# Maximum bubble pressure method

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{{Short description|Method of measuring surface tension}}
In [physics](/source/physics), the '''maximum bubble pressure method''', or in short '''bubble pressure method''', is a technique to measure the [surface tension](/source/surface_tension) of a [liquid](/source/liquid), with [surfactant](/source/surfactant)s.

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== Background ==
When the [liquid](/source/liquid) forms an interface with a [gas](/source/gas) phase, a [molecule](/source/molecule) on the border has quite different [physical properties](/source/Physical_property) due to the unbalance of attracting forces by the neighboring molecules. At the [equilibrium state](/source/Thermodynamic_equilibrium) of the liquid, interior molecules are under the balanced forces with uniformly distributed adjacent molecules.

However, relatively fewer number of molecules in the gas phase above the interface than [condensed](/source/Condensation) liquid phase makes overall sum of [force](/source/force)s applied to the surface molecule direct inside of the liquid and thus surface molecules tend to minimize their own surface area.

Such an inequality of molecular forces induces continuous movement of molecules from the inside to the surface, which means the surface molecules has extra [energy](/source/energy), which is called [surface free energy](/source/Specific_surface_energy) or [potential energy](/source/potential_energy),{{which|date=April 2011}} and such an energy acting on reduced unit area is defined as [surface tension](/source/surface_tension).

This is a frame work to interpret relevant phenomena which occurs surface or interface of materials and a number of methods to measure the [surface tension](/source/surface_tension) has been developed.<ref name="Adamson-Gast">Adamson, Arthur W.; Alice P. Gast (1997). ''Physical Chemistry of Surfaces'' (6th ed.). Wiley Interscience.</ref>

Among the various ways to determine surface tension, [Du Noüy ring method](/source/Du_No%C3%BCy_ring_method) and [Wilhelmy slide method](/source/Wilhelmy_plate) are based on the separation of a [solid](/source/solid) object from the liquid surface, and [Pendant drop method](/source/Drop_(liquid)) and [Sessile drop](/source/Sessile_drop_technique) or bubble method depend on the [deformation](/source/Deformation_(mechanics)) of the spherical shape of a liquid drop.<ref name="Adamson-Gast" />

Even though these methods are relatively simple and commonly used to determine the [static](/source/Statics) [surface tension](/source/surface_tension), in case that the impurities are added to the liquid, measurement of surface tension based on the [dynamic equilibrium](/source/dynamic_equilibrium) should be applied since it takes more time to obtain a completely formed surface and this means that it is difficult to achieve the static equilibrium as a pure liquid does.<ref name="kruss-scientific.com">[https://www.kruss-scientific.com/services/education-theory/glossary/bubble-pressure-tensiometer/ Bubble Pressure Method] at kruss-scientific.com</ref>

The most typical impurity to induce [dynamic](/source/Dynamics_(mechanics)) surface tension [measurement](/source/measurement) is a surfactant molecule which has both of [hydrophilic](/source/Hydrophile) segment, generally called “head group” and [hydrophobic](/source/Hydrophobe) segment, generally called “tail group” in a same molecule. Due to the characteristic [molecular structure](/source/molecular_structure), [surfactant](/source/surfactant)s migrate to the liquid surface bordering gas phase until an external force disperse the accumulated molecules from the interface or surface is fully occupied and thus cannot accommodate extra molecules.  During this process, surface tension decrease as function of time and finally approach the equilibrium surface tension (σ<sub>equilibrium</sub>).<ref name="lauda.de">[http://www.lauda.de/ Dynamic Methods] at lauda.de</ref>  Such a process is illustrated in figure 1. (Image was reproduced from reference)<ref name="kruss-scientific.com" />

thumb|400px|Figure 1: Migration of surfactant molecules and change of surface tension (σ<sub>t1</sub> > σ<sub>t2</sub> > σ<sub>equilibrium</sub>).

