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A 3D Spheroid Model for Glioblastoma

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A floating prolate spheroid.

¹Department of Chemical Engineering, University of Massachusetts, Amherst, MA 01003, USA. cpozrikidis@ecs.umass.edu

Journal of Colloid and Interface Science

|September 6, 2011

Summary

This study analyzes the equilibrium of needle-like particles at fluid interfaces. It develops numerical and approximate methods to determine particle position based on capillary forces, buoyancy, and weight.

Area of Science:

Fluid dynamics
Interfacial phenomena
Capillary hydrodynamics

Background:

Floating particles at fluid interfaces experience capillary forces due to surface tension.
The particle's shape and interaction with the interface determine its equilibrium position.
Understanding these forces is crucial for applications involving particle suspensions and interfacial behavior.

Purpose of the Study:

To investigate the equilibrium position of spherical and prolate spheroidal particles at the interface between two immiscible fluids.
To develop and compare numerical and approximate analytical methods for calculating capillary forces and particle equilibrium.
To analyze the influence of fluid properties, particle characteristics, and contact angle on interfacial behavior.

Main Methods:

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Accurate numerical solution of a boundary-value problem for a floating sphere.

Approximate analytical solution using an inclined flat plate model for meniscus elevation.

Local approximate formulation for prolate spheroids, leading to a nonlinear algebraic equation.

Main Results:

Numerical results for a sphere show good agreement with the approximate analytical solution.
A nonlinear algebraic equation was derived for the prolate spheroid's position and contact line elevation.
The study discusses the effects of densities, contact angle, and capillary length on the system.

Conclusions:

The methods provide accurate predictions for particle equilibrium at fluid interfaces.
The study quantifies the interplay between capillary forces, buoyancy, and particle properties.
The shape of the contact line around the particle was successfully reconstructed.