DENDRITIC GROWTH OF VISCOUS FINGERS UNDER LINEAR ANISOTROPY

As a hydrodynamic analog of the dendritic crystal growth we have perfo rmed viscous fingering experiments under the influence of linear aniso tropy through a single straight groove. One finger always tends to gro w faster on the groove, accompanied by side branches. It was found tha t (1) the finger-tip profile is well approximated by a parabola, (2) e xperimental data of the dimensionless radius-of-curvature of the tip r ho/b (b is the plate separation of the Hele-Shaw cell, the only fundam ental unit of length of the system) collapse into a single curve when plotted to the capillary number Ca (proportional to tip speed upsilon) , regardless of various values of b and mu (fluid viscosity), (3) rho/ b is proportional to Ca-1/2 for small values of Ca, (4) a crossover ta kes place around some critical value of Ca, beyond which rho/b becomes almost constant, (5) side-branch spacing A is approximately proportio nal to rho. These behaviors of viscous finger dendrites are directly c omparable with those of crystal dendrites. In addition, the crossing a ngle theta made by envelope lines for side-branch tips near a main-fin ger tip was found to increase with the increase of Ca. It was also obs erved that if the groove is terminated halfway, the finger tip cannot maintain the parabolic shape and the finger grows isotropically with t he tip-splitting mode immediately after passing by the groove end.