DIY DLS

Methods and Materials

Supermarket-bought skimmed milk was diluted 30:1 and samples placed in cheap 4 mL square plastic cuvettes sourced from eBay. This dilution ratio was determined empirically to give decent results without too much obvious multiple scattering. A basic 1 mW green (λ = 532 nm) laser pointer also sourced from eBay was used as the light source. The speckle pattern was observed on an A2 sheet of white cardboard placed L ≈ 9 m (baseline) from the scattering cuvette (ie using two bedrooms and the joining corridor). A beam stop was made from a bottle top painted on the inside with black acrylic, stuck to a lollipop stick, and held in place by a crocodile clip attached to a camera tripod. The speckle pattern was photographed here with a compact digital camera (Canon IXUS 170) mounted on a separate mini-tripod. The above image shows speckles at distances of order 10-50 cm from the centre of the pattern. The shadows of the beam stop, the camera, and the two tripods can be seen.

Results

The speckle pattern is continuously changing over time. The innermost speckles turn over at a rate of order few seconds but the outer speckles twinkle much more rapidly. This is indeed what we would we expect to see:

The typical size of casein micelles in skimmed milk is σ ≈ 200 nm (see fig 5 in this paper). Using the Stokes-Einstein relation (D = k_BT / 3πησ) the corresponding diffusion coefficient D ≈ 2 μm²s⁻¹ (taking the viscosity of water η ≈ 10⁻³ Pa s, and k_BT ≈ 4×10⁻²¹ J). Now consider a speckle at a distance, say, d ≈ 20 cm from the centre of the pattern. The corresponding scattering angle is θ ≈ d / L = 20/900 ≈ 0.02 radians (1.3°). From the theory, the corresponding scattering wavevector is q = (4πn₀ / λ) sin(θ/2) ≈ 0.35 μm⁻¹ (recall that the refractive index of water n₀ ≈ 1.33). Therefore the speckle decay rate Γ = q²D ≈ 0.25 s⁻¹. This is indeed roughly in accord with the observed speckle turnover time of a few seconds.

Moreover, as one moves outwards from the centre, note that Γ ∼ d ² (as long as θ << 1). Therefore the decay rate increases as the square of the distance from the centre of the pattern. Although this positively begs quantitative verification, such a rapid increase of the speckle fluctuation rate with distance from the centre of the pattern does seem to be what is seen.

Roughly, the experiment is probing the time decay of density fluctuations on a length scale of order q⁻¹ ≈ 3 μm. Because this is rather large, any residual flow is apparent in the scattering pattern, and the sample should be allowed to stand for a while to allow this to die away.

Future work will investigate direct measurement of the speckle intensity correlation function using something like a Texas Instruments OPT101 photodiode, and an Arduino, Raspberry Pi or other System-on-a-Chip device as an A/D converter plus data logger.

If you try this yourself -- PLEASE TAKE GREAT CARE NOT TO LOOK DIRECTLY INTO THE BEAM.