Meaning
Continuous probability density modeling maps skewed physical variables whose logarithms conform to a standard Gaussian bell curve. In polymer characterization, a log-normal distribution describes particle size spreads in recycled regrind and molar mass profiles from gel permeation chromatography. The mathematical formulation bounds values strictly above zero, capturing physical phenomena that cannot yield negative physical quantities.
Application stops where structural degradation creates bimodal distributions that require multi-peak fitting models.
Particle Measurement
Mechanical granulators chop scrap sprues into irregular fragments. Applying a log-normal distribution to sieve analysis data enables quality engineers to predict bulk density and hopper flow behavior. Mathematical transforms convert asymmetric size measurements into symmetric logarithmic metrics, allowing standard statistical calculations.
Skewed distributions highlight fine powder fractions that cause premature vent clogging in injection moulding barrels.
Viscosity Modeling
Melt flow properties in long chain polymers reflect underlying molecular weight dispersion. Fitting a log-normal distribution to gel permeation chromatography data provides exact values for weight-average molecular weight and polydispersity indices. Shear thinning calculations depend on these broad molecular tails to model wall shear stress inside hot runner channels.
Process Tolerance
Statistical process control charts track non-negative moulding defects such as sink mark depth or cycle time extensions. Utilizing a log-normal distribution prevents false control alarms caused by assuming fictitious negative dimensions.
