Question -

Consider an experiment on the International Space Station, which is illustrated below. A cylindrical capillary of length L = 10 cm and inner diameter of d_c = 100 µm (sealed at one end), is positioned to contact a droplet of water with diameter D which is floating in the ISS laboratory. Consider situations 1, 2, and 3 with droplet diameters of D₁, D₂, and D₃ (Figure 1). At the moment when the capillary contacts the surface of the droplet (Figure 2), the liquid starts rising inside the capillary due to interface pressure formed across water-air interface. Water is completely hydrophilic with the inside surface of the capillary (contact angle is θ ≈ 0^o). The temperature in the ISS laboratories is 20^oC.

a) What is the maximum height of the liquid in the capillary (Figure 3) in situations 1, 2, and 3: h_1-max, h_2-max, and h_3-max?

b) What is the diameter of droplets after liquid in capillary had reached maximum height in situations 1, 2, and 3: h_1-max, h_2-max, and h_3-max?

c) Calculate the velocity of the meniscus in Case 1 (D₁ = 100 [mm]), when the meniscus reaches ½ of the maximum level in the capillary (h_1-max/2)

Data: d_c = 100 [µm]; L = 0.1 [m]; D₁ = 100 [mm]; D₂ = 10 [mm]; D₃ = 1 [mm];

Figure 1: Droplet floating and is about to touch the capillary in situations 1, 2, and 3.

Figure 2: Droplet has just been in contact with the capillary.

Figure 3: We anticipate that after liquid rose inside the capillary and reached steady state (capillary heights of h₁, h₂, and h₃) the droplets diameters would reduce to D'₁, D'₂, and D'₃. Is this anticipation entirely correct?

Show all your work; and, state all assumptions. Please use homework format. The course is about engineering ethics, safety, and professionalism.