Water balloons may seem like a trivial matter. A toy for mischievous kids in summer. But for scientists, the behavior of balls of liquid wrapped in a thin elastic membrane is critical to everything from understanding blood cells to fighting fires.
The impact of water balloons, shot through an air cannon at a wall and captured through high-speed photography, revealed a new physics for a broad range of engineering problems, from understanding blood cells to fighting fires. Images courtesy of the researchers
Using custom-made air cannons and high-speed photography, Princeton researchers have established the definitive physical rules governing capsule impact, a research area that had gone virtually unexplored until now. The results, published March 16 in Nature Physics, reveal a surprising relationship between the behavior of capsules and water droplets. Where capsules are held together by the tension of a membrane, water droplets are held together by a force called surface tension. The researchers used that connection to adapt the well understood mathematics describing water droplets to engineering problems related to capsules.
“The most surprising thing is that the impact looks a lot like that of a drop,” said Etienne Jambon-Puillet, a postdoctoral researcher and the study’s first author. “Most people who study capsules resort to complex numerical simulations to model their deformation, where here we have derived a simple model, something that is easy to understand.”
During his Ph.D. research at Sorbonne University, Jambon-Puillet was studying the behavior of water droplets covered with small beads. Searching for a simpler way to understand the complicated problem before him, he looked to the literature to find a model for how elastic capsules work. But he came up empty. Perplexed and intrigued, he was forced to set the capsules question aside for a few years and move on to other problems.
When he joined Pierre-Thomas Brun’s Liquids and Elasticity Laboratory at Princeton, he saw the perfect opportunity to turn back to that question from his graduate school work. When a water balloon strikes a surface, what happens to the elastic shell?
“The study really makes sense in the broader context of fluid mechanics,” said Brun, an assistant professor of chemical and biological engineering and the paper’s senior author. “People for decades have been wracking their brains studying drop impact, and somehow Etienne found that there was this little puzzle that was completely untouched.”
To control the experiment’s parameters, the team custom-made elastic capsules about the size of a gumball. They then filled those to exact capacity – without stretching them – and smashed the balloons against a wall at around 100 miles per hour using a small air cannon. With the camera rolling at 20,000 frames per second, the researchers were able to take fine measurements of the thin shell as it made impact. They repeated the experiment with two different kinds of liquids, glycerol and honey, to see how the dynamics changed with greater viscosity. Again, the analogy to liquid drops held.
The team then turned to commercial water balloons to see what happens when an elastic shell is stretched with fluid, the way we typically think of filling balloons with water. Not so full you can’t throw it, but full enough to burst on impact, soaking an unsuspecting friend. (Whether that friend remains friendly is another story). It turns out there is a critical value at which a balloon traveling at a given speed must be stretched for it to burst. Anyone who’s ever thrown a dud, watching it bounce off a would-be victim and roll sadly away, knows the importance of this critical value. You either needed to fill it more or throw it harder.
Much like the rest of us, when it comes to water balloons and their ilk, engineers have been flying blind, according to Brun. Those critical values had never been formalized.
A range of technologies rely on similar fluid-filled capsules, and as bioengineering efforts become ever more sophisticated, that number of technologies is certain to grow. The stomach, the bladder, the lungs, blood cells – many organs and essential biological functions rely on such thin, expandable fluid-filled chambers.
Brun and his team have given researchers a mathematical framework to understand how these objects deform with impact. And for the engineers working on these problems, the best part is that the framework is already familiar. It was just hiding in plain sight.
“The model is fairly simple,” Brun said. “But that’s what’s beautiful about it.”
In addition to Brun and Jambon-Puillet, Trevor J. Jones, a graduate student in chemical and biological engineering, contributed to the experiment. The research was funded in part by a grant from the Princeton Center for Complex Materials (NSF MRSEC).
