By composing asymptotic expansions defined on different annular subdomains one obtains an approximate solution of the capillary problem for a circular tube. This composed function yields a comparison surface for the entire domain. Explicit error estimates uniform with respect to the boundary contact angle are given. The proof of this estimate is based on the Comparison Principle of Concus and Finn. The mam idea of the method can be extented to the capillary tube problem with general cross section.
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