# What hap­pens when a rain­drop hits a pud­dle?

The Tribune (SLO) - - Opinion - BY NATE BAR­LOW

Have you ever taken a walk through the rain on a warm spring day and seen that per­fect pud­dle? You know, the one where the rain­drops seem to touch down at just the right pace, caus­ing a dance of van­ish­ing cir­cles?

Even be­fore I en­tered the field of fluid flow re­search nearly 15 years ago, I was fas­ci­nated by the waves that ap­pear af­ter a rain­drop hits a pud­dle.

As I be­came focused on the study of un­sta­ble waves in liq­uid sheets – geared toward mit­i­gat­ing un­de­sir­able waves in industrial coat­ing and at­om­iza­tion pro­cesses – my fas­ci­na­tion with pud­dle waves turned into an ob­ses­sion. What is go­ing on? Where does the pat­tern come from? Why does the impact of rain in a pud­dle look dif­fer­ent than when rain falls else­where, like in a lake or the ocean?

It turns out that it all has to do with some­thing called dis­per­sion.

In the con­text of wa­ter waves, dis­per­sion is the abil­ity of waves of dif­fer­ent wave­lengths to each move at their own in­di­vid­ual speeds. Look­ing down on a pud­dle, we see a col­lec­tion of such waves mov­ing to­gether as one rip­ple in the wa­ter.

When a rain­drop touches down, imag­ine it as a “ding” to the wa­ter sur­face. This ding can be ide­al­ized as a packet of waves of all dif­fer­ent sizes. Af­ter the rain­drop falls, the packet’s waves are ready to be­gin their new life in the pud­dle.

How­ever, whether we see those waves as rip­ples de­pends on the body of wa­ter that the rain­drop lands on. The num­ber and spac­ing of rings that you see de­pends on the height of the pud­dle. This has been ver­i­fied in some very cool rip­ple tank ex­per­i­ments, where a drop of the same ve­loc­ity falls into a con­tainer with wa­ter at dif­fer­ent depths.

Shal­low pud­dles en­able rip­ples, because they are much thin­ner than they are wide. The bal­ance be­tween the sur­face force – be­tween the wa­ter pud­dle and the air above it – and the grav­i­ta­tional force tips in fa­vor of sur­face force. This is key, since the sur­face force de­pends on the cur­va­ture of the wa­ter sur­face, whereas the grav­i­ta­tional force does not.

An ini­tially still shal­low pud­dle becomes curved at the sur­face af­ter the rain­drop hits. The sur­face force is dif­fer­ent for long waves than for short ones, caus­ing waves of dif­fer­ent sizes to sep­a­rate into rip­ples. For shal­low pud­dles, the long waves move slowly away from the point of impact, while the short waves move fast, and the really short waves move really fast, becoming tightly packed at the perime­ter. This cre­ates the en­chant­ing pat­tern that we see.

Rain­drops may re­act dif­fer­ently in other sit­u­a­tions. Imag­ine that rain is hitting a lake or ocean – or those deep pot­hole pud­dles that re­quire ga­loshes. Here, the rain­drop hits the wa­ter, but the force due to grav­ity becomes more im­por­tant. It moves waves of all sizes at the same speed, which may over­power the rip­pling ef­fect due to the sur­face force.

The study of sur­face­force-driven waves is im­por­tant for ap­pli­ca­tions such as coat­ing pro­cesses in­volved in mak­ing batteries and so­lar cells.

The beauty of pud­dle waves is no small thing by it­self. By con­nect­ing na­ture with its pri­mal lan­guage – math­e­mat­ics – we gain ac­cess to its con­trol panel, al­low­ing us to ob­serve ev­ery lit­tle de­tail, un­cov­er­ing all the se­crets.