{"product_id":"cheeriosa-cheerios-effect","title":"Cheeriosa – The Cheerios Effect \/ Capillary Length Physics Sticker","description":"\u003cp\u003eCheeriosa, a cereal-raft fae, watches the floating rings in her milk-lake drift together into rafts.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eFloating cereal clumps together and sticks to the bowl's edge. It is not magnetic or electric: each floating ring bends the liquid surface into a meniscus. A neighbouring ring sitting on that tilted surface is pushed along it, by buoyancy and surface tension, towards the other, so rings drift together. Dominic Vella and L. Mahadevan analysed this in “The ‘Cheerios effect’” (Am. J. Phys. 73, 817, 2005). The distance over which a meniscus reaches is set by the capillary length.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eℓ\u003csub\u003ec\u003c\/sub\u003e = √(γ \/ ρg)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eℓ\u003csub\u003ec\u003c\/sub\u003e: capillary length (m)\u003c\/li\u003e\n\u003cli\u003eγ: surface tension (N\/m)\u003c\/li\u003e\n\u003cli\u003eρ: liquid density (kg\/m³)\u003c\/li\u003e\n\u003cli\u003eg: gravitational acceleration (m\/s²)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eFor clean water at room temperature (γ ≈ 0.072 N\/m, ρ ≈ 1000 kg\/m³) the capillary length is about 2.7 mm, so the attraction is strong only when objects are within a few millimetres of each other.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The rule is like attracts like: two objects with menisci curving the same way drift together, while a floating object and one that sinks the surface the opposite way repel. Milk is not pure water, so its surface tension is lower and the length a little shorter.\u003c\/p\u003e\u003ch3\u003eOn the sticker\u003c\/h3\u003e\u003cp\u003eCheeriosa bends over glowing floating rings that light her face amber from below. Printed text: \u003cstrong\u003eCHEERIOSA\u003c\/strong\u003e with the line \u003cstrong\u003eℓ = √(γ\/ρg)\u003c\/strong\u003e. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50963798753383,"sku":"13014896274029972032","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50963798786151,"sku":"37218909962015893281","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50963798818919,"sku":"18713523663441267107","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50963798851687,"sku":"18442642329481890380","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/13103643898759991163_1200.jpg?v=1793655265","url":"https:\/\/pixelatedphysics.com\/it\/products\/cheeriosa-cheerios-effect","provider":"Pixelated Physics","version":"1.0","type":"link"}