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Why anyone can make a sandcastle

Feb. 13, 2008
Courtesy Max Planck Society
and World Science staff

An­y­one build­ing sand­cas­tles on the beach will need a lit­tle skill and ima­gina­t­ion, but not an in­struc­tion man­u­al. The ex­act amount of wa­ter is ac­tu­ally fa­irly un­im­por­tant to the pro­cess, as lab­o­r­a­to­ry mea­sure­ments have con­firmed.

Struc­ture of the flu­id sur­round­ing glass beads 0.8 mil­lime­tres wide, as re­vealed by X-ray mi­cro­to­mog­raphy. A vi­deo here shows this struc­ture turn­ing in space to re­veal its full three-di­m­en­sion­al ap­pear­ance. (Requires Quick­time. Im­age cour­te­sy Max Planck Inst. for Dy­nam­ics and Self-Or­g­an­i­s­a­tion; vi­deo cour­te­sy Na­ture Ma­te­ri­als)
But why that’s so, is un­clear. The in­ter­nal struc­ture of the liq­uid “glu­ing” the grains to­geth­er varies enor­mously de­pend­ing on how much wa­ter there is, re­search­ers say. Yet the sand easily re­tains the same ap­prox­i­mate stiff­ness with mois­ture rang­ing from one to 10 per­cent or more.

Now re­search­ers have de­vised an ex­plana­t­ion. The wa­ter’s “stick­i­ness,” or abil­ity to bind sand grains to­geth­er, de­creases as its amount in­creases: that much is ob­vi­ous to an­y­one who has tried to make tow­ers from the sog­gy goop freshly scooped from un­der the waves. 

What the scientists found is that in­creas­ing the amount of wa­ter makes up for the de­creas­ing stick­i­ness, as long as more of each sand grain is wet.

“These prop­er­ties are not only sig­nif­i­cant to the build­ing of sand­cas­tles,” said study lead­er Stephan Her­ming­haus of the Max Planck In­sti­tute for Dy­nam­ics and Self-Organisa­t­ion in Göt­tin­gen, Ger­ma­ny. 

“They are rel­e­vant to the phar­ma­ceu­ti­cal and food-production in­dus­tries and help us to un­der­stand cer­tain nat­u­ral catas­tro­phes, such as land­slides. Wet gran­ules are rel­e­vant in many fields and we now have a bet­ter un­der­standing of their me­chan­i­cal prop­er­ties.”

In new ex­pe­ri­ments, Her­ming­haus and col­leagues stud­ied the de­tails of the flu­id struc­tures us­ing a tech­nique called X-ray mi­cro­to­mog­ra­phy, al­so used in med­i­cine, where it’s called com­put­er to­mog­ra­phy. Sci­en­tists X-ray an ob­ject from var­i­ous an­gles to pro­duce an out­line im­age si­m­i­lar to a stand­ard X-ray. A com­put­er eval­u­ates all of these im­ages and de­ter­mines which kind of three-di­men­sion­al struc­ture the ob­ject must have to pro­duce the out­line im­ages. 

A strong X-ray source pro­duces im­ages with res­o­lu­tion in the thou­sandths of a mil­li­me­tre, enough to see the “tiny, highly-complex flu­id struc­tures that form in a moist gran­ule,” the re­search­ers said in an an­nounce­ment of the find­ings is­sued Feb. 11. They used glass beads the size of sand grains in place of real sand to sim­pli­fy their anal­y­sis, pub­lished in the Feb. 10 ad­vance on­line is­sue of the re­search jour­nal Na­ture Ma­te­ri­als.

When small amounts of wa­ter are added to sand, the wa­ter fails to fully pen­e­trate and there­fore does­n’t push all the air out of the spaces be­tween sand grains. As a re­sult, the re­search­ers said, air and wa­ter co-exist with the sand, form­ing an an in­tri­cate, stringy struc­ture amid the grains. The liq­uid oc­cu­pies only the space di­rectly around the con­tact points be­tween grains, as for sta­bil­ity “it tries to sur­round it­self with as much ‘grain’ as pos­si­ble,” the sci­en­tists ex­plained. Air takes up the rest of the space.

