Resumen de A Student Diffusion Activity
Diffusion is a truly interdisciplinary topic bridging all areas of STEM education. When biomolecules are not being moved through the body by fluid flow through the circulatory system or by molecular motors, diffusion is the primary mode of transport over short distances. The direction of the diffusive flow of particles is from high concentration toward low concentration.
A few key examples of diffusion include: the deflation of He- or CO2-filled balloons,1 the exchange of oxygen from relatively high-concentration air to low-concentration, oxygen-starved blood cells in the lungs, the movement of ions through cell membranes, the scattered migration of photons from the center of the Sun, and the transport of water molecules from high (water) concentration to low (water) concentration during osmosis.
Through statistical notions of the random walk,2–7 physics brings a unique stochastic perspective to diffusive processes as first shown by Einstein’s Nobel Prize-winning work on Brownian motion.3 Einstein argued that it is the mean-squared displacements (or variances) of particle distributions that are proportional to the elapsed time, i.e., ⟨x2⟩=2Dt,〈x2〉=2Dt, (1) where the brackets represent averaging and D is the diffusivity or diffusion coefficient. The factor 2 holds for one-dimensional diffusion.5–7 It was in his 1905 paper3 analyzing Brownian motion that Einstein suggested the first experimental method for determining Boltzmann’s constant and thus Avogadro’s number, making the reality of atoms virtually inarguable! In biology education, the descriptor of a “chemical driving force” propelling particles down the “concentration gradient” is frequently employed to describe diffusion.8 While the idea of diffusion generating “entropic forces”5 is of great value to advanced biophysics majors, it is also important for students of introductory physics to conceptually understand the statistical, random-walk origin of the particle movements. Dreyfus et al.9 have highlighted the need for these thermodynamical/statistical mechanical paradigms to bridge the various disciplines of science education.
To illustrate the random-walk nature of diffusion with students enrolled in an introductory physics for life sciences (IPLS) course, we set up a grid of 21 one-meter wide columns on the grass, marked by parallel staked-at-the-ends strings (see Fig. 1). The columns were labeled (with cards) at the front ends by the integers –10 through +10. Participants initially lined up along the central column marked 0 [Fig. 1(a)]. It simplifies standard deviation analysis if the number of participants is divisible by three. Each student was given a penny and, on signal, flipped their coins. Students with coins coming up heads took a step to the right; students with tails moved to the left. The process of flipping coins and moving was repeated for a total of 10 trials [Fig. 1 (b) and (c)]. For each trial, the number of students in each column was recorded as in Table I. The analogy with diffusing particles is quite valid since the trial number N is directly proportional to the total time t, that is5 N=tΔt,N=tΔt, (2) with Δt the time interval between successive diffusive steps. Thus, one may treat the trial number N as the time variable in Eq. (1), while the number of students in each column x at trial t may thus be interpreted as a spreading particle-concentration function c(x,t).
