Find the separation distance for a line of oil being squashed between two flat plates I was wondering if someone could give me some help on how to start this problem, I'm really struggling to get my head around it.
A long line of oil is being squashed between two flat plates of length $L$ by a weight $W$ placed on the top of the upper plate. The initial separation distance $\delta$ is very small compared with the initial width $2L$ of the oil strip so one would expect approximations of a lubrication type to describe the flow of oil in the gap. Clearly stating and justifying the assumptions made, find an estimate for the separation distance $\delta h(t)$ as a function of time.  
 A: As a simplification, you can consider that you have a 2D viscous flow between two boundaries that approach each other. Assuming that the flow is symmetrical about the line (with the line along the Y direction), you can simplify this further to "no flow at x=0".
What you are left with is a pressure distribution $p(x,t)$ whose integral in $x$ should equal the total force on the plates, and whose derivative in $x$ describes the force on the liquid. In viscous flow, the flow rate is proportional to the pressure difference. Now the flow velocity will be proportional to the distance $x$ from the center (the further from $x=0$, the more oil needs to move past the point as the plates come closer together). Assuming "normal" viscous flow, this means the pressure has to be proportional with $x$ also. 
Finally, you need to consider the shape of the meniscus at the leading edge of the oil. This shape is determined by the contact angle between the oil and the glass, and will result in an additional force on the liquid - either pushing the oil in, or pulling it out, depending on the sign of the contact angle.
Those are the considerations I think should get you going on solving this.
