Thermophoretic Effects On Capillary Transport Of Nanofluids

Nanofluid is a dilute suspension of particles, varying in size from 1 nm to 100 nm, suspended in a base fluid (e.g. water). Compared to base fluids, nanofluids distinctively possess superior thermophysical attributes like thermal conductivity, specific heat capacity.

Hence, they can be utilized for their enhanced thermophysical properties in the narrow confinements, like heat pipes and cooling components of electronic devices where appreciable temperature differences prevail.


The principal length scale of such confinements lies in the range of microns. Consequently, the study of thermophoretic effects on the capillary transport of nanofluids in microfluidic confinements becomes immensely important.

When temperature difference prevails in a suspension, the suspended particles experience a force on account of thermophoresis, which results in varied migration rates of the particles (e.g. blackening of a lantern). Such thermal gradients may be pertinently utilized to regulate the suspension flow-rate. Furthermore, existing temperature gradients can be employed to separate different particles in a suspension. In the context of such systems, migration of nanoparticles eventually results in their preferential deposition determined by existing thermal fields. The separation of nanoparticles attains utmost importance not only in the context of achieving homogeneous suspensions but also in the design of particle retrieval systems essential for minimizing operational costs.

Figure 1: Graphical representation of the nanofluid confined in the microchannel (2D View) along with the coordinate system, used in numerical analysis. Republished with permission from Elsevier from:

Here, we have enlightened new mechanisms by which a nanoparticle-laden fluid may get transported by thermal gradient (see Figure 1). The principal forces responsible for this motion are surface-tension, viscous drag, and the thermophoresis.

First, the effect of the thermal gradients on the migration of particles has been studied. We have found that two distinct regimes exist, namely, diffusion and thermophoresis. Deposition of smaller nanoparticles is governed by diffusive forces, while, larger nanoparticle deposition is dictated by thermophoresis. Consequently, larger particles migrate towards the wall, resulting in higher concentrations near the wall, as compared to the smaller ones. The transition from diffusive particle deposition to the thermophoretically dominated migration, in turn, determines the particle-bearing capacity of the suspension.


With the increase in thermal gradients, the concentration of particles near the center of the channel, at a given distance from the origin, reduces. An estimate of the particle-bearing capacity of a given suspension can be aptly utilized in retrieving particles in multifarious engineering applications involving nanofluids in microscale confinements.

The thermophoretic force is subsequently estimated, based on the computed temperature and concentration fields, for different particle sizes, in presence of varied thermal gradients. The thermophoretic force has been observed to increase appreciably for suspensions with larger particles. Also, with the increase in thermal gradients, there has been a pronounced increase in the thermophoretic force, for a given nanofluid. Results reveal that thermal gradients clearly enhance the suspension flow rate, relative to purely surface tension driven transport (see Figure 2 [right]). However, this degree of enhancement saturates; beyond a given temperature difference, the rate of capillary transport does not increase significantly. Hence, one can optimize the energy cost, depending on the desired flow rate.

Figure 2. Displacement (x) versus time (t): a plot depicting the distance traversed by the nanofluid and corresponding time. Comparing the capillary dynamics for different particle sizes [left] and for different temperatures of the channel wall [right], and consequently, varied thermal gradients. The dark line (Tw = 323 K) corresponds to the capillary transport in absence of any thermophoretic effects. Republished with permission from Elsevier from:
It can be noted that the flow rate of the suspension is significantly greater for larger particles (see Figure 2 [left]). This is primarily attributed to the comparatively larger thermophoretic force for higher particle size. In this context, the influence of particle size on capillary dynamics can be utilized to achieve separation of nanoparticles in a heterogeneous nanofluid.

The significant relevance of the work is far-reaching. In effect, it has attempted to outline the correlation between the applied temperature difference and the resultant pumping rates of nanofluid in the microchannels; which are being gradually adopted in designing cooling systems for state of the art electronics.

Furthermore, this work demonstrates that local temperature difference can be suitably utilized to separate nanoparticles in a heterogeneous suspension. Importantly, by the appropriate temperature control, one can achieve desired rates of transport of suspensions, significantly reducing the energy costs and consequently, optimizing the engineering design.


These findings are described in the article entitled: Thermophoretically driven capillary transport of nanofluid in a microchannel, recently published in the journal Advanced Powder Technology. This work was conducted by Soumya Bandyopadhyay (Dual Degree Masters Student) and Suman Chakraborty (Professor) from the Indian Institute of Technology Kharagpur.



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