Equation of Kelvin-Thompson states that the pressure of saturated vapor over a curved medium depends on the radius of curvature of the interphase surface. A similar equation can be obtained for the dependence of the solubility of droplets or crystals on their size (the Gibbs-Freindlich-Ostwald equation.) Obviously, the Kelvin barrier is a difference in size when the curvature effect is present and absent.The authors of the equations would be offended if this is attributed only to Kelvin.

To add a touch to Dr. Mirigorod's excellent description ... my workaday understanding of the Kelvin barrier is that it is kind of an inflection point, the way that the barrier between the troposphere and the stratosphere is defined as the nonlinearity of the thermal decline with altitude. The Kelvin barrier is like that, it's the point where a particle needs a nonlinear amount of energy to "bump" it up over the radius barrier that prevents the particle from growing any larger. For instance, a certain compound may grow easily to about 15 nanometers, but to grow any larger, the particle would need an external energy bump to get it any larger. And then once it's a bit larger, it then grows increasingly easier into an Aitken Mode particle up to about 80 nanometers or so, then it might or might not have another non-linearity to grow into an accumulation mode particle. (And some Accumulation mode particles may have come from a larger particle, not all of them grow into that.)

But this actual radius for the Kelvin barrier varies by material due to the entire bouquet of complexity that Mother Nature puts into the world ... it might have some polarity, or some stacking defects, it might have some odd oscillation effects that might put the Kelvin barrier at 8 nanometers, or maybe at 25 nanometers ... the point being that every material has a subtly different surface energy that then dictates at what radius the Kelvin barrier will be.

One other way that I describe the Kelvin barrier is with what I call "the snowdog effect." A snowdog usually starts out with all the intentions of an eager 8 year old as a snowman or a snowwoman. But the child soon finds that the snowballs that he or she rolled are too heavy to mount on top of one another, so the inventive child then places the enormous snowballs next to each other, like a caterpillar or a dog. The snowballs are often too heavy to lift due to the ease that the child had in forming the behemoths. At first, the child had to struggle to get the snowball to grow in size. They would roll it and roll it but it wouldn't increase in size, because the radius of curvature of the snowball was too low, and the new snowflakes didn't want to bulk up to the larger snowball because the small radius of curvature of the snowball shrugged off each snowflake for lack of contact area. That's the snowball's "Kelvin barrier." But then once the child struggles and manually packs some snow onto the ball to grow the effective radius of curvature, the would-be snowdog builder finds that the ball can then be rolled with ease, and pick up snow easily. And the larger the snowball gets, the easier it gets to grow, because the radius of curvature continues to increase with snowball size. Within a minute or two, the child finds that he or she can no longer push the snowball. The second snowball -- if allowed to grow too large in this way -- will be impossible for the child to lift, and thus the genesis of the snowdog.

In the case of the snowball, the "energy" applied to bond the new snow to the bulk material is -- at that macroscopic scale -- from the potential energy of the snowball pushing down onto the snowflakes on the ground. Some of the energy is transferred, it may melt the ground snow a touch and refreeze, and then the bonding is complete. But this process similarly happens on a nanoscale, except instead of the potential energy, it's molecular forces, for instance van der Waals forces.