How Does Surface Tension Affect the Force Needed to Separate Glass Plates?

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The discussion centers on calculating the force needed to separate two glass plates with a water film between them, focusing on the role of surface tension. The initial problem involves a zero contact angle, leading to a specific radius of curvature calculation, while a follow-up question addresses the implications of a different angle. Participants clarify that the pressure difference (Delta P) is derived from surface tension and curvature, and this pressure is then multiplied by the area of the plates to find the normal force. A secondary problem introduces a negative sign in the pressure equation, prompting questions about its necessity. Overall, the conversation emphasizes understanding the relationship between surface tension, curvature, and the resulting forces in fluid mechanics.
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Hello ,


A Problem I found In a book , although I have the answer , I can't understand it


the problem is


Calculate the force required to separate two glass plates of area 10 cm^2 each , with a film of water .5mm thick between them . take the coefficent of surface tention (T)to be 72 dyne/cm and theta = 0

The Answer written

since theta = 0 so the radius of curvature of the cylindrical surface between the plates is r = d/2 =.025 cm

((note : I Understand this but what If theta was another angle ??))


Delta P = T/r = 72/.025 = 2880 dyne/cm^2

the Normal force required = Delta P * Area = 2880*10 =2.88*10^4 dyne = .288 N #

I nead some explanation for this


Another _Identical problem_ says

two circular plates of radus 5 cm with 5 mm thick film of water betweem them , If the surface tention = 72.7*10^3 N/m , the normal force required to pull them Apart is what ?

it is the same I know , but in the solution ((the solution this time is not in the book , it is an assistant Engineer at the college)) said that :

Delta P = T(1/R1-1/R2) , R2 = infinity , so Delta P = T/R1

My problem is Why did he write a negative sign ?? I know it won't change the answer but why is it minus or it is just a writing error ??
 
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Read http://en.wikipedia.org/wiki/Surface_tension

Zero contact angle means that the wall is tangent to the liquid surface. There are two parallel walls at distance d, therefore the radius of curvature is r=d/2. This is not true for other angles.

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Yes I do know that and I wrote that above , I asked what would be (mathematically) the radius curvature if theta was 30 degrees for example

Any way it is not my basic question here :D
 
I found some answers , but what I can't well understand is

how the pressure difference between the water and the air due to the curviture is multiplies by the (whole area) of the sheet , why ?
 
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