== Maximum bubble pressure method ==
One of the useful methods to determine the dynamic surface tension is measuring the "maximum bubble pressure method" or, simply, bubble pressure method.<ref name="Adamson-Gast" /><ref name="kruss-scientific.com" />

Bubble pressure [tensiometer](/source/Tensiometer_(surface_tension)) produces gas bubbles (ex. air) at constant rate and blows them through a capillary which is submerged in the sample liquid and its radius is already known.

The [pressure](/source/pressure) (''P'') inside of the gas bubble continues to increase and the maximum value is obtained when the bubble has the completely hemispherical shape whose radius is exactly corresponding to the radius of the capillary.<ref name="lauda.de" />

Figure 2 shows each step of bubble formation and corresponding change of bubble radius and each step is described below. (Image was reproduced from reference)<ref name="kruss-scientific.com" /><ref name="lauda.de" />

thumb|400px|Figure 2: Change of pressure during bubble formation plotted as a function of added volume.

Initially a bubble appears on the end of the capillary.  As the size increases, the radius of curvature of the bubble decreases.

At the point of the maximum bubble pressure, the bubble has a complete hemispherical shape whose radius is identical to the radius of the capillary denoted by Rcap.  The surface tension can be determined using the [Young–Laplace equation](/source/Young%E2%80%93Laplace_equation) in the [reduced form](/source/reduced_form) for spherical bubble shape within the liquid.<ref name="lauda.de" />

<math>\sigma=\frac{\Delta P_{\rm {max}} \times R_{\rm {cap}}}{2}</math>

(σ: surface tension, Δ''P''<sub>max</sub>: maximum pressure drop, ''R''<sub>cap</sub>: radius of capillary)

Later, after the maximum pressure, the pressure of the bubble decreases and the radius of the bubble increases until the bubble is detached from the end of a capillary and a new cycle begins.  This is not relevant to determine the surface tension.<ref name="lauda.de" />

Currently developed and commercialized tensiometers monitors the pressure needed to form a bubble, the pressure difference between inside and outside the bubble, the radius of the bubble, and the surface tension of the sample are calculated in one time and a data acquisition is carried out via [PC](/source/Personal_computer) control.

Bubble pressure method is commonly used to measure the dynamic surface tension for the system containing surfactants or other impurities because it does not require contact angle measurement and has high accuracy even though the measurement is done rapidly.<ref name="Adamson-Gast" /><ref name="lauda.de" />  “Bubble pressure method” can be applied to measure the dynamic surface tension, particularly for the systems which contain surfactants.<ref name="lauda.de" />  Moreover, this method is an appropriate technique to apply to [biological fluids](/source/Body_fluid) like [serum](/source/Serous_fluid){{which|date=April 2011}} because it does not require a large amount of liquid sample for the measurements.<ref name="Hubbard">Hubbard, Arthur T. (2002). ''Encyclopedia of Surface and Colloid Science'' (Vol. 1). CRC press, pp. 814–815</ref> Finally, the method is used for an indirect determination of the surfactant content of industrial cleaning or coating baths because the dynamic surface tension in a particular range of bubble formation rates shows a strong correlation with the concentration. <ref name="kruss-scientific.com" />

== References ==
{{reflist}}

==External links==
{{Refbegin}}
* [https://www.dataphysics-instruments.com/knowledge-hub/bubble-pressure/ Measurement of Dynamic Surface Tension Using the Maximum Bubble Pressure Method]
* [https://www.kruss-scientific.com/services/education-theory/glossary/bubble-pressure-tensiometer/ Measuring principle and applications of dynamic surface tension measurement with a bubble pressure tensiometer]
* [http://www.sita-process.com/information-service/process-parameter-surface-tension/bubble-pressure-method-for-measuring-the-surface-tension/ Bubble pressure method for measuring the dynamic surface tension]
{{Refend}}

Category:Fluid mechanics

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Adapted from the Wikipedia article [Maximum bubble pressure method](https://en.wikipedia.org/wiki/Maximum_bubble_pressure_method) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Maximum_bubble_pressure_method?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.