Transcript Slide 1
Outline • Correction • Wetting angle • Particle sizes Soil Physics 2010 Correction Principle, part 1: An electrical pulse propagating along a wire reflects back from the end of the wire: Knowing the speed of propagation (around c), we can figure out the distance to the end – hence “Cable Tester” Soil Physics 2010 Animation courtesy of Dr. Dan Russell, Kettering University Time Domain Reflectometry Principle, part 2: An electrical pulse propagating along a wire has its velocity changed according to the dielectric permittivity of the surrounding medium: v c er A wire running through water – even if insulated – will transmit a signal more slowly! The dielectric permittivity er (sometimes called the dielectric constant, which it isn’t!) is expressed relative to the permittivy of a vacuum (1 by definition), so it is unitless. Soil Physics 2010 Animation courtesy of Dr. Dan Russell, Kettering University TDR setup Cable Tester 1) A pulse is sent through the cable to the probe The coaxial cable is shielded from soil’s dielectric 2) The pulse goes down the bare wires, surrounded by soil 5) The returned pulse shows the effect of this delay + - 4) Both ways through the needle, the pulse is slowed by the dielectric of the soil v Soil Physics 2010 3) The pulse reflects off the ends of the needles. c er Animation courtesy of Dr. Dan Russell, Kettering University TDR in practice travel time in needle Needles have length L Soil Physics 2010 Montmorillonite trace q a 4 b 11 c 22 r d 30 2L c v t e Wetting angles But air’s wetting angle is around 150° Here, water’s wetting angle is around 30° a < 90° : “wetting phase” a > 90 ° : “non-wetting phase” The wetting angle is defined as that angle passing through the fluid being described. Soil Physics 2010 Young’s equation relates the energies of the 3 interfaces SL LG cosa SG subscripts: S solid, L liquid, G gas The contact point is pulled equally each way along a (flat) solid surface a Soil Physics 2010 Back to the capillary tube SL LG cosa SG a Soil Physics 2010 Capillary equation – final version a 2 cosa h w a g r Soil Physics 2010 Particle sizes Which is bigger? Soil Physics 2010 How to decide which is bigger? Volume? Surface area? Projected area? Longest transect? Largest inscribed sphere? Smallest circumscribed sphere? Largest circle inscribed in projection? Smallest circle circumscribing projection? …? Soil Physics 2010 Likewise for soil particles Soil Physics 2010 Volume? Surface area? Projected area? Longest transect? Largest inscribed sphere? Smallest circumscribed sphere? Largest circle inscribed in projection? Smallest circle circumscribing projection? …? Equivalent sphere Soil Physics 2010 All methods attempt to relate each real soil particle to a sphere that in some sense is the same (“equivalent”) size Equivalent by: Volume? Surface area? Projected area? Longest transect? Largest inscribed sphere? Smallest circumscribed sphere? Largest circle inscribed in projection? Smallest circle circumscribing projection? Measuring particle size: first Disperse Soil particles aggregate. Do we want to know about the primary particles, or the secondary particles? If primary, how do we disperse (disaggregate) the secondary particles? Why not measure both? How are the two distributions related? Soil Physics 2010 Measuring soil particle sizes: Sieving Sieving: • Related to smallest circle circumscribing projection • Nested sieves • Discrete sizes • Labor-intensive • $ • Time-dependence • Errors each way • Mass-dependence • Slower with more mass • Energy-dependence • Jumping • Size- and shape-dependence • 50 mm smallest • Rounder is better Soil Physics 2010 Measuring soil particle sizes: Sedimentation Gravitational Sedimentation Stokes Settling Imagine a sphere sinking through a viscous fluid – say, a silt grain in water. At terminal velocity, Force up = Force down Newton’s 1st law: Objects at rest tend to stay at rest → An object moving at a constant speed is acted upon by forces (if any) equal in magnitude: Forces slowing it, and forces accelerating it. Soil Physics 2010 Measuring soil particle sizes: Sedimentation At terminal velocity, Force up = Force down (Newton’s 1st law) Force down: Force = Mass * acceleration = (s-w)(4/3 p r3) * g (Newton’s 2nd law) Soil Physics 2010 Measuring soil particle sizes: Sedimentation At terminal velocity, Force up = Force down (Newton’s 1st law) Force up (viscous drag): =6prhv viscosity (Stokes said so) Soil Physics 2010 Measuring soil particle sizes: Sedimentation At terminal velocity, Force up = Force down (Newton’s 1st law) 3) * g ( )(4/3 p r 6prhv= s w Solve for v: 4p s w r g 2 s w r g v 18prh 9h 3 Soil Physics 2010 2 Measuring soil particle sizes: Sedimentation 2 s w r g v 9h 2 Particles ≥ r will fall at least Dh within a known time t. Sampling at a known depth and time, you know the size of the biggest particle in your sample. Soil Physics 2010 Dh Measuring soil particle sizes: Sedimentation 2 s w r g v 9h 2 Assumptions: Particles are smooth spheres Particles fall slowly (laminar flow) All particles have the same density Dilute: particles don’t affect each other Fluid is otherwise at rest Terminal velocity is reached instantly Soil Physics 2010