The dilatational rheology of complex fluid-fluid interfaces is linked to the stability and bulk rheology of emulsions and foams. Dilatational rheology can be measured by pinning a bubble or droplet at the tip of a capillary, subjecting the interface shape to small amplitude oscillations, and recording the resulting pressure jump across the interface. The complex dilatational modulus is obtained by differentiating the interfacial stress with respect to the area change of the interface. In this paper, we perform a regular asymptotic expansion to analyze the interface response in pressure-controlled capillary pressure tensiometers to determine the dilatational modulus as a function of the measured radius of curvature. We show that small amplitude oscillatory dilation of a spherical bubble is neither stress nor strain rate controlled. The resulting dilatational modulus contains contributions from both surface tension effects as well as extra stresses. Depending on the specifics of the interface, each contribution can be a function of the dilation rate and the radius of the bubble. Thus, the radius of curvature can be used as a control parameter with which to separate surface tension and interfacial rheology effects, aiding in validation of interfacial constitutive models. We examine the limits of validity of the small amplitude assumption and provide guidelines for determining the operating limits of a capillary pressure tensiometer. Finally, we compare several existing devices, including a microtensiometer we developed previously that oscillates the pressure inside small (R ∼ 10 μm) droplets.
Skip Nav Destination
Article navigation
January 2015
Research Article|
January 01 2015
Regular perturbation analysis of small amplitude oscillatory dilatation of an interface in a capillary pressure tensiometer
Anthony P. Kotula;
Anthony P. Kotula
Center for Complex Fluids Engineering,
Carnegie Mellon University
, Pittsburgh, Pennsylvania 15213
Search for other works by this author on:
Shelley L. Anna
Shelley L. Anna
a)
Center for Complex Fluids Engineering,
Carnegie Mellon University
, Pittsburgh, Pennsylvania 15213
Search for other works by this author on:
a)
Author to whom correspondence should be addressed; electronic mail: [email protected]
J. Rheol. 59, 85–117 (2015)
Article history
Received:
June 10 2014
Accepted:
November 13 2014
Citation
Anthony P. Kotula, Shelley L. Anna; Regular perturbation analysis of small amplitude oscillatory dilatation of an interface in a capillary pressure tensiometer. J. Rheol. 1 January 2015; 59 (1): 85–117. https://doi.org/10.1122/1.4902546
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Rheo-SINDy: Finding a constitutive model from rheological data for complex fluids using sparse identification for nonlinear dynamics
Takeshi Sato, Souta Miyamoto, et al.
Learning a family of rheological constitutive models using neural operators
Deepak Mangal, Milad Saadat, et al.
Linear viscoelasticity of nanocolloidal suspensions from probe rheology molecular simulations
Dinesh Sundaravadivelu Devarajan, Rajesh Khare
Related Content
Microfabricated deflection tensiometers for insoluble surfactants
Appl. Phys. Lett. (September 2010)
Extensional rheometry at interfaces: Analysis of the Cambridge Interfacial Tensiometer
J. Rheol. (September 2012)
Measurement of surface tension by sessile drop tensiometer with superoleophobic surface
Appl. Phys. Lett. (March 2018)
A simple levitated-drop tensiometer
Rev. Sci. Instrum. (September 2019)
Development of revolving drop surface tensiometer
Rev. Sci. Instrum. (January 2012)