Shape-dependent orientation of thermophoretic forces in microsystems

Abstract

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.

Knudsen torque: A rotational mechanism driven by thermal force

“…The analysis and numerical simulation are validated using a case with two noncoaxial circular cylinders. Knudsen force is calculated and compared with the analytical solution [19], and an agreement within 0.01% is obtained.…”

“…The advantage of this approach is that equations of macroscopic physical quantities, such as the temperature, velocity, and pressure field, can be explicitly formulated and are readily used to investigate the underlying fundamental mechanism. Following the same approach employed in our previous work [19], the velocity distribution function and macroscopic variables of gas are expanded as power series of k = √ π 2 Kn. Using the perturbation technique, a set of governing equations and the corresponding boundary conditions for the macroscopic quantities of various orders can be derived and are summarized in Table I, in which dimensionless variables P ij , u i , and τ denote the nonequilibrium parts of the pressure, velocity, and temperature, respectively.…”

“…More recently, benefitting from the advanced microfabrication techniques, a relatively new type of thermal force, entitled as Knudsen force, acting on uniformly heated micro-or nanostructures, was discovered and experimentally measured in several microdevices [11][12][13]. Such a force is significant enough to create an impact on the performance of microdevices, and therefore has provoked a series of numerical and theoretical studies on its fundamental mechanism [14][15][16][17][18][19]. Generally speaking, Knudsen force is created by gas motion induced by the nonuniform gas temperature.…”

Thermally Induced Knudsen Forces for Contactless Manipulation of a Micro-Object

“…Such technologies include microstructure actuation [ 5 , 6 ], gas sensing [ 7 , 8 , 9 ], atomic force microscopy [ 1 , 4 ], and high-precision force measurements [ 3 ], among others. In addition to experimental [ 2 , 10 ] and theoretical approaches [ 1 , 11 , 12 , 13 ], numerical approaches have also been used to study the Knudsen forces [ 7 , 10 , 14 , 15 , 16 , 17 ]. Computational studies are particularly significant to reproduce the thermally induced flow field in complex systems that is difficult to observe experimentally.…”

Multiscale simulation of molecular gas flows by the general synthetic iterative scheme

“…fewer intermolecular collisions, the three quantities become larger and the difference between |q t | and |q r | intensifies. Furthermore, p n on each surface becomes more unbalanced, which mainly contributes to the arising of Knudsen force[48,49]. To include the effect of the shear viscosity index, we also calculate the flows with ω = 0.5 (now δ = 1/1.2, ω 0 = 0.629 and ω 1 = 1.728 to remain the same values of f t and f r ).…”