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Qualitative Differences Between the Semi-separable and the "Almansi-Type" Stokes Stream Function Expansions in the
Maria Hadjinicolaou1, Eleftherios Protopapas2
1Applied Mathematics Laboratory, School of Science and Technology, Hellenic Open University, Patras, Greece. hadjinicolaou@eap.gr.
Advances in Experimental Medicine and Biology
|January 1, 2022
Summary
This study models biofluid flow using Stokes equations, distinguishing rotational and irrotational flows via Gegenbauer functions. A new reduction formula clarifies complex Almansi-type solutions, aiding disease characteristic analysis in biofluids.
Area of Science:
- Fluid dynamics
- Biofluid mechanics
- Mathematical modeling
Background:
- Modeling creeping motion of Newtonian fluids around particles is crucial for understanding biofluid dynamics, like blood plasma flow.
- Stokes equations in spheroidal coordinates are employed to describe this motion.
- Distinguishing between rotational and irrotational flow is vital for biofluid analysis, especially in disease states.
Purpose of the Study:
- To model Newtonian fluid creeping motion around particles using Stokes equations in spheroidal coordinates.
- To obtain complete solutions for irrotational (E^2ψ=0) and rotational (E^4ψ=0) Stokes flow using Gegenbauer functions.
- To demonstrate the advantages of semiseparable solutions and provide a reduction formula for Almansi-type solutions.
Main Methods:
- Utilizing a stream function (ψ) within Stokes equations.
- Employing spheroidal coordinates for fluid flow modeling.
- Deriving solutions in separable and semiseparable forms using Gegenbauer functions.
- Developing a reduction formula to transform Almansi-type solutions into semiseparable forms.
Main Results:
- Complete sets of solutions for both irrotational and rotational Stokes flow were obtained in separable and semiseparable forms.
- Each solution component (eigenflow) clearly identifies either rotational or irrotational flow characteristics.
- A reduction formula was derived, converting Almansi-type solutions to the advantageous semiseparable form.
Conclusions:
- The semiseparable solution form offers advantages for analyzing biofluid flow characteristics.
- The derived reduction formula allows for the revelation of hidden physical information within Almansi-type solutions.
- This approach provides valuable insights for studying biofluids and their correlation with various diseases.
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