As more wa­ter is added, more air is pushed out. Then the forc­es bind­ing sand grains to­geth­er, called cap­il­lary forc­es, be­come weaker. Cap­il­lary forc­es re­sult from both an at­trac­tion that liq­uid molecules have for a neigh­bor­ing sol­id, called ad­he­sion forc­es, and at­trac­tion be­tween molecules of the liq­uid it­self, called co­he­sion forc­es. More wa­ter leads to fee­bler cap­il­lary forc­es be­cause the amount of sur­face ar­ea in con­tact with the flu­id goes down com­pared to the amount of flu­id it­self. The ra­tio of these quan­ti­ties af­fects the strength of the forc­es.

But with more wa­ter, enough more of the sand sur­face is wet to com­pen­sate for forc­es’ weak­en­ing, ac­cord­ing to Her­ming­haus and col­leagues. Only af­ter a great amount of grain sur­face is wet does fur­ther ad­di­tion of wa­ter fail to make up for the weak­en­ing forc­es. Then the cas­tle is ready for a tum­ble.

* * *

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Anyone building sandcastles on the beach will need a little skill and imagination, but not an instruction manual. The exact amount of water is actually fairly unimportant to the process, as laboratory measurements have confirmed. But why that’s so, is unclear. The internal structure of the liquid “gluing” the grains together varies enormously depending on how much water there is, researchers say. Yet the sand easily retains about the same stiffness with moisture ranging from 1% to 10% or more. Now researchers have devised an explanation. The water’s “stickiness,” or ability to bind sand grains together, decreases as its amount increases: that much is obvious to anyone who has tried to make towers out of the soggy sand-goop freshly scooped from under waves. What the researchers found is that up to a point, increasing the amount of water makes up for its decreasing stickiness. “These properties are not only significant to the building of sandcastles,” said study leader Stephan Herminghaus of the Max Planck Institute for Dynamics and Self-Organisation in Göttingen, Germany. “They are relevant to the pharmaceutical and food-production industries and help us to understand certain natural catastrophes, such as landslides. Wet granules are relevant in many fields and we now have a better understanding of their mechanical properties.” In new experiments, Herminghaus and colleagues studied the details of the fluid structures using a technique called x-ray microtomography, also used in medicine, where it’s called computer tomography. Scientists x-ray an object from various angles to produce an outline image similar to a standard x-ray. A computer evaluates all of these images and determines which kind of three-dimensional structure the object must have to produce the outline images. A strong x-ray source produces images with resolution in the thousandths of a millimetre, enough to see the “tiny, highly-complex fluid structures that form in a moist granule,” the researchers said in an announcement of the findings issued Feb. 11. They used glass beads the size of sand grains in place of real sand to simplify their analysis, published in the Feb. 10 advance online issue of the research journal Nature Materials. When small amounts of water are added to some sand, the water fails to fully penetrate and therefore doesn’t push all the air out of the spaces between sand grains. As a result, the researchers said, air and water co-exist with the sand, forming an an intricate, stringy structure amid the grains. The liquid occupies only the space directly around the contact points between grains, as for stability “it tries to surround itself with as much ‘grain’ as possible,” the scientists explained. Air takes up the rest of the space. As more water is added to the sandpile, more air is pushed out. Then the forces binding sand grains together, called capillary forces, become weaker. Capillary forces result from both an attraction that liquid molecules have for a neighboring solid, called adhesion forces, and attraction between molecules of the liquid itself, called cohesion forces. More water leads to feebler capillary forces because the amount of surface area in contact with the fluid goes down compared to the amount of fluid itself. The ratio of these two quantities affects the strength of the forces. But with more water, enough more of the sand surface is wet to compensate for forces’ weakening, according to Herminghaus and colleagues. Only after a great amount of grain surface is wet does further addition of water fail to make up for the weakening forces. Then the castle is ready for a tumble.