Influence of forming conditions on fiber tilt

Abstract

Fiber tilt describes the projection of fiber length in the thickness direction of paper. The projection is described by the tilt angle of fibers with respect to the plane of the sheet. A simple model for fiber tilt is based on jet-to-wire velocity differential in combination with cross-flows on the wire. The tilt angle of a fiber is found to vary as the sine of its in-plane orientation angle. The phase of variation is a large multiple of the fiber-misalignment angle associated with the cross flow. The multiple can decrease from 40 to 8 as the cross-flow angle increases from 1° to 10°, showing a high degree of nonlinearity. Application of the model was demonstrated by characterizing previously published tape-peels conducted at 45° intervals on both sides of a lightweight-coated base sheet. Degree of fiber pullout, a surrogate for fiber tilt, was indicated by measuring the mean gray value of images of the tape surface against a dark background. On tape peels from each side of the sheet, gray value versus angle was well described by a sine wave, but the phase of the wave was different on each side. By comparing the phases of the sine waves with those of the model, top and bottom fiber misalignment angles were calculated. The model is most sensitive to variations in misalignment angles less than 2.5°.