Experimental investigation on flow rate limitations in open capillary vanes

Estimating zero‐g flow rates in open channels having capillary pumping vanes

“…The data taken from Tables I-III and Table V of Reference [12] are as given in Table VI. Here Q is the theoretical ow rate and the contact angle = 0…”

“…We will look for solutions to (12) and (13) in which u is symmetric about the planes y = 0 and z = 0 and v and w satisfy the corresponding obvious symmetry conditions in y and z as indicated, for example, by (13). We may therefore conÿne our attention to the domain in which y and z are non-negative.…”

“…Note that each term of the series in (20) is a harmonic (in y and z) eigenfunction; the quadratic term satisÿes (12). The functional form for w 3 is assumed as a double Fourier series, as follows:…”

“…In the ensuing sections, the idealizations involved and the formulation are explained; the numerical algorithm is brie y discussed; and numerical convergence results are presented for a range of values of the parameters. The only data available in the literature for the ow rates are in [11][12][13]; unfortunately, these are for non-zero Reynolds numbers and the lengths of the devices used were not large enough for the assumption of slow variation in X required by our method. Nevertheless, some comparisons are given in Section 8.…”

“…Prior to the present paper, the only published theoretical estimates of the ow rates are due to Jaekle [10] and subsequent improvements by Dreyer and co-workers [11][12][13]. This method uses an integral analysis of the continuity and momentum equations with an averaged velocity in the ow direction and neglects cross ows.…”