Hydrodynamic Interactions
A key aspect in the study of colloidal systems are the hydrodynamic interactions. This type of interaction arises because the Brownian motion of particles generated disturbances in the fluid and flows occur which affect the motion of neighboring particles. Thus, generating and responding to the local velocity of the fluid, colloidal particles experience hydrodynamic interactions with neighboring particles. The dynamics of colloidal system due to hydrodynamic interactions develops differently in confined systems than in systems in bulk, because it also is a hydrodynamic interaction between particles and container walls. Hence the importance of studying systems in quasi-two-dimensional.
Although this type of interaction is present in virtually any complex fluid that plays an important role in the transport and dynamic processes, such interactions are still far from fully understood. This is due to the complexity involved to describe the hydrodynamic coupling between many particles, and between those borders.
So, the purpose of this paper is to study the effect of hydrodynamic interactions in colloidal aqueous suspensions dynamic quasi-two-dimensional. Such suspensions are built to confine a monolayer of colloidal particles between two glass plates.
There have been systems that consist of polystyrene spherical particles of diameter s = 1.9mm, immersed in water and trapped between two plates at a separation of 2.92 mm.
The performance of the systems was as follows, 1.2 ml of solution is placed between a slide and covered with a coverslip which is pressed until it gets a two-dimensional system and sealed with epoxy resin.
After using the technique of digital video microscopy, we observe with the microscope the system performed and select an area to burn for two hours. The camera gets used a picture of 650x480 pixels every thirtieth of a second. Through these paintings we can find the position of the particles in every thirtieth of a second. With which we can build the paths and get the information of the dynamics of the system.
Made systems ranging from dilute to concentrated fractions of area are as follows: 0.22, 0.30, 0.36, 0.48, 0.56, 0.63, 0.74, 0.8. Some of the static properties we have obtained in our systems, is the radial distribution function, which gives the probability of finding a particle at a distance r and reflects the structure of the system.
To study the diffusion of these systems, we find that the diffusion coefficients D (r) associated with each direction of movement x are,
<Δ x 2> = 2DX (r) t,
where the angular brackets mean an average balance in an ensemble. A sufficiently large distances, where the particles no longer interact, Dx (r) reduces to 2D0, where D0 is the coefficient of self for short periods.
We simplify the problem by measuring the effective hydrodynamic coupling between each pair of particles. To measure the diffusion coefficients D (r) of the trajectories of two particles is built on the collective motion and is projected on the perpendicular and parallel initial separation vector between two particles, and thus build four modes actual motion between two particles.
After we obtain the diffusion coefficients of the four modes of motion for each system. The four diffusion coefficients tend to self-diffusion coefficient D0 as 1/r2. A typical plot of these coefficients for dilute systems is shown in Figure 1.
Figure 1. Diffusion coefficients for the four modes of motion between two particles in a dilute system.