Adhesion Force: Liquid bridge force
Forces Acting on Powder
When considering the behavior of powders, there are forces other than contact forces to take into account. Among them, the adhesion force, which occurs between particles or between particles and walls as they attempt to adhere to each other, is a crucial element when handling powders.
Liquid bridge force
Capillary force, also known as liquid bridging force, is one of the adhesive forces that come into play when particles are connected by a liquid. This force’s magnitude is determined by factors such as surface tension and Laplace pressure. These factors combine to define the capillary force. In other words, understanding capillary force requires comprehension of surface tension and Laplace pressure. Let’s delve deeper into these two forces.
Two forces related to liquid bridge force:
- Surface Tension
Surface tension is one of the forces related to capillary force. You might have observed a phenomenon where water forms a raised shape without overflowing the rim of a cup when you pour water into it. This effect is due to surface tension. Surface tension is the force that acts at the interface between a liquid and a gas, tending to minimize the surface area. It’s a force driven by intermolecular interactions and its magnitude is determined by the nature of the substance.
Let’s consider the example of water in a cup. Inside the liquid, water molecules are attracted to each other through intermolecular forces, causing them to pull on each other from all directions. This results in a balanced state within the liquid. On the other hand, for water molecules at the surface, the attraction towards the gas side is much weaker compared to the attraction within the liquid. As a result, even though the water at the surface is being pulled inwards by the liquid, the weak attraction to the gas allows the water to form a raised shape without spilling over the cup’s rim. In essence, the surface tension is causing the surface to contract.
While we used the cup example here, surface tension is always at play in systems where interfaces exist. Therefore, in the case of capillary bridges where particles are connected by a liquid, surface tension at the liquid interface also contributes to the overall capillary force.
- Laplace Pressure
The Laplace pressure refers to the pressure difference between the interior and exterior of a liquid caused by the curvature of the liquid’s surface. External pressure is often considered a fixed value, such as atmospheric pressure. Therefore, calculating the pressure difference helps determine the internal pressure. Although the Laplace pressure originates from surface tension, it affects the liquid’s interior rather than its surface. The magnitude of this force is influenced by the curvature of the liquid surface. Specifically, when the curvature is small, meaning the radius of curvature of the curved surface is large, the pressure difference is small. Conversely, when the curvature is large, indicating a smaller radius of curvature, the pressure is large.
The formula is as follows:
A circle drawn along a curve along the surface is known as the curvature radius, and when taken on mutually orthogonal planes, they are denoted as R1 and R2. From this relationship, it can be understood that when surface tension is strong, the pressure difference increases, and when the surface curvature is large (small curvature radius), the pressure difference also becomes significant.
When particles are connected by a liquid bridge, what kind of forces does the capillary force become?
The forces related to capillary forces are as follows: surface tension, which is the force causing the surface to contract and acts on the liquid surface, and Laplace pressure, which is an internal force determined by the surface shape within the liquid. Considering these characteristics, when thinking about the forces acting from the liquid onto the particles, it can be understood that the surface tension acts at the edges where the liquid contacts the particles, while the Laplace pressure acts on the contact surface.
Therefore, since each force operates in different regions, the combination of these two forces expresses the capillary force, which encompasses their effects.
Capillary Bridge Model and Liquid Quantity
The capillary bridge model discussed in this session applies to specific conditions where the liquid quantity is approximately 20% or less. The reason for this constraint lies in the shape and structure of the liquid between particles. In this capillary force model, the forces are considered in systems where particles are connected in pairs. In actual systems, as the liquid quantity increases, the structure can involve connections among three or more particles through the liquid, and with even more liquid, the structure may have liquid present between all particle gaps.
Therefore, it’s important to note that the assumptions about the shape and forces of the liquid in this model can only be applied to situations with low liquid quantities.
Conclusion
The capillary bridge force is a combination of the surface tension acting on the liquid surface and the pressure within the liquid represented by the Laplace pressure.
