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If a wet cloth is rolled together and squeezed, twisted or wringed out, water gets separated leaving behind a less wet cloth. This is an everyday life experience. However the science behind it is not known, nor mentioned in text-books, imho.

What happens between fiber and the fluid? What is the phenomenon, or, is there a model or a law ? What physical properties (like Viscosity, Bulk modulus) are involved? How much compressive or shear stress in needed to overcome surface tension or adhesion forces to cause separation of wettable cloth and liquid? Does the fluid stand in the fabric by capillary support?

All that is known.. is that a fluid cannot take shear stress and is incompressible.

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Wringing shear is a combination of tension and compression, the latter pushes out water. Compression appears essential for separation seen in a high speed g centrifuge or low speed laundromats. Gravity induces a weak compressive force on fabric, water dripping to surrounding surfaces. In a spaceship maybe wet cloth stays wet for longer durations.

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I can provide a qualitative explanation for why this process works in the first place. In a wet cloth, gravity tries to pull the water down, and the cloth matrix (the holes in the cloth) provides resistance for the water flow (due to effects like friction and surface tension). In hydrology, they call this field capacity, i.e amount of water that still gets retained in a soil medium even after effect of gravity.

But when you squeeze the cloth and close the holes, you are forcing the water out of the cloth matrix, making them lump together and form a continuous body. This greatly reduces the fabric-water interactions. So since this water body has much smaller resistance to flow, gravity wins and water is separated.

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How much compressive or shear stress in needed to overcome surface tension or adhesion forces to cause separation of wettable cloth and liquid?

Thats a tricky question and I don't think I can answer that. But a good place to start would be by calculating the surface energies. Before squeezing, the surface energies would be really low because there are so much fabric-water interactions. After squeezing the surface energy is higher because there are much lesser of those interactions as only the boundary of the waterbody is in contact with the fabric. The difference of these two energies would be the work you need to put in the system in order to make this change.

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See Eur. J. Phys.37 (2016) 065806 (RG). They propose a model of cloth wringing. They suggest that initially the volume of wet rolled cloth contains fibers, water, and air, and calculate the volume change with wringing. The calculations with the model seem to agree with experimental results.

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