1. You design a tent ceiling with conical pores. How should you orient the cones in the ceiling to keep the rain droplets trapped in the pores. Explain your choice using Laplace equation and taking into account the gravity effect and the difference in the advancing and receding contact angles.
2. A liquid bridge of length /, density p, and surface tension a, is trapped in a cylindrical capillary of radius r
a) Assuming that the liquid bridge is sitting a halfway down to the lower end of the capillary and the advancing contact angle is θa and receding contact angle is θr, find a critical condition when the liquid bridge becomes unstable and will fall down the capillary.
b) Assuming that the lower end of the liquid bridge is sitting at the capillary edge (i.e. the contact angle is not defined), analyze the shape of the lower meniscus as a function of the length of the liquid bridge. Setting the condition of meniscus detachment as θa = 90°, find the critical length of the liquid bridge for σ = 0.1 N/m, ρ = 1000kg/m3, R = 0.1 mm.
3. A die in the extrusion box is made of a slit and a tube connected in a chain. The channels have the same opening H and length L. H is the gap thickness for a slit and H is the diameter for a tube. The width of the slit is W. Find a relation between the mean velocity and pressure drop applied to the ends of this device.
4. A container with water is connected with the atmosphere by a cylindrical pipe of diameter d= 1 cm and 10 cm length.
a) Find the time T at which the liquid column decreases by two times? Analyze the dependence T=T(h) using Matlab.
b) Find the time T at which the liquid column decreases by two times if container is connected with the atmosphere by a slit-like pipe of diameter d= 1 cm, and 10 cm length, and width W = 1cm.