Shape-dependent orientation of thermophoretic forces in microsystems

It is generally acknowledged that the direction of the thermophoretic force acting on microparticles is largely determined by the imposed temperature gradient, and the shape of the microparticle has little influence on its direction. We show that one type of thermophoretic force, emerged due to the advent of microfabrication techniques, is highly sensitive to object shape, and it is feasible to tune force orientation via proper shape design. We reveal the underlying mechanism by an asymptotic analysis of the Boltzmann equation and point out the reason why the classical thermophoretic force is insensitive to the particle shape, but the force in microsystems is. The discovered phenomenon could find its applications in methods for microparticle manipulation and separation.

Figure 1

Schematic illustration of the model problems. (a) Classic thermophoresis; (b) heated microbeam.

Figure 2

Flow structure shown in the left-half domain and temperature contour [$O\left(k^0\right)$] shown in the right-half domain of the classical thermophoresis particle: (a) flow field of [$O\left(k^1\right)$]; (b) flow field of [$O\left(k^2\right)$].

Figure 3

Shape effect on the thermophoretic force.

Figure 4

Flow structure, temperature contour, and pressure variation of gas surrounding a rectangular microbeam; (a) flow structure (left-half domain) and temperature distribution (right-half domain); (b) a magnified subplot of the flow field near the lower right corner; (c) pressure variation along two lines BA ($y=3.5$) and CD ($y=-1.5$).

Figure 5

Flow structure (left-half domain) and temperature contour (right-half domain) of gas surrounding a microbeam with a square cross section with rounded corners.

Figure 6

Flow structure, temperature contour, and pressure variation of gas surrounding a cylindrical microbeam; (a) flow structure (left-half domain) and temperature distribution (right-half domain); (b) pressure variation along the curve ${\mathrm{A}}^{\prime }{\mathrm{B}}^{\prime }$ located halfway between the two cylinders.

Figure 7

(a) Knudsen force acting on a unit of the perimeter as a function of the radius of the corner and the aspect ratio of the microbeam; (b) the ratio of the width of the top gap and the width of the bottom gap; (c) the ratio of the width of the side gap and the width of the bottom gap; (d) the relative size of the beam with respect to the chamber.

Figure 8

Evolution of the flow structure near the lower left corner of the beam; (a) $w/g=1.0$; (b) $w/g=1.25$; (c) $w/g=1.5$; (d) $w/g=1.75$; (e) $w/g=2.0$; (f) $w/g=3.0$.