The spreading of small viscous stripes of oil

The dynamics of spreading of small amounts of viscous fluids are usually investigated using spherical droplets of oils. Recently we applied Frenkel’s method to this problem and obtained a wide angle relation between the edge speed and the dynamic contact angle and this gave good agreement with literature data. In this work we give a simple extension of the method to the spreading of a stripe, rather than droplet, of oil. The small angle limit for the time dependence of the width of the stripe on a high energy surface is d₀ varies as (t+t₀ to)^1/7 and is in agreement with previous work. Results of optical observations on the time dependence of the width of stripes of polydimethytsiloxane (PDMS) oils of viscosities of 10 000, 30000 and 100000 cS on glass and on lithium niobate substrates are also presented. Fits to these data give a time dependence close to that predicted. Furthermore, order of magnitude estimates of the value of a logarithmic cut-off factor appearing in the theory are consistent with those obtained by previous studies on the spreading of spherical droplets of PDMS oils. This work establishes a spreading problem with a plane spreading liquid front and which is used in an accompanying paper to study the feasibility of a new surface acoustic wave technique for the study of dynamic wetting.