Hello, everyone. Last month I discussed a first-principles
empirical equation for predicting if corrosion could
occur. However, the equation only indicates if corrosion
might occur and provides no information on how fast corrosion
will occur and the type or types of package corrosion that are
The corrosion rate through spray package materials determines
the package service lifetime—the length of time before a spray
package leaks. Currently there are nine known factors that influence
the magnitude of spray package corrosion rates:
1. Water pH
2. Type of package metal
3. Surface tension
4. Chemical activity for each electrochemically active (ECA)
ion and molecule in a formula
5. Package metal surface treatment
6. The cathode-to-anode area ratio
7. Emulsion stability
8. Package age (time)
9. Corrosion inhibitors (both added and ingredients that
unexpectedly act as inhibitors)
These factors could contribute to or cause corrosion either independently
or synergistically with one or more of the other factors.
One possible empirical equation for predicting spray package
corrosion rates is listed below. Temperature is not included in
this equation because increasing temperature typically does not
accelerate spray package corrosion rates.
The first symbol in the equation, ß, is a conversion constant. The
corrosion penetration rate could be inches/per year or millimeters/
per year, depending on the units for ß.
The Γ symbol indicates that a factor is the multiplication of
multiple components. In addition, all factors are multiplied
together instead of added to account for synergy between one or
The letters equal to one (e.g., h = 1) under the Γ symbol and
the letters above the Γ symbol indicate that there are ranges of
components for each factor. For example, the surface tension
factor for a formula with three surface-active ingredients is equal
to the multiplication of the probabilities for each surface-active
ingredient—or stated in the equation form:
Surface tension factor = Ψ4 (surface tension1)f(1) times Ψ4(surface
tension2)f(2) times Ψ4(surface tension3)f(3)
Notice that each of the nine factors has multiple components.
Let’s briefly discuss the significance of each factor and its components.
The first factor estimates how pH affects the corrosion rate magnitude.
The symbol Ψ1 is the probability that formula water or
contaminant water pH will decrease or increase the corrosion rate
and the exponent “a” determines how much pH affects the rate.
The exponent is typically a single number.
Spray package metals could be tinplated steel, tin-free-steel,
aluminum and aluminum foils. Both coated/laminated metals
and uncoated metals corrode at different rates when exposed to
the same formula. Consequently, the second factor accounts for
how different types of metals influence the rate of spray package
corrosion. The exponent f(h) is a complex function that generates
a single number for each metal type exposed to a specific formula.
W. Stephen Tait, Ph.D.
Chief Science Officer & Principal Consultant,
Pair O Docs Professionals, LLC
Predicting corrosion with
first principles–Part 2
28 Spray February 2019