Finding Out How a Drop of Liquid Moves

Lynn M. Savage

When studying the interactions of liquids and solid surfaces, such as is occasionally required in semiconductor and biomaterials research, scientists keep in mind several rules of thumb. One is that the force required to slide a drop of liquid down a tilted flat surface has a linear relationship with the width of the drop. Tracking the parameters involved in moving a drop along a surface ultimately tells us, for example, how hydrophobic or hydrophilic a surface is and which liquids can wet a given material best.

Now, however, researchers at Lamar University in Beaumont, Texas, have found that a couple of commonly held beliefs about drop behavior are not accurate.

Video frames acquired with a CCD-equipped goniometer show a water droplet on glass coated with octadecyl trimethylammonium (A, B) and a water droplet on Teflon tape (C, D). Images A and C show the droplets as placed. Note the larger contact angle of the droplet on Teflon, caused by the substrate’s very high hydrophobicity. Images B and D show each droplet just prior to movement of the leading edge (left side of droplet). Courtesy of Rafael Tadmor, Lamar University.

Led by Rafael Tadmor, the investigators used a goniometer — a precision instrument designed for the measurement of liquid-solid or vapor-solid interfaces — to study droplets of either water or of hexadecane. The goniometer, made by Fibro System AB of Stockholm, Sweden, had a built-in CCD camera that captured video of drops in motion on one of three materials: mica covered by a monolayer of octadecyl trimethylammonium (OTA), glass covered with OTA, or Teflon.

The researchers allowed each drop to come to rest after it was placed on a surface, then recorded the contact angle, which comprises the angle between the plane of the surface material and the edge of the drop. They then tilted the surface until the drop began to move, recording the motion with the camera (see figures). Using the video frame just prior to the start of drop movement, they measured the angles formed by the leading and trailing edges of the drops as well as the forces required to slide them.

They not only disproved the relationship between drop width and force, they found a curious trait for some combinations of drop and surface materials. Unlike as previously believed, the force needed to start a drop moving was not always proportional to the cube root of the drop’s volume. Rather, it more typically is a decaying function of the volume as well as a growing function of the time that the drop rested on the surface — larger and younger drops require less force to get into motion.

According to the investigators, their experiments show that it should be easier to predict the contact angle, given a known amount of force, than vice versa, as once thought.

Langmuir, April 1, 2008, pp. 3181-3184.