I have long been an advocate of foliar feeding nutrients as one of the most financially rewarding applications that can be made to a crop, and the practice has become mainstream in many regions. 

Thus, it comes as a surprise that in some areas growers still consider foliars to be an ineffective tool. I would suggest they are ineffective only when they are not properly designed and applied. 

Some of the first published papers on foliar feeding I have read were based on research conducted for the Atomic Energy Commission by Sylvan H Wittwer and Harold B Tukey in the late ‘40s and ‘50s. Their congressional testimony is as relevant and exciting today as when it was first published. (Approximately 1952?)

I cleaned up the document and made some slight edits to make it more readable, but kept all the underlining in the original report. You can read the 24 page report (and bibliography) here. You will find valuable and intriguing information. Here are some excerpts:

• not only can plants absorb nutrients through the roots, but also through the foliage, the fruit, the twigs, the trunk, and even the flowers.
• the most exciting news is the foliage feeding of plant—that plants can take up nutrients through the foliage. Here is a case where the farmer has really gotten ahead of the scientist as so often happens. He has learned that foliage feeding is helpful and he has adopted the practice. 
• The first point I should like to make is that the materials do enter the leaves rather easily.
• In the final analysis, we find that a leaf is a very efficient organ of absorption. We find that the materials move into the upper surface of the leaf as well as the lower surface. We find that it enters at night and during the daytime. Further, we find the leaf surface of a 12-year-old apple tree in Washington State to be equivalent to one-tenth of an acre, even though that tree only occupies about one-hundredth of an acre. So there is a large feeding area.
• Not only do these materials enter rather easily—and this is interesting, too, because all the textbooks used to tell how the plant was covered by an impervious cuticle—now we find textbooks are re-written and the leaf is reported as a beautiful mechanism for absorption. 
• If we apply it to the leaf we find it moves downward through the plant—at the rate of a foot an hour. It is very interesting that it moves so freely. If we apply it to a middle leaf it moves both ways very effectively.
• We have seen that materials are absorbed by the plant and move rather freely in the plant. The amounts may at first seem relatively small, but to off set this handicap, the efficiency is high. In fact, this is the most efficient method of applying fertilizer to plants that we have yet discovered. If we apply these materials to the leaves in soluble forms, as much as 95 percent of what is applied may be used by the plant. If we apply a similar amount to the soil, we find about 10 percent of it to be used. 
• For example, the soil may be cool and low in phosphorus at just the time it is needed by a transparent vegetable or strawberry plant. Or there are cases where the soil locks up certain materials that are applied, like potash and magnesium. Under such conditions we find leaf application very significant and very effective.
• But now we are highly suspicious that here may be a case where materials are actually being leached out of the leaves maybe by overhead irrigation, maybe by rain, and having a profound effect upon the crop.