cos \theta$
  • $\gamma_{SV}$: solid-vapor interfacial tension
  • $\gamma_{SL}$: solid-liquid interfacial tension
  • $\gamma_{LV}$: liquid-vapor interfacial tension
  • $\theta$: equilibrium contact angle
• Provides a framework for understanding the thermodynamics of wetting and the factors that influence the contact angle

Factors affecting wetting

• Surface chemistry: The chemical composition and functional groups present on the solid surface influence its interaction with the liquid (hydrophilic vs hydrophobic surfaces)
• Surface roughness: Micro- and nanoscale topography can enhance or reduce wetting by altering the actual contact area between the liquid and solid
• Liquid properties: Surface tension, viscosity, and polarity of the liquid affect its ability to spread on a surface
• Environmental conditions: Temperature, humidity, and the presence of contaminants can modify the wetting behavior

Measuring contact angle

• Contact angle measurement is essential for characterizing the wettability of surfaces and studying interfacial phenomena
• Several techniques are available, each with its own advantages and limitations
• The choice of method depends on factors such as sample geometry, surface properties, and the desired accuracy and reproducibility

Sessile drop method

• Most common and straightforward technique for measuring contact angles
• Involves placing a small liquid droplet on a flat, horizontal solid surface and capturing its profile using a camera or goniometer
• The contact angle is determined by analyzing the shape of the droplet and fitting a tangent line at the three-phase contact point

Wilhelmy plate method

• Measures the average contact angle around a thin, vertical plate partially immersed in a liquid
• The plate experiences a force due to the liquid's surface tension, which is related to the contact angle by the Wilhelmy equation: $F = p \gamma_{LV} \cos \theta$
  • $F$: force acting on the plate
  • $p$: perimeter of the plate
  • $\gamma_{LV}$: liquid-vapor interfacial tension
  • $\theta$: contact angle
• Suitable for studying dynamic wetting behavior and measuring contact angles on fibers or powders

Capillary rise method

• Based on the phenomenon of capillary rise, where a liquid is drawn up into a narrow tube or capillary due to surface tension forces
• The height of the liquid column in the capillary is related to the contact angle by the Jurin's law: $h = \frac{2 \gamma_{LV} \cos \theta}{\rho g r}$
  • $h$: height of the liquid column
  • $\gamma_{LV}$: liquid-vapor interfacial tension
  • $\theta$: contact angle
  • $\rho$: density of the liquid
  • $g$: acceleration due to gravity
  • $r$: radius of the capillary
• Useful for measuring contact angles in porous materials or studying wetting in confined geometries

Advantages vs disadvantages

• Sessile drop method:
  • Advantages: simple, fast, and requires small sample volumes
  • Disadvantages: sensitive to surface roughness and heterogeneity, limited to flat surfaces
• Wilhelmy plate method:
  • Advantages: measures average contact angle, suitable for dynamic wetting studies
  • Disadvantages: requires specialized equipment, may be affected by plate surface properties
• Capillary rise method:
  • Advantages: applicable to porous materials and confined geometries
  • Disadvantages: requires precise control of capillary dimensions, may be influenced by gravity and evaporation effects

Surface free energy

• Surface free energy is a measure of the excess energy associated with the surface of a material compared to its bulk
• Plays a crucial role in determining the wetting behavior, adhesion, and other interfacial phenomena
• Can be estimated from contact angle measurements using various theoretical approaches

Solid-liquid interactions

• The surface free energy of a solid influences its interaction with liquids
• Solids with high surface energy tend to be more easily wetted by liquids, while those with low surface energy are more difficult to wet
• The work of adhesion between a solid and a liquid depends on their respective surface free energies and the interfacial tension between them

Dispersive vs polar components

• Surface free energy can be divided into dispersive (non-polar) and polar components
• Dispersive interactions arise from temporary fluctuations in electron density and include London dispersion forces
• Polar interactions involve permanent dipoles, hydrogen bonding, and other specific interactions (acid-base)
• The relative contributions of dispersive and polar components determine the overall surface properties and wetting behavior

