Geometric Property and Appearance

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Geometric Property and Appearance

• Physical Properties of Bio-Materials (II)

Poching Wu, Ph.D. Department of Bio-Mechatronic
Engineering National Ilan University
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Roundness and Sphericity
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Roundness

• where
• Ap largest projected area of object in natural
• position
• Ac area of smallest circumscribing circle

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Sphericity1

• where
• de the diameter of a sphere of the same volume
• as the object, m
• dc the diameter of the smallest circumscribing
• sphere or usually the longest
  diameter of the
• object, m

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Sphericity2

• where
• di the diameter of largest inscribed circle, m
• dc the diameter of the smallest circumscribed
• circle, m

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Sphericity3

• where
• a longest intercept, m
• b longest intercept normal to a, m
• c longest intercept normal to a and b, m

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Measurement of Surface Area

• Leaf area is an indicator of photosynthetic
  capacity and growth rate of a plant.

• Planimeter
• Air flow planimeter
• Imaging process technique
• Coating Method (using nickel powder)
• Prediction by measurement of length and width of
  a leaf

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Projected Area
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Air Flow Planimeter
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Egg Surface Area
By the relationship between weight and surface
area of egg
By summation of surface areas

• where
• S surface area, m2
• k a constant (4.56 5.07)
• m 0.66
• W weight, grams

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Density, r
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Displacement Method

• where
• WH2O weight of displaced water, kg
• r density of water, kg/m3
• W weight of sample in air, kg
• SGH2O specific gravity of water

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Specific Gravity Balance
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Quantachrome Multi-pycnometer
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The Theory of Pycnometer
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The state of the sample cell with sample
Eq.(1)

• where
• Pa is the ambient pressure
• Vc is the cell volume
• Vp is the powder volume
• na is the number of moles of gas occupying the
  cell
• volume
• R is the gas constant
• Ta is the ambient temperature.

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When the reference volume (VR ) is pressurized to
approximately 17 pounds per square inch above
ambient, the state of the reference volume can be
expressed as
Eq.(2)

• where
• P1 represents a pressure above ambient
• n1 is the number of moles of gas in the reference
  
• volume.

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When the selector valve is turned to connect the
samples cell, the pressure will fall to a lower
pressure P2, given by
Eq.(3)
Substituting Eq.(1) (2) into Eq.(3), gives
Eq.(4)
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or
Eq.(5)
Then
Eq.(6)
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Since Pa is made to read zero on the digital
meter, that is, all pressure measurements are
relative to Pa, Eq.(6) becomes
Eq.(7)
or
Eq.(8)
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Porosity, Packing Factor

• where
• Vp volume of pore, m3
• Vt total volume, m3
• Vs volume of solid, m3
• rs solid density, kg/m3
• rb bulk density, kg/m3

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Porosity of Granular and
unconsolidated Materials
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