Contents
Daily Dose 004 | FLUID MECHANICS
How do you find the Contact Angle of a liquid in tube?
In Fluid Mechanics, the contact angle refers to the angle formed at the three-phase contact line where the liquid, the solid surface, and the gas (usually air) interface meet. The contact angle is the angle between the liquid-solid interface and the solid-gas interface.
In the case of capillary rise, which will be a problem type you see on the FE Exam, the contact angle is an important parameter that determines the extent of liquid rise within a capillary or narrow tube. This angle is related to the balance between cohesive and adhesive forces.
A smaller angles indicate better wetting of the solid surface by the liquid, which leads to capillary rise.
On the other hand, a larger contact angle signifies poorer wetting and may result in limited or no capillary rise.
The contact angle is an essential parameter in understanding capillary action and how liquids interact with surfaces in confined spaces, such as in porous materials or capillary tubes. It has implications in various fields, including materials science, engineering, biology, and Fluids, where precise control of capillary rise is crucial for optimizing processes and applications.
Key Definition
What is CAPILLARY ACTION?
CAPILLARY ACTION is the movement of a substance within the spaces of a porous material and is driven by the forces of adhesion, cohesion, and surface tension.
Due to the forces of cohesion (molecules like to stay close together) and adhesion (molecules are attracted and stick to other substances) water, and other substances exhibit a level of “stickiness”.
Adhesion of a substance to the walls of a vessel will cause an upward force on the liquid at the edges and result in a meniscus which turns upward.
The surface tension acts to hold the surface intact.
CAPILLARY ACTION occurs when the adhesion to the walls is stronger than the cohesive forces between the liquid molecules.
The height to which CAPILLARY ACTION will take in a uniform circular tube is limited by surface tension and, of course, gravity.
The Process
How can you determine the Contact Angle of a liquid in tube?
Determining the contact angle between a liquid and the solid surface of a capillary (or narrow tube) requires us to understand the relationships between the cohesive and adhesive forces of various substances.
In the real world, finding this angle would involve experimental techniques, however, on the FE Exam, you will be provided with information about the liquid, solid surface, and the conditions you otherwise would get through experiment.
The process of determining the contact angle may involve applying principles of Fluid Mechanics, surface science, and interfacial phenomena.
When presented with such a problem on the FE Exam, here’s a step-by-step process to tackle it:
- Step 1: Understand the Setup
- Step 2: Identify Relevant Equations
- h = (4σ*cos(β)/γd)
- h = Height of the liquid in the vertical tube
- σ = Surface Tension
- β = Angle made by the liquid with the wetted tube wall
- γ = Specific weight of the liquid
- d = Diameter of the capillary tube
- Step 3: Gather the Given Information
- Step 4: Substitute the Values into the Capillary Rise Formula
- β = cos-1(h*γd/4σ
- Step 5: Convert Contact Angle to Radians (or degrees)
- θ (in radians) = θ (in degrees) * π / 180
- Step 6: Check for Validity
- Step 7: Interpret the Result
Carefully read the problem statement to understand the experimental setup. Identify the liquid, the solid surface, and the gas phase (usually air) involved.
Take note of any specific conditions or assumptions provided in the problem.
In many cases, contact angle problems can be solved using the Capillary Rise equation that is found on page 178 of the FE Reference Handbook, which is written as:
Where:
Collect all the necessary values of the liquid.
In some cases, this may be as simple as plucking the values of σ, γ, and d from the problem statement.
In other cases, you may need to use the density (ρ), gravitational acceleration (g), radius of the capillary tube (r) or reference tables to define the appropriate values.
With all the values defined, plug them into the Capillary Rise formula and rearrange to isolate and solve for the contact angle, β.
The formula will be:
Depending on the mode in which your calculator is set and the result in which the problem statement is asking for, convert the contact angle to radians (or degrees) using the formula:
Make sure the calculated contact angle is physically meaningful.
Contact angles should be within the range of 0 to 180 degrees, as angles outside this range may not correspond to physically possible wetting behaviors.
Interpret the obtained contact angle in the context of the problem.
A contact angle close to 0 degrees indicates good wetting (complete wetting), while a contact angle close to 180 degrees indicates poor wetting (complete non-wetting).
Contact angles in between indicate varying degrees of partial wetting.
Check out the video to see an FE Exam Fluid Mechanics Practice Problem that deals with Capillary Action and how you can go about solving it in the most efficient manner.
As always, we are here to help, Prepineer
