Surface Tension - Using hot soapy water to wash clothes

[brotherbobby]

I mention the details in the book (verbatim) in the form of a paragraph in green below. Later I ask my questions in blue font for better reading.

"Surface tension also explains why hot, soapy water is used for washing. To wash clothing thoroughly, water must be forced through the tiny spaces between the fibers (Fig. 12.16). To do so requires increasing the surface area of the water, which is difficult to achieve because of surface tension. The job is made easier by increasing the temperature of the water and adding soap, both of which decrease the surface tension." (University Physics, 13th Edition)

1. Let's begin with the diagram. I know that the excess pressure within a (spherical) water molecule with a single surface is $p=\frac{2T}{R}$. Assuming hot water and soap bring about a reduction in T, it will reduce p. In which direction is water (with soap) supposed to travel in the diagram? Shouldn't air and water be on one side and the clothing and its inner fibers with dirt on the other?
2. Let's see the text above in green from the book. To force water through the fiber spaces in the clothing, it says the surface area of water needs to be increased! Increased? Shouldn't the surface area of water be decreased so that the water, with the same volume, can move through the clothing fiber spaces?

I present my own explanation, highlighting crucial points in red.

In order to force the soapy water through the fiber spacings, their surface area need to be reduced. A sphere is known to have the maximum surface area for a given volume. A decrease in the surface tension of water using soap and heat effects a decline in its surface area with the same volume of water. This reduced size of the soap water helps it make its way into the clothing. (Please note that nowhere in my explanation have I used the concept of excess pressure).

A help would be welcome.

 

[256bits]

Some other terms are wettability, surfactants, hydrophilic, hydrophobic surfaces and molecules if you want to explore further.

Let's begin with the diagram. I know that the excess pressure within a (spherical) water molecule with a single surface is p=2TR. Assuming hot water and soap bring about a reduction in T, it will reduce p. In which direction is water (with soap) supposed to travel in the diagram? Shouldn't air and water be on one side and the clothing and its inner fibers with dirt on the other?

The fabric, say a shirt, is usually dry when added to the wash. Being dry, air is surrounding all the fibres, which instead of the one layer shown would be of several layers, as threads are made up of long fibres twisted together, and weaved together to make the cloth. If soiled after wearing, the fabric can contain dirt and other extraneous particles within and around the fibres. To flush out these particles, water has to be able to penetrate into the small spaces between the fibres, enclose the particle and move it away from the fabric. Surface tension of the water hinders this process. the water may just "bead" on the surface and not penetrate into the "pores", and displace the air.

Let's see the text above in green from the book. To force water through the fiber spaces in the clothing, it says the surface area of water needs to be increased!
...
A sphere is known to have the maximum surface area for a given volume

Why do you say that? ie a sphere has the maximum surface area per volume.
Compare for the same volume , the ratio of surface area / volume for a sphere, cube, or any other shape.