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Nanofluid bioconvection in water-based suspensions containing nanoparticles and oxytactic microorganisms: oscillatory instability.

Kuznetsov AV - Nanoscale Res Lett (2011)

Bottom Line: Physical mechanisms responsible for the slip velocity between the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, are accounted for in the model.An approximate analytical solution of the eigenvalue problem is obtained using the Galerkin method.The obtained solution provides important physical insights into the behavior of this system; it also explains when the oscillatory mode of instability is possible in such system.

View Article: PubMed Central - HTML - PubMed

Affiliation: Dept, of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910, USA. avkuznet@eos.ncsu.edu.

ABSTRACT
The aim of this article is to propose a novel type of a nanofluid that contains both nanoparticles and motile (oxytactic) microorganisms. The benefits of adding motile microorganisms to the suspension include enhanced mass transfer, microscale mixing, and anticipated improved stability of the nanofluid. In order to understand the behavior of such a suspension at the fundamental level, this article investigates its stability when it occupies a shallow horizontal layer. The oscillatory mode of nanofluid bioconvection may be induced by the interaction of three competing agencies: oxytactic microorganisms, heating or cooling from the bottom, and top or bottom-heavy nanoparticle distribution. The model includes equations expressing conservation of total mass, momentum, thermal energy, nanoparticles, microorganisms, and oxygen. Physical mechanisms responsible for the slip velocity between the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, are accounted for in the model. An approximate analytical solution of the eigenvalue problem is obtained using the Galerkin method. The obtained solution provides important physical insights into the behavior of this system; it also explains when the oscillatory mode of instability is possible in such system.

No MeSH data available.


Related in: MedlinePlus

The case of rigid upper and lower walls, Rb = 0 (no microorganisms): (a) Oscillatory and non-oscillatory instability boundaries in the (Rac, Rn) plane. (b) Critical wavenumber in the (Rac, Rn) plane. (c) Square of the oscillation frequency, ω2, versus the nanoparticle concentration Rayleigh number (for oscillatory instability to occur, ω2 must be positive so that ω remains real).
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Figure 1: The case of rigid upper and lower walls, Rb = 0 (no microorganisms): (a) Oscillatory and non-oscillatory instability boundaries in the (Rac, Rn) plane. (b) Critical wavenumber in the (Rac, Rn) plane. (c) Square of the oscillation frequency, ω2, versus the nanoparticle concentration Rayleigh number (for oscillatory instability to occur, ω2 must be positive so that ω remains real).

Mentions: For Figure 1a,b,c, the following values of dimensionless parameters are utilized: Lb = 1500, Le = 94, Ln = 5000, Pr = 5, NA = 5, ϖ = 17, and Rb = 0 (which corresponds to the situation with zero concentration of microorganisms). Rn is changing in the range between -1.2 and 1.2. In Figure 1a, the boundary for non-oscillatory instability (shown by a solid line) is obtained by setting ω to zero in Equation 54, solving this equation for Ra and then finding the minimum with respect to m of the right-hand side of the obtained equation. The boundary for oscillatory instability (shown by a dotted line) is obtained by the following procedure. Two coupled equations are produced by taking the real and imaginary parts of Equation 54. One of these equations is used to eliminate ω, and the resulting equation is then solved for Ra; the critical value of Ra is again obtained by calculating the minimum value that the expression for Ra takes with respect to m.


Nanofluid bioconvection in water-based suspensions containing nanoparticles and oxytactic microorganisms: oscillatory instability.

Kuznetsov AV - Nanoscale Res Lett (2011)

The case of rigid upper and lower walls, Rb = 0 (no microorganisms): (a) Oscillatory and non-oscillatory instability boundaries in the (Rac, Rn) plane. (b) Critical wavenumber in the (Rac, Rn) plane. (c) Square of the oscillation frequency, ω2, versus the nanoparticle concentration Rayleigh number (for oscillatory instability to occur, ω2 must be positive so that ω remains real).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3211144&req=5

Figure 1: The case of rigid upper and lower walls, Rb = 0 (no microorganisms): (a) Oscillatory and non-oscillatory instability boundaries in the (Rac, Rn) plane. (b) Critical wavenumber in the (Rac, Rn) plane. (c) Square of the oscillation frequency, ω2, versus the nanoparticle concentration Rayleigh number (for oscillatory instability to occur, ω2 must be positive so that ω remains real).
Mentions: For Figure 1a,b,c, the following values of dimensionless parameters are utilized: Lb = 1500, Le = 94, Ln = 5000, Pr = 5, NA = 5, ϖ = 17, and Rb = 0 (which corresponds to the situation with zero concentration of microorganisms). Rn is changing in the range between -1.2 and 1.2. In Figure 1a, the boundary for non-oscillatory instability (shown by a solid line) is obtained by setting ω to zero in Equation 54, solving this equation for Ra and then finding the minimum with respect to m of the right-hand side of the obtained equation. The boundary for oscillatory instability (shown by a dotted line) is obtained by the following procedure. Two coupled equations are produced by taking the real and imaginary parts of Equation 54. One of these equations is used to eliminate ω, and the resulting equation is then solved for Ra; the critical value of Ra is again obtained by calculating the minimum value that the expression for Ra takes with respect to m.

Bottom Line: Physical mechanisms responsible for the slip velocity between the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, are accounted for in the model.An approximate analytical solution of the eigenvalue problem is obtained using the Galerkin method.The obtained solution provides important physical insights into the behavior of this system; it also explains when the oscillatory mode of instability is possible in such system.

View Article: PubMed Central - HTML - PubMed

Affiliation: Dept, of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910, USA. avkuznet@eos.ncsu.edu.

ABSTRACT
The aim of this article is to propose a novel type of a nanofluid that contains both nanoparticles and motile (oxytactic) microorganisms. The benefits of adding motile microorganisms to the suspension include enhanced mass transfer, microscale mixing, and anticipated improved stability of the nanofluid. In order to understand the behavior of such a suspension at the fundamental level, this article investigates its stability when it occupies a shallow horizontal layer. The oscillatory mode of nanofluid bioconvection may be induced by the interaction of three competing agencies: oxytactic microorganisms, heating or cooling from the bottom, and top or bottom-heavy nanoparticle distribution. The model includes equations expressing conservation of total mass, momentum, thermal energy, nanoparticles, microorganisms, and oxygen. Physical mechanisms responsible for the slip velocity between the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, are accounted for in the model. An approximate analytical solution of the eigenvalue problem is obtained using the Galerkin method. The obtained solution provides important physical insights into the behavior of this system; it also explains when the oscillatory mode of instability is possible in such system.

No MeSH data available.


Related in: MedlinePlus