Owens-Wendt approach

• A widely used method for estimating the surface free energy of solids from contact angle data
• Assumes that the surface free energy can be split into dispersive and polar components: $\gamma_S = \gamma_S^d + \gamma_S^p$
  • $\gamma_S$: total surface free energy of the solid
  • $\gamma_S^d$: dispersive component of the solid surface free energy
  • $\gamma_S^p$: polar component of the solid surface free energy
• The work of adhesion between a solid and a liquid is given by: $W_A = 2(\sqrt{\gamma_S^d \gamma_L^d} + \sqrt{\gamma_S^p \gamma_L^p})$
  • $W_A$: work of adhesion
  • $\gamma_L^d$: dispersive component of the liquid surface tension
  • $\gamma_L^p$: polar component of the liquid surface tension
• By measuring contact angles with liquids of known surface tension components, the solid surface free energy can be determined

Fowkes theory

• Another approach for estimating surface free energy based on the concept of interfacial interactions
• Proposes that the work of adhesion between a solid and a liquid is the sum of the dispersive and polar contributions: $W_A = W_A^d + W_A^p$
  • $W_A^d$: dispersive contribution to the work of adhesion
  • $W_A^p$: polar contribution to the work of adhesion
• The dispersive component is given by: $W_A^d = 2\sqrt{\gamma_S^d \gamma_L^d}$
• The polar component is often approximated using the geometric mean: $W_A^p = 2\sqrt{\gamma_S^p \gamma_L^p}$
• Fowkes theory provides a framework for understanding the role of specific interactions in wetting and adhesion

Wetting on real surfaces

• Real surfaces often deviate from the ideal, smooth, and homogeneous assumptions of classical wetting theories
• Surface roughness, chemical heterogeneity, and other factors can significantly influence the wetting behavior
• Several models have been developed to account for these effects and predict the apparent contact angle on real surfaces

Surface roughness effects

• Surface roughness can enhance or reduce the wettability of a surface, depending on the liquid-solid interactions
• Roughness increases the actual surface area available for contact, leading to amplification of the intrinsic wetting behavior
• For hydrophilic surfaces, roughness promotes wetting and reduces the apparent contact angle
• For hydrophobic surfaces, roughness can lead to superhydrophobicity and increase the apparent contact angle

Wenzel model

• Describes the wetting behavior on rough surfaces where the liquid completely penetrates the surface features
• The apparent contact angle is given by the Wenzel equation: $\cos \theta^* = r \cos \theta$
  • $\theta^*$: apparent contact angle on the rough surface
  • $r$: roughness factor (ratio of actual surface area to projected area)
  • $\theta$: intrinsic contact angle on a smooth surface of the same material
• Predicts that roughness amplifies the intrinsic wetting behavior, making hydrophilic surfaces more hydrophilic and hydrophobic surfaces more hydrophobic

Cassie-Baxter model

• Applies to heterogeneous wetting, where the liquid sits on top of the surface features, trapping air pockets underneath
• The apparent contact angle is given by the Cassie-Baxter equation: $\cos \theta^* = f_1 \cos \theta_1 - f_2$
  • $\theta^*$: apparent contact angle on the heterogeneous surface
  • $f_1$: fraction of the solid-liquid interface
  • $\theta_1$: intrinsic contact angle on the solid surface
  • $f_2$: fraction of the liquid-air interface
• Explains the superhydrophobicity observed on many natural and artificial surfaces (lotus leaf effect)

Heterogeneous surfaces

• Real surfaces often exhibit chemical heterogeneity, with patches of different composition or functionality
• The wetting behavior on heterogeneous surfaces can be described by a weighted average of the contact angles on the individual patches
• The Cassie equation for chemically heterogeneous surfaces: $\cos \theta^* = f_1 \cos \theta_1 + f_2 \cos \theta_2$
  • $\theta^*$: apparent contact angle on the heterogeneous surface
  • $f_1$, $f_2$: area fractions of the two different surface patches
  • $\theta_1$, $\theta_2$: intrinsic contact angles on the individual patches
• Understanding the effects of heterogeneity is essential for designing surfaces with tailored wetting properties

