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They seem to have increased friction after going through a dishwasher. The unpleasant (to me) squeaky feel is probably slip-stick friction exciting resonance in the glassware. But why? What has happened to the surface of the glass to make it like this?

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    $\begingroup$ Unwashed dishes have oils, sugars, and all other manner of filth and grime. Thus, a lower coefficient of friction so they don't squeak when you rub your finger across them. After washing, they are more free of these oils, etc and ceramics and glass regain their high coefficient of friction, which allows for them to squeak via the mechanism you mentioned. Thus, "squeaky clean" (made this a comment because I don't want to detract from John's awesome answer) $\endgroup$ – Jim Nov 26 '14 at 14:29
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A completely clean silica surface has a very high surface energy and a very high coefficient of friction. However silica surfaces adsorb pretty much anything at the least excuse, so glassware from your cupboard will have a layer of various molecules adsorbed from its environment, and this greatly reduces the coefficient of friction.

Dishwash powder is pretty aggressive, which is not surprising when you consider what it has to wash off. In my time working in the industry the powders used high concentrations of sodium and potassium hydroxide and would not only strip the glass clean but actually dissolve off a layer of glass as well. I believe current dishwash powders are less aggressive (not least for safety considerations!) but they will still leave the glass surface very clean and hence very high friction.

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    $\begingroup$ Also, dishwashers are able to achieve higher temperatures than hand washing, so are able to dissolve grease & soap much faster. $\endgroup$ – theo Nov 26 '14 at 11:12
  • $\begingroup$ Neat, learned something cool. $\endgroup$ – Nit Nov 26 '14 at 11:43
  • $\begingroup$ Of course, cleaning the glass is accomplished in part by dissolving a thin layer of glass from the surface. $\endgroup$ – Hot Licks Nov 26 '14 at 17:57
  • $\begingroup$ @HotLicks the answer actually mentions that. $\endgroup$ – hobbs Nov 27 '14 at 0:33
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    $\begingroup$ @PiotrDobrogost: sodium hydroxide reacts with silica to produce sodium silicate, so sodium hydroxide will dissolve silica but only exceedingly slowly. However this is chemistry not physics. $\endgroup$ – John Rennie Nov 27 '14 at 15:37

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