Beer Bottle Condensation: What Forces Produce Droplets?

philosophy, Physics
Dan asked us¹... "My question concerns condensation droplets. What dictates how droplets form, then combine with each other? When you blow warm breath onto a cool surface, at first nothing appears to happen. Keep it up and droplets appear. These small droplets merge into bigger droplets. What physical laws dictate how this occurs? Also, what role does gravity play on vertical surfaces such as a chilled bottle of beer, producing tiny rivulets of moisture running down the sides?" Initial Commentary The answer, which follows, although it has some basis in well-known physical principles, depends in part upon observation, mental visualization, and (finally) blatant speculation. This is an interesting procedure, since so many of life’s mundane occurrences are in reality quite fascinating when closely examined. Initial Condensation We breathe in and…
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Capillary Action from the Forces of Adhesion and Cohesion

Chemistry, Plants
What is capillary action? The easiest way to define it is to give the simplest example of it at work. A capillary is a tube with a fine bore, typically less than a millimeter. For the purpose of our discussion, we will use a scientist's glass capillary tube, which is both straight and clear. The liquids we will discuss as examples are water and mercury. Not All Liquids Exhibit Capillary Action Take note of Figure 1. Two capillary tubes (not drawn to scale) are immersed in liquid – the left tube in water, the right in mercury. The water rises up its tube and forms a concave meniscus at top. The mercury does not rise up its tube. It forms what looks like the upper portion of a sphere –…
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What Makes Ice Slippery Compared to Other Solids? A Combination of Factors?

Chemistry, Physics
[caption id="attachment_17673" align="alignleft" width="380"] Image: Tvb hof - Own work, CC BY-SA 3.0[/caption] “Be careful if you will be driving this evening,” the weather forecaster declares. “The road will be a sheet of ice.” Whether tar and gravel, asphalt, or concrete, roads most of the year are not slippery. Yet come winter, those roads can be dangerously slippery. What makes ice and icy roads so slippery? What Makes Ice Slippery One line of thinking is that ice is slippery because water (H₂O) expands as it freezes. When a heavy object rests upon a sheet of ice, the pressure imparts energy to the molecules immediately beneath the weight, pressing them down, melting it. The water acts much like a lubricant, making the ice slippery. In truth, if the ice is reasonably…
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Polymeric Water Clusters

Chemistry, Physics
[caption id="attachment_12642" align="alignright" width="480"] Ice floating in water. Image Morguefile by larryfarr[/caption] Polymeric water clusters? What are they? And what do they have to do with life? There’s no point in discussing how important water is to life. It is the single most necessary compound for the existence and survival of human, animal, and plant life. Why Special? What makes water special is its unusual behavior. Typical of liquids, as water approaches freezing, its density increases. Yet just before freezing, it suddenly decreases. This is why ice floats. Once it forms, ice insulates the water beneath it. It prevents large bodies of water from freezing solid. How? Hydrogen bonding. To understand hydrogen bonding, we must first consider the shape of the water molecule. Geometry of a Water Molecule A water…
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Understanding the Spherical Polar Coordinate System

Mathematics
[caption id="attachment_9496" align="alignright" width="480"] A cone in the spherical polar coordinate system. CC-SA 3.0 Unported by Lantonov[/caption] Do you have a basic knowledge of the spherical polar coordinate system? A coordinate system provides a way to describe and plot math functions using two or three variables. If there are two variables the graph is 2D. If there are three variables, the graph is 3D. The Cartesian Coordinate System The most familiar coordinate system is the Cartesian coordinate system. Typical variable names are x and y in 2D (although variables can have any name), and x, y, and z in 3D. Every point of every 2D function has a unique value in (x, y). Every 3D function similarly has a unique value in (x, y, z). The Polar Coordinate System This…
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Oil and Water Do Not Mix – Why?

Chemistry
[caption id="attachment_8586" align="alignright" width="440"] Oil and water just plain do not mix.[/caption] Oil and water do not mix! Some liquids are miscible; that is, they mix completely. Other liquids do not permanently mix. They are immiscible. The best known example of this is oil and water. “Putting those two together is like mixing oil and water.” This means that for practical purposes, the two don’t get along at all. Why Don’t They Mix? Oil and water don’t mix for a basic physical reason curiously easy to explain by comparison with a magnet. Consider first the formula, and then the structure, of water and we’ll see how this is so. The Formula of Water Water is most commonly written H₂O. Two hydrogen atoms (H) are combined with one oxygen atom (O).…
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Introduction to Cylindrical Coordinates

Mathematics
What are cylindrical coordinates? A coordinate system is a system that provides a way to describe points and other features of geometric figures in Euclidean space. Generally the best coordinate system is that system which adequately does the job in simplest fashion. In this article, we will use (r, Φ, z) for our new coordinate system. Many use this, but others use a different assortment of letters, unfortunately. Forewarned is forearmed. Cylindrical Coordinates - Introspection When we're working in two dimension, we are able to draw our coordinate axes using the sheet of the paper, representing a plane. Two orthogonal axes are drawn, one horizontal the other vertical. When using r and Φ the way we view the axes is really different from how we view them when they represent x…
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