Huenda baluni za maji zikaonekana kuwa jambo dogo. Mchezo kwa ajili ya watoto mischievous katika majira ya joto. Lakini kwa wanasayansi, tabia ya mipira ya kioevu iliyofungwa katika utando mwembamba wa elastic ni muhimu kwa kila kitu kutoka kuelewa chembe za damu hadi kuzima moto. "Madhara ya puto la maji, lililopigwa na bunduki ya hewa kwenye ukuta na kupigwa picha kwa kasi kubwa, ilifunua fizikia mpya kwa ajili ya matatizo mbalimbali ya uhandisi, kuanzia kuelewa chembe za damu hadi kuzima moto.""" Kwa kutumia bunduki za hewa zilizotengenezwa kwa ajili ya matumizi ya watu na upigaji picha wa kasi, watafiti wa Princeton wameweka sheria za kimwili za kudhibiti athari za capsule, eneo la utafiti ambalo lilikuwa halijachunguzwa hadi sasa. Matokeo ya utafiti huo, yaliyochapishwa katika jarida la Nature Physics, yanafunua uhusiano wa kushangaza kati ya tabia ya vidonge na matone ya maji. Kapsuli huunganishwa pamoja kwa nguvu ya utando, lakini matone ya maji huunganishwa pamoja kwa nguvu inayoitwa nguvu ya uso. Watafiti walitumia uhusiano huo kurekebisha hesabu inayoeleweka vizuri inayoelezea matone ya maji kwa matatizo ya uhandisi yanayohusiana na vidonge. "Kitu cha kushangaza zaidi ni kwamba athari inaonekana sana kama ile ya tone", alisema Etienne Jambon-Puillet, mtafiti wa baada ya udaktari na mwandishi wa kwanza wa utafiti huo. "Watu wengi ambao hujifunza vidonge hutumia mifano ngumu ya tarakimu kuiga deformation yao, ambapo hapa tumepata mfano rahisi, kitu ambacho ni rahisi kuelewa. ""Wakati wa utafiti wake wa PhD katika Chuo Kikuu cha Sorbonne, Jambon-Puillet alikuwa akisoma tabia ya matone ya maji yaliyofunikwa na shanga ndogo." Alipotafuta njia rahisi ya kuelewa tatizo hilo gumu, alitafuta katika vitabu vya kisayansi mfano wa jinsi vidonge hivyo vinavyofanya kazi. Lakini hakupata chochote. Kwa sababu ya kuchanganyikiwa na kuvutiwa, alilazimika kuahirisha swali la vidonge kwa miaka michache na kuendelea na matatizo mengine. Alipojiunga na Pierre-Thomas Brun's Liquids and Elasticity Laboratory huko Princeton, aliona fursa nzuri ya kurudi kwenye swali hilo kutoka kwa kazi yake ya shule ya kuhitimu. Puto la maji linapogonga uso, ni nini hutokea kwa ganda lenye kunyoosha? "Utafiti huo una maana kweli katika muktadha mkubwa wa mitambo ya umajimaji", alisema Brun, profesa msaidizi wa uhandisi wa kemikali na kibiolojia na mwandishi mwandamizi wa karatasi hiyo. "Watu kwa miongo kadhaa wamekuwa wakichanganya ubongo wao kusoma athari ya kushuka, na kwa njia fulani Etienne alipata kwamba kulikuwa na fumbo hili dogo ambalo halikuchukuliwa kabisa. ""Kudhibiti vigezo vya majaribio, timu ilifanya vifuniko vya elastic vya kawaida kuhusu ukubwa wa mpira wa gumbaa." Kisha wakajaza hadi kufikia uwezo wao kamili bila kuwakaza na kuipiga ukuta kwa mwendo wa karibu maili 100 kwa saa kwa kutumia bunduki ndogo ya hewa. Kamera hiyo ilipokuwa ikipiga picha kwa kasi ya picha 20,000 kwa sekunde, watafiti waliweza kupima kwa uangalifu ganda hilo laini lilipokuwa likigonga. Walirudia jaribio hilo kwa kutumia aina mbili tofauti za kioevu, gliseroli na asali, ili kuona jinsi mwendo ulivyobadilika na viscosity kubwa. Kwa mara nyingine tena, ulinganifu huo na matone ya umajimaji ulithibitika. Kisha, watafiti walitumia puto za maji za kibiashara ili kuona nini kinatokea wakati shell ya elastic inapofungwa na kioevu, njia ya kawaida ya kujaza puto na maji. Si kamili hivyo huwezi kutupa, lakini kamili ya kutosha kulipuka juu ya athari, soaking rafiki unsuspecting. (Je, rafiki huyo hubaki kuwa rafiki ni hadithi nyingine). Kwa mfano, kuna kiwango cha juu ambacho puto linaloenda kwa kasi fulani lazima liwe na urefu wa kutosha ili liweze kupasuka. Mtu yeyote ambaye amewahi kutupa dud, kuangalia ni bounce mbali na uwezekano wa mhasiriwa na roll huzuni mbali, anajua umuhimu wa thamani hii muhimu. Ili iwe ni lazima uijaze zaidi au uitupe kwa nguvu zaidi. "Kama ilivyo kwa wengine wetu, wakati wa puto la maji na aina zao, wahandisi wamekuwa wakiruka kwa upofu, kulingana na Brun.""" Maadili hayo muhimu hayakuwa yamewahi kutambuliwa rasmi. Teknolojia nyingi zinategemea vidonge vinavyofanana vilivyojaa umajimaji, na kadiri jitihada za uhandisi wa kibiolojia zinavyozidi kuwa za hali ya juu, ni hakika kwamba idadi hiyo ya teknolojia itakua. Mkojo, kibofu cha mkojo, mapafu, chembe za damu - viungo vingi na kazi muhimu za kibiolojia hutegemea vyumba hivyo vyepesi vinavyoweza kupanuka vilivyojaa umajimaji. Brun na timu yake wametoa watafiti mfumo wa hisabati kuelewa jinsi vitu hivi deform na athari. Kwa wahandisi wanaofanya kazi katika sekta hii, ni muhimu kujua kwamba mfumo wa kazi ni rahisi. Ilikuwa tu ikijificha kwa macho ya watu wote. "Mfano ni rahisi sana", Brun alisema. "Lakini hiyo ndiyo jambo zuri kuhusu hilo". Mbali na Brun na Jambon-Puillet, Trevor J. Jones, mwanafunzi wa kuhitimu katika uhandisi wa kemikali na kibiolojia, alichangia jaribio hilo. Utafiti huo ulifadhiliwa kwa sehemu na ruzuku kutoka Kituo cha Princeton cha Vifaa Vikali (NSF MRSEC).