Abstract
We consider the general problem of laser pulse heating of spherical metal particles with the sizes ranging from nanometers to millimeters. We employ the exact Mie solution of the diffraction problem and solve the heat-transfer equation to determine the maximum temperature rise at the particle surface as a function of optical and thermometric parameters of the problem. Primary attention is paid to the case when the thermal diffusivity of the particle is much larger than that of the environment, as it is in the case of metal particles in fluids. We show that, in this case, for any given duration of the laser pulse, the maximum temperature rise as a function of the particle size reaches a maximum at a certain finite size of the particle. We suggest simple approximate analytical expressions for this dependence, which cover the entire parameter range of the problem and agree well with direct numerical simulations.
- Received 1 June 2011
DOI:https://doi.org/10.1103/PhysRevX.1.021024
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Published by the American Physical Society
Popular Summary
Laser heating of small metal particles in fluids has been explored and exploited in many applications in physics, chemistry, biology, and medicine, including cancer treatment. In most of the cases, knowing how the temperature at the surface of a heated particle depends on the characteristics of the laser as well as the optical and thermal properties of the particle and its surrounding fluid could lead to ways to control and optimize the laser-induced heating. Surprisingly, a systematic theoretical analysis of the phenomenon has been lacking. In this paper, we provide the missing analysis and offer users of the laser-heating technique simple ways of quantitatively estimating and controlling the effects of heating.
Formulating a theoretical description of the laser-heating problem is not fundamentally difficult. The problem is essentially described by equations for heat diffusion both inside the particle and in the fluid in the presence of sources. Finding the temperature at the surface of the particle requires solving the equations under physically meaningful boundary conditions. While exact solutions are possible, at least as long as the laser intensity is sufficiently small and the particle’s shape is simple, they are extremely cumbersome to use and can only be analyzed numerically.
Our approach to obtaining the temperature at the surface of the particle is a different, heuristic one. Assuming that the shape of the particle is spherical and using dimensional analysis, we divide the physically relevant region of the optical-thermal parameter space into a number of different regimes, depending on the relative sizes of the particle radius, the thickness of a skin layer of the particle, and the heat-diffusion lengths inside the particle and in the hosting fluid. For each regime, we then use physical intuitions and heuristic arguments to simplify the original heat-diffusion equations and solve the reduced equations—to arrive at a simple expression for the temperature rise at the particle surface upon laser heating. Our complete analysis provides a comprehensive set of analytical expressions that cover a wide range of realistic situations, including the broad laser spectrum from far ultraviolet to ultrainfrared and the range of particle radius from nano- to millimeters.
These expressions are accurate and easy to use in practice. We believe that they will be of considerable value to researchers who develop and use techniques based on laser heating of metal particles.