A piece of soft tissue is mounted between two fluid containers. The tissue is assumed composed of an incompressible solid and a incompressible fluid. The fluid container left of the sample is at a pressure of 40 kPa. The fluid container right of the sample is at a pressure of 10 kPa. The sample rests on the right hand side on a porous filter. The hydraulic permeability of the tissue is 4 10-16 m4 /Ns, while hydraulic permeability of the porous filter is orders of magnitude higher than the hydraulic permeability of the tissue. The cross section through which fluid can flow is 5 mm2 . The aggregate modulus H of the tissue is 0.5 MPa. The thickness of the sample is 1 mm.

2.1 What is the volume flow Q of the fluid per second through the sample? (4 marks)

2.2 We define a coordinate x across the sample as seen on the figure. X=0 at the contact with the porous filter and x=1 at the other end of the sample. Quantify the total stress (sigma)xx as a function of x in the sample in the steady state situation. (4 marks)

2.3. Quantify the effective stress (sigma)eff xx as a function of x in the sample in the steady state situation. (4 marks)

2.4 Quantify the strain (sigma) xx as a function of x in the sample in the steady state situation. (4 marks)

2.5 What is the value of the x-displacement ux of the left border (x=1) of the sample in steady state? (4 marks) 2.6 In which direction does the displacement ux go, to the left or to the right? (4 marks)

40 kPa X 10 kPa Porous filter Tissue sample