# Confusion of the scale of contact line dynamics and capillary flow

• A
• mrmudd
In summary, the conversation discusses the scale at which capillary flow and contact line dynamics are important, specifically in cases where gravity is removed from the problem. The Washburn's equation is mentioned, which states that the penetration length is proportional to the radius of the capillary tube. There is confusion about the limiting length scale for this equation and how contact angles play a role in driving flow. It is explained that the importance of contact angles varies depending on the system, with larger containers and greater amounts of liquid making them less significant. However, for smaller containers and amounts of liquid, contact angles become more important in determining the rate of flow.

#### mrmudd

I'm having some trouble getting my head around the scale at which capillary flow and contact line dynamics are important. In the simple case of liquid rise in a capillary tube, a smaller tube will allow for greater rise since a larger height is required to achieve an equal weight of the liquid column to balance the capillary pressure. That's totally fine and makes complete sense.

My problem is when gravity is removed from the problem. Consider now Washburn's equation where the penetration length L is proportional to the radius of the capillary tube. This is where I start to get to confused. I can understand that at small length scales, viscous dissipation will be greater thus slowing down the flow. However, if we assume a very large pipe, say 0.5 meter radius; the rate at which the pipe is filled with liquid due solely to the contact line is no way going to be faster than 1 mm radius tube. I suppose there is a limiting length scale above which Washburn's equation cannot be applied; however, I cannot seem to find it anywhere.

On this note, the scale at which a contact line drives the flow is elusive to me. Consider in zero gravity, a container filled with fine powder and a tiny water droplet. Obviously, the a hydrophilic contact angle will result in the imbibition of water into the pore space between the powder and that effect will dominate the final configuration of liquid in the powder. Now if we scale up the exact problem (still in zero gravity) to something like a swimming pool filled with boulders. The contact angle between the water and the boulder would play very little effect in driving any flow into the space between the boulders. So there has to be some way of quantifying the scale at which contact angles play an important roll. It must include the mass of liquid and surface tension, right?

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Any insight into this matter would be greatly appreciated! In regards to your question about the scale at which contact angles play an important role in driving flow, it is actually quite complex and varies depending on the system. Generally speaking, the larger the container and the greater the amount of liquid, the less important contact angle is in driving the flow. This is because the gravitational force acting on the liquid is much larger than the surface tension forces at these scales. However, for smaller containers and/or smaller amounts of liquid, the surface tension forces become more significant and the contact angle plays a larger role in driving the flow. In these cases, the contact angle will determine how the liquid spreads across the surface and the rate at which it does so.

## 1. What is "confusion of the scale" in contact line dynamics and capillary flow?

Confusion of the scale refers to the phenomenon where the dynamics of contact lines (the interface between a liquid and a solid surface) and capillary flow (the movement of a liquid due to surface tension) are often studied separately, despite their interconnected nature.

## 2. Why is understanding contact line dynamics and capillary flow important?

Understanding these phenomena is crucial for various applications, such as microfluidics, inkjet printing, and coating processes, where precise control of the contact line and capillary flow is necessary.

## 3. What causes the confusion of scale in these two areas?

The confusion of scale is mainly caused by the fact that contact line dynamics and capillary flow occur on different length scales. Contact line dynamics occur at the microscale, while capillary flow occurs at the macroscale. This makes it challenging to study them simultaneously.

## 4. How can researchers overcome the confusion of scale in studying these two areas?

One approach is to use multiscale modeling, where different length scales are considered simultaneously. Another way is to use advanced experimental techniques, such as high-speed imaging, to capture the dynamics of both contact lines and capillary flow.

## 5. What are some potential future developments in the study of contact line dynamics and capillary flow?

Some potential future developments include the development of new theoretical models that can accurately describe the dynamics of both phenomena, as well as the use of advanced materials and techniques to manipulate and control contact lines and capillary flow for various applications.