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case 5 hw answers_1 - BMED 2100 Biomaterials Science...

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04/14/09 1 BMED 2100 Biomaterials Science & Engineering Spring 2009 Case Study #5: Answers to HW questions 5. ANSWER – see Maple file output at end. Table 4.2 comes from the Ph.D. thesis (1993) by a former doctoral student at Rensselaer, Mary Beth Schmidt. The Table shows contact angles measured for captive air bubbles on different biomaterial surfaces immersed in water and glycerol. These data were used to calculate surface energy according to the method explained in the excerpt, below, from Mary Beth’s Ph.D. thesis (see indented section , below). Read her method, and then use appropriate data from the Table to solve equations (3.2a) and (3.2b) simultaneously for the two unknowns γ 1 d and γ 1 p , which are the so-called dispersive ( γ 1 d ) and polar ( γ 1 p ) components of the surface energy of “biomaterial 1”, where γ 1 d + γ 1 p = γ 1 . Although Table 4.2 shows data from 3 different biomaterials (cp Ti, Ti-6Al-4V, and Synamel, which is a form of hydroxyapatite), compute your results for “biomaterial 1” , Synamel. Show that your values for γ 1 d , γ 1 p , and γ 1 agree with Mary Beth’s results for the as-prepared version of Synamel in Table 4.2. Excerpt from the Ph.D. thesis entitled “In vitro cell attachment and detachment behavior for selected biomaterials” by Mary Beth Schmidt, BME, RPI, 1993. The contact angle was determined indirectly, based on the geometry of a captive air bubble on the immersed biomaterial surface (Figure 3.3). The bubbles were approximately 40 µ l in volume and were assumed to be spherical. The image of the captive bubble was digitized using a video camera (Sony DXC-1821, Japan), equipped with a macro lens (1:3.5, f = 50mm, Olympus, Japan), and PC-based image analysis software (Image Pro IT, Media Cybernetics, Rockville, MD). The digitized image was displayed on a high- resolution monitor (Sony PVM-I9 10). Bubble height (h) and contact radius (r) were

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