Radiation pressure - optical force

To describe such trajectories, consider the net photo-phoretic force F ad on a particle of radius tp by a light beam (whose waist size wa is much larger, i.e. tp wa) here the refractive index of the particle ( par) is larger than that of the surrounding medium (wmed) so that the particle acts like a spherical lens (Helmbrecht et al, 2007). The net force Frad resulting from the refraction of incident light (a laser beam) which transfers momentum to the particle has been described by Helmbrecht et al (2007) as 

Any such particle motion wiU immediately encounter a drag force, which, from Stokes law, may he written as 

The magnirndes of such terminal velocities identified as photophoretic velocities are in the range 1 to 80 pm/s for particles having diameters in the range of 1 to 10 pm. However, for particles of comparable diameter, the velocity of siUca particles (which were transparent to the laser light used) was six times less than that of melamine particles. Therefore, separation of particles of the same size but having different optical properties appears feasible (Helm-brecht et ah, 2007). 

There are unresolved complexities in such a continuous separation technique for particles due to the uncertainties in determining the effective power (= 2Pr (rplwdf ). Also, the incident Ught has two components, an axial and a radial component, each leading to a separate PP velocity. See HeUn-brecht et ah (2007) for additional references on the subject. 

You have an adsorber packed with an adsorbent such that e = 0.40. However, the adsorbent particles are also porous, with a void volume fraction of Ep = 0.30, and ps (= 2.0 g/cm ) is the actual density of the material of the solid adsorbent particles. 

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Ashkin and Dziedzic (1977) used the radiation pressure force of a laser beam to levitate microdroplets with the apparatus presented in Fig. 15. A polarized and electro-optically modulated laser beam illuminated the particle from below. The vertical position of the particle was detected using the lens and split photodiode system shown. When the particle moved up or down a difference signal was generated then a voltage proportional to the difference and its derivative were added, and the summed signal used to control an electro-optic modulator to alter the laser beam intensity. Derivative control serves to damp particle oscillations, while the proportional control maintains the particle at the null point. 

The radiation pressure exerted by light is very weak. A bright laser beam of several milliwatts of power can exert only a few piconewtons (pN) of force. However, a force of 10 pN is enough to pull a cell of E. coli through water ten times faster than it can swim.213 In about 1986, it was found that a laser beam focused down to a spot of - one K ( 1 pm for an infrared laser) can trap and hold in its focus a retractile bead of 1 pm diameter. This "optical tweezers" has become an important experimental tool with many uses.213 214 For example, see Fig. 19-19. Not only are optical tweezers of utility in studying biological motors but also mechanical properties of all sorts of macromolecules can be examined. For example, DNA can be stretched and its extensibility measured.215 Actin filaments have even been tied into knots 216... 

Demonstration of levitation of micron-sized latex particles by radiation pressure dates back to 1970 in the experiments reported by Ashkin [Ashkin 1970]. The average force accelerating (or slowing down) atoms in a laser field was derived by A.Kazantsev in 1972 [Kazantsev 1974]. Later in 1972-1974 he classified the optical forces as spontaneous, induced and mixed. In particular, it was he who first presented the dipole potentials for velocity broadened lines of resonance atoms in the logarithmic form... 

The radiation field exerts direct forces and torques on condensed matter via the Minkowski stress [64]. Radiation pressure 11, is on the order of If, DE k, I/c k, P/Ac where D is the electric displacement, I is the irradiance, c is the speed of light, P is the incident power, and A is the area. If the direct optical force is to cause a deformation, the radiation pressure would have to overcome the aligning effect of... 

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