effect of gradient wetting surface on liquid flow in rectangular microchannels driven by capillary force and gravity: an analytical study

a model is presented for predicting liquid flow velocity in a rectangular microchannel driven by capillary force, gravity and an extra driving force due to the surface wettability gradient. the nth power function, cosθ_x = cosθ₀ + cosθ_l− cosθ0 ð þ (x/l)ⁿ, for the cosine of contact angle (ca) with typical n order of 0.5, 1 and 2 is applied to analyze how the inner surface wettability gradient of the microchannel affects the flow velocity. flow simulations revealed that the velocity of liquid flow decreases with the length of microchannel and the wettability gradient (e.g. from 80° to 2°) on channel surface will accelerate the motion of liquid when the flow-front approaches to the end of the microchannel although the gradient surface may decrease the initial motion of liquid due to the great ca at channel entrance in comparison to the uniform ca channel (with respect to the lowest ca of 2°). the linear function (n=1) of wetting gradient profile may achieve relatively more stable and higher flow velocity than the other n power functions. the analysis of driving force along the moving path matches well with the flow velocity predicted by the model.