Dynamic wetting

• Dynamic wetting refers to the time-dependent behavior of liquids spreading on solid surfaces
• Characterized by advancing and receding contact angles, which differ from the equilibrium contact angle
• Important in processes involving the motion of liquids on surfaces, such as coating, printing, and microfluidics

Advancing vs receding angles

• Advancing contact angle ($\theta_A$): the maximum stable angle observed when a liquid is slowly added to a droplet on a surface
• Receding contact angle ($\theta_R$): the minimum stable angle observed when a liquid is slowly withdrawn from a droplet on a surface
• The advancing angle is always greater than or equal to the receding angle ($\theta_A \geq \theta_R$)

Contact angle hysteresis

• The difference between the advancing and receding contact angles: $\Delta \theta = \theta_A - \theta_R$
• Arises from surface roughness, chemical heterogeneity, and other factors that cause the liquid-solid interface to be pinned
• A measure of the resistance to the motion of a liquid droplet on a surface
• Surfaces with low hysteresis exhibit easy droplet mobility and self-cleaning properties

Factors influencing hysteresis

• Surface roughness: Pinning of the contact line on surface asperities leads to increased hysteresis
• Chemical heterogeneity: Variations in surface composition or functionality can cause local differences in wettability and hysteresis
• Liquid properties: Viscosity, surface tension, and the presence of surface-active agents can affect the dynamic wetting behavior
• Droplet size: Smaller droplets are more sensitive to surface heterogeneities and may exhibit greater hysteresis

Measurement techniques

• Tilted plate method: The surface is slowly tilted until a droplet begins to slide; the advancing and receding angles are measured at the front and back of the droplet
• Sessile drop method with volume change: Liquid is slowly added to or withdrawn from a droplet using a syringe, and the advancing and receding angles are recorded
• Wilhelmy plate method with immersion/emersion cycles: The plate is dipped into and pulled out of the liquid, and the force is measured to determine the advancing and receding angles
• Capillary bridge method: A liquid bridge is formed between two surfaces, and the advancing and receding angles are measured as the surfaces are separated or brought together

Applications of wetting

• Wetting phenomena play a crucial role in numerous industrial and technological applications
• Understanding and controlling wetting is essential for optimizing processes, improving product performance, and developing new functionalities

Adhesion and bonding

• Wetting is a prerequisite for good adhesion between a liquid adhesive and a solid substrate
• The work of adhesion depends on the surface free energies of the materials and the interfacial tension, which can be estimated from contact angle measurements
• Designing surfaces with appropriate wettability can enhance the strength and durability of adhesive bonds (dental composites, pressure-sensitive adhesives)

Printing and coating

• Wetting is critical in printing processes, where ink must spread uniformly on the substrate to form high-quality images
• In coating applications, the wetting behavior determines the coverage, thickness, and adhesion of the coating layer
• Controlling the surface energy and roughness of the substrate can optimize the wetting and spreading of inks and coatings (inkjet printing, paint application)

Microfluidics and lab-on-chip

• Wetting plays a key role in the flow and manipulation of liquids in microfluidic devices
• The contact angle and surface wettability influence the capillary forces that drive liquid motion in microchannels
• Patterning surfaces with regions of different wettability allows for the control of liquid spreading, mixing, and reactions on a chip (point-of-care diagnostics, drug discovery)

Superhydrophobicity and self-cleaning

• Superhydrophobic surfaces exhibit extreme water repellency, with contact angles greater than 150° and low hysteresis
• Inspired by natural examples like the lotus leaf, these surfaces are characterized by a combination of micro- and nanoscale roughness and low surface energy
• Water droplets easily roll off superhydrophobic surfaces, collecting and removing dirt and contaminants in the process (self-cleaning windows, stain-resistant textiles)
• Designing and fabricating superhydrophobic surfaces involves creating hierarchical roughness and modifying the surface chemistry to reduce the surface free energy